In previous economics classes, you have examined how markets function. In this course, we'll be focusing on the labor market. During the last few weeks of your introductory microeconomics class, you received a very general introduction to the study of labor markets. To fully understand the material in this course, a solid foundation in microeconomic analysis is essential. If you need to review any microeconomics concepts, you may find review material by clicking here .
The labor market is like other markets in that a commodity (labor services) is bought and sold. It differs from most product markets in several important ways. Among these differences are:


 labor services are rented, not sold, labor productivity is affected by pay and working conditions, and the suppliers of labor care about the way in which the labor is used.
We'll examine the effects of each of these differences as we move through this course.
As you should recall from your principles course, economists distinguish between positive and normative economics. Positive economics involves an attempt to describe how the economy operates using the scientific method. Economists engaged in positive economic analysis build economic models that consist of testable hypotheses. Normative economics, on the other hand, relies on value judgments to evaluate the overall functioning of the economy.
Some examples might help to illustrate the distinction between positive and normative analysis.
Suppose an economist says: "Earnings increase with education because education raises a worker's productivity." This is an example of positive economic analysis because this question can involves a testable hypothesis. Suppose another economist argues that society should subsidize education for all individuals. This is an example of normative economic analysis because it involves a value judgment about what is best for society.
Economic theories rely on a process of abstraction. This sometimes sounds intimidating to students, but that's primarily because of a common misunderstanding concerning what is meant by abstract analysis. Think about other uses of the term "abstract." Examples that often come to mind are abstract art and abstracts of journal articles. What do these cases have in common?
Abstract art is an attempt to represent a complex reality by a reliance on simple shapes and forms. Journal article abstracts are short, simplified, summaries of the material in the article. As these examples should suggest, abstraction is simply a way of simplifying reality so that it may be more easily understood. Abstraction in economic analysis involves focusing on the most important and essential relationships while suppressing the less essential details. To engage in this type of analysis in a meaningful way, economists rely on the ceteris paribus assumption. As you should recall from your principles class, ceteris paribus means: "all other things constant."
By invoking this assumption, economists attempt to focus on the most essential relationships while holding constant those factors that are less fundamental. This makes it possible to come up with relatively simply theories (called economic models) that rely on a small number of hypotheses.

The validity of an economic model is generally evaluated by how well it can explain and predict behavior. Economists tend to focus on testing the predictions of a model, rather than on examining the assumptions of a model. Presumably, though, a model's predictive ability will be affected by whether or not the assumptions are consistent with individual behavior. Economists rely on statistical analysis (called econometric analysis) to evaluate the predictive success of their models.
One of the most basic concepts of positive economic analysis is the concept of scarcity. As you should recall from your principles course, economists assume that resources are scarce relative to society's wants and needs. (You may recall the standard definition of economics that states that economics is the study of how limited resources are used to satisfy unlimited wants.) The fundamental economic problem facing every individual and every society is how to deal with the problem of scarcity.
A fundamental hypothesis of positive economic analysis is that individuals deal with the problem of scarcity by making choices based upon rational self-interest. By this, economists simply mean that individuals make choices that provide the highest expected level of satisfaction given the information and constraints facing the individual at the time a choice is made. In your principles course, this concept was discussed in the framework of utility maximization, where utility is a measure of the level of individual happiness or satisfaction. For individuals who operate businesses, utility maximization results in profit-maximizing behavior (under a wide variety of conditions).
As your text notes, the only normative concept on which virtually all economists agree is that a
Pareto improvement is a desirable change. As you may recall from your principles class, a Pareto improvement is a change that benefits one or more individuals and harms no one. A desirable outcome occurs once one reaches a state of Pareto efficiency (also commonly called Pareto optimality), a situation in which no further Pareto improvements can be made. Once a state of
Pareto efficiency is achieved, any change that benefits one or more people will result in harm to someone else. Since it is not possible to determine whether the harm to one person outweighs the benefits to others (since interpersonal comparisons of utility are not possible), it is not possible to evaluate whether any change in such a state increases or decreases social welfare when an economy has achieved a state of Pareto efficiency.
One criticism of relying solely on the criterion of Pareto efficiency is that it tends to support the status quo, since it is often difficult to find practical examples of changes in a society that do not harm at least one person. Still, if an economic system is to be devised, it is preferable that it result in outcomes that are Pareto efficient.
Under ideal conditions a market economy will result in Pareto efficient outcomes. If there is perfect information and all of the benefits and costs from trade are captured by the individuals involved in transactions, voluntary trades will result in Pareto improvements. If there are no barriers to such transactions, these trades will take place until no further Pareto improvements are possible. This is expected to occur in both output and resource markets (such as the labor market).

In practice, however, market failure does occur do to a variety of factors. In particular, market failure may result from:
 imperfect information,

 transaction barriers,
 price distortions, the nonexistence of markets when externalities are present,
 public goods, and
 capital market imperfections.
Let's review each of these possibilities.
Voluntary trade between individuals will result in Pareto improvements as long as each individual can find out about the possibility of such a trade and knows what they will be getting from the trade. In many markets, however, imperfect information exists so that some individuals will not know that such trades are available or do have incorrect expectations of the characteristics of the product they are acquiring. In the case of the labor market, workers may not always know all of the risks and characteristics of jobs that they accept. They also do not have perfect information about all of the potential employment opportunities that may be available.
On the other side of the market, firms do not have perfect information concerning the ability, motivation, collegiality, and other characteristics of potential workers. Because of this imperfect information, some employment choices will result in decisions that are not Pareto improvements.
Government often steps in to correct for this type of market failure by issuing regulations or providing information. OSHA requirements designed to improve worker safety are partly justified on this basis. State employment agencies that provide listings of job opportunities are another example of an attempt to correct for imperfect information.
Laws prohibiting transactions prevent markets from achieving potential improvements. Laws specifying minimum wages, mandated overtime premiums, regulating working conditions, prohibiting child employment, etc. all prevent transactions that would have provided mutual benefit to the employer and employee if the prohibited transactions had been realized. Similar transaction barriers prevent Pareto improvements in occupations that are prohibited by law.
Transaction costs (such as transportation costs) or financial barriers may also result in some transactions not being realized.
Price distortions occur when the price of a good does not reflect the social cost of the good.
Taxes, tariffs, subsidies, and similar types of intervention may cause a price to diverge from the marginal cost of producing the good. (As noted below, taxes and subsidies may be appropriate corrections for market failure when externalities are present.) If a tax results in an artificially high price of a commodity, too little of the commodity will be consumed. A subsidy, on the other hand, that results in an artificially low price will result in overconsumption of the commodity.

As you should recall from your principles class, externalities are side effects of production or consumption that provide either benefits or costs to those not directly involved in the transaction.
When negative externalities are present, overproduction takes place since the market price understates the social cost of producing the good. Underproduction occurs when positive externalities are present since the benefit to society is greater than the benefit received by individual consumers. If property rights are established, negotiations among all of the affected parties may result in Pareto improvements (this is the Coase theorem discussed in your microeconomics principles course). Your textbook uses the example of smokers and nonsmokers in an office negotiating over whether smoking should be allowed in the workplace as an example of such a situation.
In practice, however, markets will generally fail to take external costs and benefits into account
(as Coase himself noted in his classic paper). In this case, government may correct for negative externalities by taxing or regulating the activity; a correction for positive externalities involves subsidies or regulations.
Public goods are goods that are nonrival in consumption. Once the good is produced, it is available for everyone's consumption; one person's consumption does not reduce either the quantity or quality of the product available to anyone else. As you should recall from your principles class, public goods tend to be underproduced because of the free-rider problem.
Negotiations over working conditions is an example of a public good in the workplace. If a safer work environment is created, it benefits all workers, not just the worker who negotiated the improvement. The problem, of course, is that everyone has an incentive to let someone else complain to management about unsafe working conditions. In such a situation, such negotiations will often not take place.
One of the reasons for the existence of unions is that they provide a mechanism for negotiation over public goods in the workplace. Government also often attempts to correct for the presence of public goods in labor markets.
The capital market is the market for investment in both physical and human capital. In the absence of government subsidized and guaranteed student loan programs, however, is that private lenders had little incentive to provide funds for human capital investments. Loans for the acquisition of physical capital can be secured by the use of collateral. No such collateral is available for investments in human capital. This is, of course, the main reason for the existence of government subsidized and guaranteed student loans.
Throughout this course, we'll examine many situation in which policymakers are faced with a tradeoff between equity and efficiency. Attempts to make market outcomes more equitable often results in the loss of economic efficiency. Unemployment compensation programs provide a more equitable distribution of income, but reduce the incentive for unemployed workers to get back to work. Disability programs and welfare programs often have similar equity and efficiency implications.

In some of your classes, you are asked to work on group projects. Typically, each member of the group receives the same grade, regardless of his or her individual contribution to the group effort. This is an equitable outcome, but has serious adverse efficiency implications. In such a situation, it is not uncommon for most of the members of the group to rely on one or two individuals to perform most of the work. This reduces the overall quality of the group project.
(This is one of the reasons why group projects are not used in this course.)
In labor markets, labor is supplied by households and demanded by firms. These are the opposite of the roles that are played by households and firms in product markets. Be sure to keep this distinction in mind.
A national labor market is one in which most job search by employers and firms takes place on a national level. Most job search takes place at a local level in a local labor market . The markets for college professors, top management positions in large corporations, and similar occupations are national labor markets. Secretaries, carpenters, truck drivers, electricians, and lathe operators are employed through local labor markets. A national labor markets exists only when there are few employers and employees in most geographical regions. Local labor markets exist when there are many employers and employees in most geographical regions.
An internal labor market is said to exist within a firm if the firm fills higher level positions in the firm primarily by promotion from within the firm. Firms often rely on internal labor markets because:
 this reduces hiring and training costs,
 it improves employee morale and motivation, and
 it reduces the effect of uncertainty (since the firm has already observed worker productivity.
Another distinction that is often used to categorize jobs is that between the primary and secondary labor market. Jobs in the primary labor market are characterized by high wages and stable employment relationships. Workers employed in the secondary labor market receive low wages and experience unstable employment relationships. Examples of jobs in the primary labor market include: accountant, lawyer, teacher, carpenter, and plumber. Workers in fast-food restaurants, gas station attendants, dishwashers, janitors, etc. are employed in the secondary labor market. While primary labor market jobs have obvious advantages, the secondary labor market offers job opportunities that would not be available in the primary labor market to high school and college students, adults engaged in extensive child-care activities, and retired individuals.
High school and college students are not likely to find primary labor market jobs during summer vacations or for part-time work during the academic year. Those adults who are "stuck" in secondary labor market occupations because of limited job skills and education, however, are not as pleased with finding their only employment prospects in this sector.

The labor force consists of all noninstitutionalized individuals aged 16 or above who are either working or actively seeking work. Those who choose to be full-time students, or retire, or withdraw from the labor force for child-rearing purposes, or who give up looking for work are not counted as part of the labor force
Individuals are unemployed only if they are not working for pay at any job and are actively seeking work.
The unemployment rate is defined as:
As was discussed in your introductory macroeconomics class, the unemployment rate generally rises during recessions and falls during periods of economic expansions. It is interesting to note, though, that when unemployed workers become discouraged and leave the labor force (these workers are called discouraged workers ), the measured unemployment rate declines. (To see this, observe that while both the numerator and the denominator in the equation above decline, the fraction declines because the numerator falls by a larger percentage.) Thus, the unemployment rate may decline when the number of discouraged workers rises. Similarly, the observed unemployment rate may increase when discouraged workers become more optimistic about the state of the economy and start looking for work.
Thus, to measure the state of the labor market, it is important to examine movements into and out of the labor force as well as changes in the unemployment rate. A convenient measure of this is provided by the labor force participation rate , defined as:
Typically, the labor force participation rate increases during periods of economic expansion and declines during periods of recession. Note that the changes that occur in the labor force participation rate over the course of the business cycle tend to dampen the fluctuations that occur in the unemployment rate. To see this, note that during a recession, unemployment rises. But because some workers become discouraged, unemployment does not rise by as much as it would if the labor force participation rate were constant. Similarly, during an expansion, unemployment rates decline, but the decline is smaller due to the increase in the labor force participation rate that generally occurs when an expansion occurs.
The Bureau of Labor Statistics (BLS) collects and reports unemployment and labor force participation rate data for a wide variety of subgroups of the population, sorted by age, gender, marital status, and race. Data on these variables may be found at the BLS website .
Be careful to not confuse the unemployment rate with the number of people eligible to receive unemployment compensation. While all of those who receive unemployment compensation are legally required to be unemployed, a worker could be unemployed but not eligible to receive unemployment compensation (since eligibility is not available to those who voluntarily quite their job or who have not worked for a long enough time period prior to being laid off).

An examination of unemployment statistics during the past century indicates that unemployment rates in the latter half of the 20th century were, on average, higher than those during the first half of the century. The variation in unemployment rates, however, has been much lower since the end of the Great Depression. The increased level of the unemployment rate may be the result of higher rates of structural unemployment (as discussed in your principles of macroeconomics course) or may be due to the reduced cost of being unemployed (as a result of the introduction of unemployment compensation). The reduced variation in unemployment rates are generally seen to be the result of improvements in macroeconomic policy decisions by the government and
Federal Reserve Board.
During the past 50 years, the labor force participation rate for males has declined slightly. This is, however, true primarily for relatively young and relatively old males. The decline in male labor force participation rates is due to increased years of educational attainment and retirement decisions.
The labor force participation rate for females has increased rather dramatically during the same period. The largest increase has been for married females (partly because single and divorced females always had relatively high labor force participation rates). We'll examine the reasons for the change in female labor force participation rates in a later section of this course.
The economy is often separated into three basic sectors:
1.
the primary sector (the agricultural sector),
2.
the secondary sector (the industrial sector), and
3.
the tertiary sector (the service sector).
The agricultural sector is called the primary sector because economies must produce enough food for the population to survive before anything else can be produced. For most of the history of our species, most work was devoted to agrarian activities. It is only in recent centuries that the industrial and service sectors have become important. As your text notes, employment in the primary sector has been steadily declining as a share of total employment. Employment in the service sector has been growing steadily as a share of total employment. The share of employment in the industrial sector of the U.S. economy had been relatively stable for most of the past century, but has been declining slightly for the past two decades.
To account for these changes, there are two fundamental concepts that have to be considered: the rate of technological improvement in each sector and the income elasticity of demand for the output of each sector. (As you learned in your microeconomics principles class, income elasticity
= % change in quantity demanded / % change in income.)
In the agricultural sector, there has been a rapid pace of technological improvement but the income elasticity of demand is relatively low. Technological change results in increased output per worker and higher income in the economy. Yet, most people do not eat substantially more food when income rises. Thus, increases in productivity in this sector result in a need for fewer workers in this sector. Today, fewer than 3% of the population is employed in the agricultural sector of the U.S. economy.
The service sector has also been characterized by a fairly high rate of productivity growth. The income elasticity of demand for products in this sector, however, is substantially higher than for the agricultural sector. Increased output per worker has been accompanied by increased demand

for the output of this sector as income rises (due to productivity increases throughout the economy). For most of this century, the demand for this sector's output was growing at approximately the same rate as productivity was rising. It is only in recent years that productivity has been growing faster than the demand for output in this sector.
In the service sector, productivity growth is relatively low but the income elasticity of demand for service sector output is relatively high. Productivity growth is low in the service sector because labor is an essential ingredient in the quality of the final product. Patients visiting physicians or dentists do not find the experience to be of the same quality if their physicians or dentists rushed through their examinations. Musical groups can increase their productivity in live performances by playing music faster, but it's not likely that this will be perceived as being of the same quality as a normal speed performance. Professors can talk faster to raise productivity, but this is also likely to lower the perceived quality of the service. While computers, improved diagnostic devices, and other changes may increase productivity in the service sector, it's likely that the overall rate of productivity growth will be substantially lower than in other sectors of the economy. As incomes rise (due to overall productivity growth), however, households tend to spend a growing share of their income on education, medical services, restaurant services, motel and hotel services, etc. Since productivity growth in this sector is unable to keep up with the growth in demand, the share of total employment in the service sector must increase. Figure 2.3
(p. 31) in your text illustrates these trends nicely.
If we are to measure changes in wages (or income) over time, it is important that some adjustment be made for the effect of inflation. Nominal wages are not adjusted for inflation and are said to be expressed in terms of "current dollars" (since they are measured in terms of the value of the dollar at that particular time). Real wages are wages that have been adjusted to take into account the effect of inflation. Real wages are expressed in terms of dollars from a given base year and are said to be expressed in "constant dollars."
Some form of price index is used to convert nominal wages into real wages. A price index is constructed using the following formula:
In practice, this price index is often expressed as a percentage by multiplying the formula above by 100. The most commonly used price index is the Consumer Price Index (CPI). The basket of goods used for the CPI is determined by the mix of goods consumed by a typical family of 4 in selected Standard Metropolitan Statistical Areas (SMSAs). The specific mix of goods is determined from the Consumer Expenditure Survey, a survey administered every 5 years by the
Bureau of Labor Statistics. More information on the CPI can be found at the Bureau of Labor
Statistics' CPI home page .
Suppose the cost of the basket of goods used to compute the CPI is twice as high today as it was in the base year. An inspection of the equation above indicates that the CPI will be 2 (or 200 expressed as a percentage). (In the base year, the price index will always be equal to 1, or 100 as a percentage.) Suppose that an individual's current wage is $12 an hour when prices are, on average, twice as high today as in the base year. A bit of reflection should convince you that the real wage, as measured in terms of the base year's dollars equals $6. In general, the real price of an item is measured as:

(Note that the price index is not measured as a percentage in this calculation.)
As you may recall from your micro principles course, one of the problems with the CPI is that it contains an inflationary bias (known as a substitution bias). There are also some serious problems associated with the effect of quality changes. A good summary of these problems and some remedial measures that the BLS has recently adopted to correct for these problems in contained in an online Federal Reserve Board of San Francisco article .
In general, economists assume that individual workers and firms respond to changes in real wages and not nominal wages. Workers are concerned with the purchasing power of their wage over time, not just the number of dollars they receive. For this reason, whenever we refer to wages in the future, we will mean the real wage unless the nominal wage is specifically mentioned.
There are a few basic definitions that will be used throughout the rest of this class. It is very important that you use these terms precisely and not confuse them:

 wage = payment per unit of time earnings = wage x hours (labor payment over an interval of time, typically a week, month, quarter, or year)
 total compensation = earnings + fringe benefits
 fringe benefits = payments-in-kind + deferred compensation
(where: payments-in-kind include any payments in the form of goods and services such as the use of a company provided car, or employer-provided meals, uniforms, health insurance, or similar benefits; and deferred compensation involves items such as pension
 plans and other programs that provide payments at some point in the future.) income = total compensation + unearned income
(in practice, when data on income is reported, income is generally measured as: income = earnings + unearned income since researchers generally do not have accurate measures of the value of fringe benefits)
As the diagram below illustrates, it is argued that there is an inverse relationship between the wage rate and the quantity of labor demanded. This negative relationship between the wage and the quantity of labor demanded is the result of two effects:

 a substitution effect, and a scale effect.

Suppose that the wage rate increases. The substitution effect of the wage increase involves the substitution of other resources (such as capital, energy, materials, and other categories of labor) for the category of labor that has become more expensive. As the wage rate rises, the substitution effect results in a reduction in the quantity of labor demanded.
The scale effect resulting from a wage increase is a bit more complex. As the wage rate rises, the scale effect involves the following chain of effects:



 higher wages result in higher average and marginal costs of production, higher average and marginal and average costs result in an increase in the equilibrium price of the product, as the price of the product rises, the equilibrium quantity of the product demanded declines (a reduction in the "scale" of production), and the reduction in output results in a reduction in the quantity of all inputs used to produce this product (including this category of labor).
Thus, both the substitution and scale effects result in a reduction in the quantity of labor demanded when the wage rate rises.
Be sure to not confuse a change in the quantity of labor demanded with a change in the demand for labor. A change in the wage changes the quantity of labor demanded, but does not affect labor demand. Labor demand changes only if the labor demand curve shifts in some manner (as discussed below).
Your text notes that labor demand is affected by:
 the demand for the product, and
 the prices of other resources.
(other factors affecting labor demand will be examined later in the course)
Let's examine how each of these factors affects labor demand.

As discussed in your micro principles class, the demand for labor (and any other resource) is a derived demand. This means that the demand for a resource is derived from the demand for the output that the resource produces. For example, the demand for workers in automobile factories is derived from the demand for automobiles. When the demand for the final product rises, the demand for labor increases. As the diagram below indicates, an increase in demand for labor is represented by a rightward shift in the labor demand curve (since the quantity of labor demanded is greater at each wage along the curve D').
The effect of changes in the prices of other resources is not quite as straightforward. Consider, for example, the effect of an increase in the price of capital on the demand for labor. The substitution effect resulting from a higher price of capital raises the demand for labor. The scale effect, on the other hand, will lower the quantity of both labor and capital demanded. Thus, the effect of a higher price of capital on labor demand will depend on whether the substitution effect or the scale effect is larger in magnitude.
Another example might help to illustrate this point. Suppose that the wage rate rises for adult workers in the fast-food industry. How will this affect the demand for teenage workers in this industry? On the one hand, each fast-food restaurant will try to substitute teenagers for adults in each location. Since adults and teenagers are not perfect substitutes, firms will still need some adult workers. This results in higher production costs and a higher equilibrium price of output.
As the price of fast-food products rises, firms cannot sell as much and will be forced to shut down some locations and layoff workers (including both teenagers and adults). This scale effect results in a reduction in the demand for teenage workers. When the price of adult workers rises, the demand for teenager workers will rise if the substitution effect is larger than the scale effect; the demand for teenage workers will fall if the scale effect is larger than the substitution effect.
To be sure that you understand this concept, think about the effect on the demand for adult workers if a lower minimum wage was introduced for teenage workers.
When discussing labor demand, it's important to distinguish whether we are talking about labor demand at the level of a market, an industry, or a firm. To understand these distinctions, it is important to understand the following definitions: An industry consists of all of the firms that produce a given type of output. An industry's demand for labor consists of the total demand for a

particular type of worker in a given industry. For example, we could investigate the demand for carpenters in the construction industry, or the demand for carpenters in the education industry
(note that carpenters are hired in many industries). The market for a given category of labor consists of all of the firms that might hire a given type of labor, regardless of the industry in which the firm operates. Thus, the market for carpenters includes the demand for carpenters in all industries. An industry's labor demand curve is determined by adding together the labor demand curves for all of the firms in the industry (this involves a horizontal summation of all of the individual firms' labor demand curves -- if you don't recall this concept, you may wish to review the material on demand in a micro principles text). The market demand for labor is determined by adding together all of the industry demand for labor curves.
As you may recall from prior economics classes, economists define the short run as the period of time in which capital is fixed. In the long run, all inputs, including capital, may be changed. The main difference between the short-run and long-run demand for a given category of labor is that there are more possibilities for substituting other factors of production in the long run. Thus, it is expected that the quantity of labor demanded will change by a larger amount in the long run when the wage rate rises. This is illustrated in the diagram below.
We'll be examining individual labor supply curves in a great deal of detail in later chapters of the course. For now, we'll only discuss market labor supply. The market labor supply curve is expected to be upward sloping because an increase in the wage in a particular labor market will:
1.
cause some workers in this market to work additional hours,
2.
induce some workers to shift from other labor markets to this relatively more remunerative alternative employment, and
3.
will cause some individuals who are not currently in the labor force to enter this market.
A possible labor supply curve is illustrated below.

Changes in the wage in this market result in changes in the quantity of labor supplied, but do not affect labor supply. Labor supply changes only if some other factor changes and the labor supply curve shifts. The diagram below illustrates an increase in labor supply from S to S'.
Market labor supply will increase when the wage rate in other labor markets falls and will decrease when the wage rate rises in other labor markets. Changes in worker tastes and preferences will also affect market labor supply.
In a perfectly competitive labor market, the labor supply curve facing each firm is horizontal. Recall that there are so many buyers and sellers in a perfectly competitive market that each buyer and seller is a "price taker." In this case, each firm may hire as many or as few workers as it wishes at the prevailing market wage rate. This possibility is illustrated in the diagram below.

An equilibrium occurs in a labor market at the combination of wages and employment at which market demand and supply intersect (as illustrated in the diagram below). In this example, the equilibrium wage is w* and the equilibrium level of employment is L*.
If the wage rate is above the equilibrium, the quantity of labor supplied exceeds the quantity demanded and a surplus occurs. In this case, the existence of unemployed workers will be expected to result in downward pressure on the wage rate until an equilibrium is restored.
If the wage rate is below the equilibrium, a labor shortage will occur. Competition among firms for workers is expected to result in increases in the wage until an equilibrium occurs.

Shifts in demand and supply curves have been covered extensively in your principles of microeconomics course, so there's no need to discuss these concepts in great detail here
(if you are not comfortable with this, you may wish to review this material). Let's just note that: o o o o an increase in labor demand results in an increase in both the equilibrium wage and the equilibrium level of employment, a reduction in labor demand results in a decrease in both the equilibrium wage and the equilibrium level of employment, an increase in labor supply results in a lower equilibrium wage, but a higher equilibrium level of employment, and a reduction in labor supply results in a higher equilibrium wage, but a lower equilibrium level of employment.
You may wish to draw these possibilities on a piece of paper to be sure that you understand these concepts.
There are two major types of unions: industrial unions and trade unions (trade unions are also known as craft unions). Industrial unions attempt to organize all of the workers in an industry, regardless of the type of work that is done. Trade unions attempt to organize all of the workers performing a particular type of job, regardless of the industry in which the worker operates. The United Auto Workers (UAW) and United Mine Workers (UMW) are examples of industrial unions. Examples of trade unions include: the International
Brotherhood of Electrical Workers (IBEW) and the Meat Cutters union.
So, who represents electricians at GM? Is it the IBEW or the UAW? It turns out that the workers themselves vote on who will represent them. In each unionized firm, workers are organized into shops, groups of workers performing similar tasks. Each shop votes on which union will serve as their bargaining agent for collective bargaining purposes. Each shop is represented by only one union in negotiations with the employer.
Under a collective bargaining agreement, unions negotiate a wage with the employer. An effective union negotiates a wage that is above the equilibrium wage. In the diagram below, this is represented by a union negotiated wage of w'. As this diagram suggests, one of the costs of receiving a higher wage is a reduction in the level of employment
(from L* to L'). Note also that there are more people who wish to work at a wage of w' than there are jobs available. This factor limits the ability of the union to negotiate higher wages.

In some cases, however, unions are able to convince the government to pass laws that give unions some control over labor supply (in general, it is illegal under the Taft-Hartley
Act for unions to otherwise limit labor supply). State and local zoning laws generally require that plumbing and electrical work be completed only by licensed plumbers and electricians. Since unions control the process of licensing, this gives unions substantial ability to control labor supply inm these industries. The American Medical Association, the American Dental Association, and the American Bar Association have a similar ability to limit supply in their labor markets. The diagram below illustrates the effect of a labor supply restriction.
As with a collective bargaining agreement, a supply restriction results in a higher wage
(w') and a reduced level of employment (L'). The difference, though, is that there are no unemployed workers in this market since the supply restriction prevents these additional workers from ever appearing in this market.

As your text notes, economists argue that workers are overpaid only if the wage is above the equilibrium and are underpaid if the wage rate is below the equilibrium. To economists, this is a concept involving positive economics, not normative economics.
Non-economists often appeal to some standard of "fairness" in evaluating whether people are overpaid or underpaid. Economists note that labor is not efficiently allocated to alternative tasks when the wage is either above or below the equilibrium.
Workers receive economic rent when they receive a payment that exceeds the opportunity cost of supplying their labor. The opportunity cost of supplying labor is the value of this time in its next-best alternative use. Another name for this opportunity cost is the "reservation wage." The reservation wage is the lowest wage offer an individual will accept. If the wage falls below the reservation wage, the individual will not work. As long as the wage is at or above the reservation wage, the individual will choose to work.
Suppose that a professional athlete receives $300,000 a year, but could have received only $50,000 in their next-best alternative employment. In this case, the athlete is receiving $250,000 in economic rent.
As your text notes, unemployment rates in Europe during the past 30 years have tended to be much higher in Europe than in the United States. Your text suggests that this is because nonmarket forces are more important in wage setting in European economies.
This week, we'll examine the determination of the equilibrium level of employment under a variety of market structures.
Economists assume that firms attempt to maximize their profits. One question that might be asked is whether the employment of an additional unit of labor raises or lowers a firm's profits.
To analyze this, recall that: economic profits = total revenue - total costs
When an additional worker is hired, total revenue will rise (under most practical situations). On the other hand, total costs rise as well. The increase in revenue results in an increase in profits while the increase in costs lowers the level of profits. Thus, the addition of an additional worker will increase profits only if the additional revenue resulting from this labor is greater than the additional costs. Profits will decline if costs increase by more than revenue.
To examine this issue, economists rely on two measures:
 the marginal revenue product (MRP) of labor, and

 the marginal factor cost (MFC) of labor.
The marginal revenue product of labor is defined to be the additional revenue that results from the use of an additional unit of labor. In a similar manner, the marginal factor cost of labor is defined to be the additional cost associated with the use of an additional unit of labor. (Your textbook defines this using the somewhat less conventional term of marginal expense ( ME ) of labor.) In this course, I'll use the term "marginal factor cost" since this is the term you probably saw in your micro principles course and are likely to see in any subsequent economics classes.
A little bit of reflection should convince you that a profit-maximizing firm will:
 increase the use of labor if MRP > MFC, and
 reduce the use of labor if MRP < MFC.
The marginal revenue product of labor can also be expressed as:
MRP = MR x MP where MR (marginal revenue) equals the additional revenue resulting from the sale of an additional unit of output and MP (marginal product, also known as marginal physical product or
MPP in many micro principles texts) is the additional output resulting from the use of an additional unit of labor, holding the use of other inputs constant. Suppose, for example, that you wished to compute the marginal revenue product of labor when MR = 4 and MPP = 5. In this case, the employment of an additional worker results in a 5 unit increase in output (holding other inputs constant) while revenue increases by $4 when an additional unit of output is sold. In this case, the marginal revenue product of labor will equal $20 (= $4 x 5).
Using a little bit of algebra, the marginal revenue product can be defined as:
Similarly, marginal revenue and marginal product are defined as: and:
The relationship among MRP, MR, and MP can also be seen quite clearly in an algebraic manner:

Since MRP is equal to the product of MR and MP, to determine the relationship between MRP and the level of labor use, we need to understand how MR and MP change when the level of labor changes.
As you may recall from your micro principles course, the law of diminishing returns can be stated as: law of diminishing returns - as additional units of a variable input are added to a production process in which other inputs are fixed, the marginal product of the variable input will ultimately decline.
While it is possible that MP may initially increase, a profit-maximizing firm will never hire workers in the range in which this occurs. (To see this, note that if it is profitable to hire the second worker and the third worker has a higher marginal product, it will always be optimal to hire the 3rd worker. A profit-maximizing firm would never hire only two workers in this case.)
Thus, marginal product declines over the range of labor use that will be considered by a firm.
The diagram below illustrates the relationship between marginal product and the level of labor use.
As this diagram indicates, it is possible that the marginal product of labor will become negative beyond some level of labor use. Once again, though, we do not have to worry about this because profit-maximizing firms will never hire additional workers if the additional labor results in a decrease in the level of output!
If the firm is operating in a perfectly competitive output market, marginal revenue is constant and is equal to the market price. In an imperfectly competitive output market (such as a monopoly or monopolistically competitive market), the firm faces a downward sloping demand curve and marginal revenue is less than the price. (If you don't recall these concepts, you may wish to review this material from your microeconomics course (or visit these web pages to review the material on perfectly alternative output markets). The relationship between output and marginal revenue under both perfect competition and imperfect competition is summarized in the diagram below.

Let's examine the shape of the MRP curve. We know that MP declines as labor use rises. In the case of a perfectly competitive output market, MR is constant. If the output market is imperfectly competitive, MR declines as labor use rises. Thus, we can safely predict that the MRP curve will be downward sloping, as illustrated in the diagram below (since MRP is the product of two terms, one of which always declines and the other is either constant or declining when labor use rises).
If the labor market is perfectly competitive, each buyer and seller of labor is a price taker. In this case, the firm faces a perfectly elastic labor supply curve (as noted in Chapter 2 of your text and in the mini-lecture for Chapter 2). Since the wage is constant at all levels of labor use in this market structure, the marginal factor cost of labor is just the market wage. If workers are paid $7 an hour, the marginal factor cost of an additional hour of labor is $7. The relationship between marginal factor cost and the level of labor use is illustrated below.

The diagram below combines the MRP and MFC curves for a firm in a perfectly competitive labor market. Notice that the MRP curve will be downward sloping ad have this same basic shape regardless of whether the output market is perfectly or imperfectly competitive. The only difference is that MRP will be lower when the output market is imperfectly competitive (since
MR < P in this case).
The diagram above can be used to determine the profit-maximizing level of labor use.
Suppose that the firm chooses to employ Lo workers. At this level of labor use, MRP > MFC.
The firm can increase its profits in this case by increasing the level of employment (since the additional revenue generated by an additional unit of labor exceeds the cost of this additional labor). If it hires L' workers, however, the additional cost of the last unit of labor exceeds the additional revenue generated by this labor. In this case, the firm could increase its profits by hiring fewer workers. Profits are maximized at a level of labor use equal to L*. Profits would be lower at any alternative level of labor use.

The analysis above may be used to derive a labor demand curve. Consider the diagram below.
From this diagram, we can see that the optimal level of employment at a wage of Wo is Lo.
When the wage rises to W', the profit-maximizing level of employment falls to L'. At a wage of
W", the profit maximizing level of employment us L". A careful examination of this diagram indicates that for any given wage, the MRP curve provides a measure of the optimal quantity of labor demanded by the firm. Since the MRP curve tells us the quantity of labor demanded at each and every possible wage rate in the short run, it is the firm's short-run labor demand curve.
This will be the case for any profit-maximizing firm that operates in a perfectly competitive labor market (regardless of the degree of competition on the output market).
As noted last week, the market demand curve for labor is simply the horizontal summation of all of the individual firms' labor demand curves.
The situation is a bit more complex when there is imperfect competition in the labor market.
Let's examine the case of a monopsony to illustrate this situation. A monopsony occurs when there is a single buyer of a good. In the case of a labor market, a monopsony occurs when only one firm hires workers in a given labor market. A small "company town" is a classic example of a monopsony labor market. A hospital in many communities may also serve as a monopsony in the market for nurses, lab technicians, and radiologists. While there are few pure monopsonies, many firms have some degree of monopsony power. Let's examine what this entails.
A monopsony firm faces the entire market labor supply curve. The labor supply curve in the diagram below represents such a possibility. In this example, the firm must pay a wage of $7.00 an hour when 7 workers are hired and must raise the wage to $7.50 an hour to induce an 8th worker to work for the firm. Of course, when the 8th worker is hired at this higher wage, the firm will have to raise the wages of the first 7 workers to $7.50 an hour. Because of this, the additional cost of adding the 8th worker is the $7.50 an hour paid to the 8th worker plus a $.50

increase in the wage of the first 7 workers (costing the firm $3.50 an hour in wage increases for these 7 workers). In this case, the marginal factor cost of adding the 8th worker is $11 (= $7.50 +
$3.50).
Since the cost of an additional laborer will always be greater than the wage in a monopsony market, the MFC curve lies above the labor market supply curve (since the supply curve provides the wage rate that must be paid at each level of labor use). Note that the vertical distance between the MFC and the labor supply curve rises as the level of labor usage increases since pay raises must be given to a larger number of workers as the initial level of employment increases.
As in any profit-maximizing firm, an optimal level of employment occurs at the level of labor use at which MRP = MFC. In the diagram below, this occurs at a level of employment equal to
Lo. The wage, however, must equal the wage rate that must be paid to attract Lo workers to this firm. As noted above, this wage is determined by the supply curve. At a level of employment of
Lo, the firm must pay a wage equal to wo.

Note that the intersection between the MRP and MFC curves determines the level of employment while the supply curve determines the wage that must be paid in a monopsony market.
Let's examine what happens when a minimum wage law (or a union-negotiated wage agreement) is introduced into a monopsony market. The diagram below illustrates the effect of introducing a minimum wage (or a union-negotiated wage) equal to w' in a monopsony market. The firm, without this intervention, would have paid a wage of wo and employed Lo workers. The minimum wage (or negotiated wage) of w', however, alters the supply curve facing the firm so that it is horizontal at a wage of w' until it crosses the original supply curve (the reason for this is that the firm may pay wages above w', but may never drop the wage below this level). In the range in which the supply curve is horizontal, however, the marginal factor cost of labor is just equal to this wage (since the firm doesn't have to raise anyone's wages when another worker is employed. The MFC curve jumps up to its former location at the level of labor use at which the labor supply curve resumes its upward slope. This results in a discontinuous MFC curve (as illustrated below).
When faced with these MRP, MFC, and labor supply curves, a profit-maximizing monopsonist will find it optimal to employ L' workers at the minimum wage (or negotiated wage) of w'. The firm's profits would be lower if it used either less or more labor than this level. This is a somewhat interesting result: the introduction of a minimum wage law (or a union) in a monopsony market may result in increased wages and increased employment!
The diagram below illustrates another possible outcome. In this case, the minimum wage (or union-negotiated wage) is set at w''. In this case, the optimal level of employment remains at Lo.
So, it's also possible that the introduction of a minimum wage law may lead to an unchanged level of employment (and higher wages).

More generally, if the minimum wage (or union-negotiated wage) is between wo and w", employment will increase when the minimum wage is introduced. If the new wage is set at w", employment remains unchanged. A minimum wage (or union-negotiated wage) above w" will result in a decline in employment in this labor market.
Let's examine who bears the cost of a payroll tax (such as a social security tax, or an income tax).
In the diagram below, the curves D and S represent the labor demand and supply curves in the absence of a tax. The equilibrium wage is wo and the equilibrium level of employment is Eo in this case.
The introduction of a payroll tax, however, raises the cost of labor to each firm. We normally think of the labor demand curve as telling us the quantity of labor demanded at each wage. In this case, however, it is more convenient to think of it as representing the maximum amount that firms are willing to pay to hire any given number of workers. When a tax is introduced, firms are still willing to pay the same amount for labor at any given level of employment, but some of that is taxed away before it becomes a worker's wage. In the diagram above, a payroll tax is

introduced equal to the vertical difference between the curves D and D'. The original demand curve, D, tells us the total amount a firm will pay to hire any given quantity of labor. The aftertax demand curve, D', tells us how much workers will be paid at any given level of employment.
Once the tax is introduced, the new after-tax demand curve (D) and the market labor supply curve (S) intersect at an employment level of E'. This indicates that the introduction of a payroll tax, lowers the equilibrium quantity of labor employed. The wage rate "wn" is the workers net wage, the wage received after the tax has been paid. The wage rate "wg" is the gross wage, the total hourly labor cost to the firm in this labor market. The vertical distance between wg and wn is equal to the amount of tax paid per hour of labor.
As this diagram suggests, employers and employees share the burden of this tax. Employees pay part of the tax by accepting a lower after-tax wage (wo-wn), Employers pay part of the tax by paying a higher hourly labor cost (wg-wo). As you may recall from your principles of microeconomics class, workers will bear a larger share of the burden of this tax when labor demand is more elastic and labor supply is less elastic (your text illustrates an extreme case in which employees bear all of the burden when labor supply is perfectly inelastic).
Your text notes that those economies that have higher levels of payroll taxes have tended, in recent decades, to have higher levels of unemployment rates.
This week, we'll be examining labor demand in the long run. The long run differs from the shortrun in that all inputs are variable in the long run. (As noted earlier, the short run is defined as the period of time in which capital cannot be changed.)
For simplicity, we will assume that a firm produces output using two types of inputs: labor and capital. All of the results that we will derive generalize in a straightforward manner when there are many inputs. The analysis of the multi-factor case, however, requires mathematical tools beyond the scope of this course. For now, we can think of labor as representing all of the inputs that are variable in the short run and capital as representing all of the inputs that are fixed in the short-run. Under this assumption, we can define as firm's short-run production function as:
Q=f(L,K) where: Q = quantity of output produced
L = amount of labor input
K = amount of capital input
The production function, f, is a mathematical function that provides the maximum quantity of output that can be produced for each possible combination of inputs used by the firm. A convenient way of representing this production function is through the use of a graph containing isoquant curves. An isoquant curve is a graph of all of the combinations of inputs that result in the production of a given level of output. (Note that the term "iso" means equal in Latin, thus the term "isoquant" literally means "equal quantity").
The diagram below contains a possible isoquant for a firm.

This isoquant suggests that the firm could produce 50 units of output per day using either 20 units of labor and 5 units of capital or 3 units of labor and 15 units of capital. In fact, any combination of labor and capital along this curve allows the firm to produce 50 units of output per day. Note that this curve is downward sloping because the firm can replace workers with machines or replace machines with workers and still manage to produce the same level of output.
In the diagram below, the firm can produce 50 units of output using any of the input combinations given by points: A, B, or C. What happens, though, at point D? Is the firm producing more or less output at point D than at point C. When students are first asked this question, a common response is: "You cannot answer this since point D involves using more capital but less labor than is used at point C." But, what happens if we compare points B and D.
At point D, the firm is using more labor and more capital than it is using at point B. If it uses more of each input it can produce more total output (assuming productive efficiency). Thus, we know that this firm can produce more output at point D than at point B. Since the firm produces
50 units of output at points A, B, and C, the output level corresponding to point B is higher than at any of the points on the isoquant. More generally, we can state that any point that lies above and to the right of an isoquant curve corresponds to a higher level of output. Using similar logic, the level of output will be lower if the firm selects a combination of inputs that lies below and to the left of an isoquant (as at point E in this diagram).

An isoquant curve passes through each and every point in this diagram. Two additional isoquant curves have been added to form the diagram below.
The isoquant curves considered above tell us about the physical ways in which inputs can be combined to produce output. Notice that they do not tell us anything about the costs associated with alternative levels of input use. (This topic will be considered below.)
The marginal rate of technical substitution of L for K (MRTS
LK
) is defined as the additional amount of capital needed to replace a unit of labor, holding output constant. Mathematically, the
MRTS
LK
can also be expressed as:
Let's examine this expression carefully. The vertical bar at the end of this expression is a mathematical term that indicates that the expression to the left is evaluated given the condition

stated at the bottom right of this line. This condition requires that Q = Q-bar (that's how this is pronounced). What this means, more intuitively, is that the expression to the left is evaluated only for points on a given isoquant (one corresponding to an output level of Q-bar). The term in parentheses is nothing more than the negative of the slope of a line connecting two points on the isoquant. Taking the limit of this expression as the change in L tends to zero, however, results in this being the negative of the slope of a tangent line to the isoquant.
The diagram below illustrates how the negative of the slope of the tangent line serves as a measure of the MRTS.
The law of diminishing MRTS states that the MRTS declines as the level of labor use rises along an isoquant. An equivalent way of stating this law is to state that isoquant curves are convex. Let's consider the intuition underlying this law.
This law suggests that it takes a large amount of capital to replace a unit of labor when capital use is high but little labor is used. As labor becomes more plentiful and capital becomes more scarce, however, less capital is required to replace an additional unit of labor. Roughly speaking, the law of diminishing MRTS indicates that it is relatively difficult to replace additional quantities of an input when the level of that input becomes relatively low. This seems to be characteristic of most production processes. Consider, for example, the situation on a farm.
When a farm is highly mechanized and has only a small number of workers operating the farm equipment, a very large amount of capital would be required to replace a worker. If a firm, though, has many workers but few tools, the introduction of a small amount of capital (such as a tractor) can replace a relatively large number of workers.
Consider the following relationship:
This equation provides us with an approximate relationship between the change in each input and the change in output. An example might help to illustrates this. Suppose that the level of

labor increases by 2 units when the marginal product of labor is 5. In this case, we'd expect to see output change by approximately 10 units. Similarly, if the MP of capital is 10, the addition of 3 extra units of output would cause output to increase by approximately 30 units. This relationship holds only approximately because changes in the level of labor or capital use result in changes in the MP of labor and capital (the law of diminishing returns is part of the explanation for this).
The error will be small, though, when the changes in L and K are relatively small.
Suppose, we consider two points along an isoquant. Since output is constant (i.e., the change in
Q is zero) along an isoquant, the relationship above suggests that:
Manipulating this expression a bit results in:
More precisely, since output was constrained to remain constant, this expression can be written as:
Taking the limit of this equation as the change in L becomes infinitesimally small, this becomes:
Notice that the approximate equality becomes an equality in the limit because the error in the approximation tends to zero as the changes in L and K become infinitesimally small.
A careful reader will note that the left-hand side of the equation above is equal to the definition of the MRTS. This tells us that the MRTS can also be expressed as the ratio of the MP of labor to the MP of capital. We'll make use of this result below.
A firm's total costs in this model can be expressed as:
TC = wL + cK where: TC = total cost w = wage c = price of capital
L = quantity of labor
K = quantity of capital

Just as we used isoquants to represent combinations of inputs that allow the production of a given level of output, we use isocost curves to represent all of the combinations of inputs that result in a given level of total cost.
The diagram below contains an isocost curve corresponding to a level of total costs equal to
TCo.
Notice that the intercepts of this isocost curve equal the level of total costs divided by the price of the factor on each axis. (To demonstrate this, set the level of the other input equal to zero and solve for L or K.) The slope equals -w/c. More generally, the slope of any isocost curve relating any two factors of production will equal the price of the factor on the horizontal axis divided by the price of the factor on the horizontal axis. To see this, let's solve the total cost curve equation above for K (the variable on the vertical axis):
K = (-w/c)L +(TC/c)
Since this is written in standard slope-intercept form (Y = mx+b), we know that the coefficient multiplying the variable on the horizontal axis (-w/c) is the slope. The intercept on the vertical axis, as noted above, is TC/C, the constant term at the end of this expression.
Any combination of inputs that lie above an isocost curve corresponds to a higher level of total costs. Combinations of inputs that lie below a total cost curve correspond to lower levels of cost.
There are an infinite number of possible total cost curves. The diagram below illustrates a few such curves. Notice that all of the isocost curves are parallel to each other (since they all have a slope equal to -w/c).

Note that TC' > TCo > TC'' in this example.
A profit-maximizing firm must minimize it's level of costs. To investigate this process of costminimization, we must combine an isoquant curve with a family of isocost curves (as in the diagram below).
The problem facing the firm is to minimize the costs of producing a given level of output (Q= 50 in this example). To produce 50 units of output, the firm must remain on the Q=50 isoquant.
Cost-minimization requires that it select the combination of inputs that results in the lowest level of total costs. Consider point A in the diagram above. While the firm is producing 50 units of output at this point, any other point on the isoquant between points A and B would allow the production of this level of output at a lower level of total costs. Suppose the firm shifts to the combination of inputs given by point C in the diagram. Production at this point is less expensive than at point A (since it corresponds to a lower isoquant), but this still isn't the lowest possible cost. Any point on the isoquant between points C and D would allow for lower cost production.

In general, we can observe that when an isocost curve crosses an isoquant at two points, there will always be some points between these two points at which costs would be lower.
Consider, however, the situation at point E. No other combination of inputs can result in lower costs while still allowing the production of 50 units of output. Points such as point f would have lower costs, but would not allow the production of 50 units of output (since point F lies below the isoquant).
Thus, we can note that a firm minimizes its total cost of producing any given level of output when it operates at a point of tangency between its isoquant and an isocost curve. At this point of tangency, the slopes of the isoquant and the isocost curve must be equal. Thus:
-MRTS = -w/c or, simplifying:
MRTS = w/c
This cost-minimization condition, more intuitively, requires that the firm use a mix of inputs at which the firm's value of labor in terms of capital (the MRTS) equals the relative cost of labor in terms of capital (w/c).
An alternative way of expressing this condition is to make use of the fact that the MRTS will always equal the ratio of the MP of labor to the MP of capital:
Using a little algebraic manipulation, we have the cost-minimization rule given by:
This cost-minimization rule (one that you probably learned in your micro principles course -without the more formal derivation) requires that the marginal product per dollar spent on any one input must equal the marginal product per dollar spent on any other input.
The substitution effect associated with a change in the wage rate is the change in the mix of inputs that results from the change in relative prices, holding output constant. The scale effect is the change in the mix of inputs that occurs because of the change in the level of output resulting from a change in factor prices, holding relative factor prices constant. Let's examine each of these changes using isoquants and isocost curves.
Suppose the wage rate rises. Since the slope of the isocost curve is -w/c, the isocost curves all become steeper when the wage rate increases. When faced with these new, steeper, isocost curves, a firm will use a new mix of inputs at which the new isocost curves are tangent to the original isoquant. Given the law of diminishing MRTS, this will occur at a point at which less labor and more capital is used (as illustrated by the movement from point A to point B in the diagram below). Notice that the substitution effect of a wage increase involves a reduction in the use of labor and an increase in the use of capital.

The scale effect associated with an increase in the wage involves the following steps:

 higher wages lead to higher average and marginal costs,
 higher average and marginal costs result in a higher price of the product, consumers buy less of the product when its price rises, and
 firms use less of all inputs when they produce less output.
The scale effect associated with an increase in the wage is illustrated by the shift from point B to point C in the diagram below. Note that the scale effect involves a reduction in the use of both inputs.
It should be noted that the total effect resulting from a change in the wage is given by the combination of both the substitution and scale effects. As the diagram above illustrates, both the substitution and scale effects result in a reduction in the use of labor when the wage rate rises.
This is why the labor demand curve is downward sloping in the long run (notice that the law of diminishing returns doesn't apply in the long run since all inputs can change).
The effect of a change in the wage rate on capital demand, however, is ambiguous. The substitution effect resulting from a higher wage results in an increase in the use of capital.

Capital use declines, though, as a result of the scale effect. A higher wage will result in an increase in the use of capital if the substitution effect is larger in magnitude than the scale effect
(as illustrated in the diagram above). When an increase in the price of one resource results in an increase in the demand for another, we say that the two resources are gross substitutes .
Obviously, two inputs will be gross substitutes only if the substitution effect is larger than the scale effect.
Capital demand would decline when the wage rate rises if the scale effect is larger than the substitution effect. In this case, we'd say that labor and capital are gross complements .
Labor demand elasticity is a measure of the sensitivity of labor demand to a change in factor prices. This week, we'll examine how the Hicks-Marshall laws of derived demand affect the magnitude of the elasticity of labor demand. The relationship between union strategy and labor demand elasticity will also be examined as part of this discussion.
The first type of labor demand elasticity that we will examine is the own-wage elasticity of labor demand , defined as:
The own-wage elasticity of labor demand is a measure of how sensitive is the demand for a particular category of labor to a change in the wage rate in that specific labor market. For example, the own-wage elasticity of labor demand for plumbers is a measure of the % change in employment for plumbers that results from a 1% change in the wage rate for plumbers. The i subscripts in the definition just refer to the specific labor markets used in the numerator and denominator of the expression above. It is expected that the elasticity of labor demand will vary substantially across labor markets.
An inspection of the definition above should indicate that the own-wage elasticity of labor demand will always be negative as a result of the negative slope of labor demand curves. We say that labor demand is:
When labor demand is elastic, a 1% increase in the wage will cause employment to fall by more than 1%. If labor demand is inelastic, a 1% wage increase will cause employment to fall by less than 1%. Employment will fall by 1% when the wage rises by 1% if labor demand is unit elastic.

Students who are first exposed to the concept of elasticity often confuse elasticity and slope.
Slope involves a relationship between the change in the level of the wage and a change in the level of employment. Elasticity involves percentage changes in these variables. A constant change in the level of a variable will not result in a constant percentage change in that variable.
Note, for example that:

 an increase from 1 to 2 is a 100% increase,

 an increase from 2 to 3 is a 50% increase.
 an increase from 3 to 4 is a 33% increase. an increase from 4 to 5 is a 25% increase an increase from 10 to 11 is a 10% increase.
 an increase from 100 to 101 is a 1% increase.
Even though the change in the level is one unit in each of the cases listed, the percentage change is smaller when the starting value is larger.
As indicated in the diagram below, at the top left portion of the labor demand curve the percentage change in quantity demanded is relatively large because the level of quantity is low.
Since the wage rate is relatively high in this region, though, any given change in the wage will be a relatively small percentage change. At the bottom right section of this labor demand curve, though, this relationship is reversed. Thus, we can observe that when the wage is high and the quantity of labor demanded is low, labor demand will be relatively elastic (since the numerator is larger in magnitude than the denominator). As labor use increases, though, the percentage change in quantity demanded falls as the level of quantity rises while the percentage change in wage increases as the wage declines.
This argument indicates that own-wage elasticity declines continuously as labor use rises along a linear demand curve. The diagram below illustrates this relationship.

Because of this, the only time it makes sense to speak of "an elasticity" for a linear demand curve is if the demand curve is perfectly elastic (own-wage elasticity is infinite) or if the demand curve is perfectly inelastic (own-wage elasticity = 0).
If we consider two demand curves that pass through a common point, though, we can use the slopes of the curves to compare the elasticity of demand at that particular starting point. In this case, a steeper curve will be more inelastic than a flatter curve. This is illustrated in the diagram below.
Suppose that initially the level of wage and employment is given by point A. If the wage rate rises (as illustrated above), there will be a larger reduction in employment along the flatter demand curve D' than along the steeper demand curve D. When we use differences in slopes to illustrate differences in elasticity in future examples, note that it is always assumed that the two curves share the same starting point, even when they are drawn in separate diagrams.

Before discussing the determinants of own-wage elasticity of labor demand, it is important to recall that the negative slope of the labor demand curve is the result of the substitution and scale effects that occur in response to a change in the wage rate. As the wage rises, the substitution effect results in a reduction of labor use and an increase in the use of other inputs, holding the level of output constant. The scale effect resulting from the wage increase is a result of the reduction in sales and output that accompanies an increase in production costs. Both the substitution and scale effects associated with a wage increase result in a reduction in the quantity of labor demanded when the wage rate rises.
The own-wage elasticity of labor demand tells us the magnitude of the change in the quantity of labor demanded that occurs when the wage rate changes. Since changes in the wage affect the quantity of labor demanded through the substitution and scale effects, anything that influences the magnitude of the own-wage elasticity of labor demand must somehow affect the magnitude of either the substitution or the scale effect (or both). Let's keep this point in mind while investigating the determinants of labor demand.
The Hicks-Marshall laws of derived demand state that own-wage elasticity of labor demand will be relatively high when:
1.
the price elasticity of demand for the final product is relatively high,
2.
it is relatively easy to substitute other factors for this category of labor,
3.
the supply of other factors of production is relatively elastic, and
4.
this category of labor accounts for a relatively large share of total costs.
Let's examine each of these laws.
First Hicks-Marshall law
The first Hicks-Marshall law is due to the scale effect associated with a change in the wage. As we noted earlier, the scale effect associated with a wage increase involves the following change of events:
1.
higher wages lead to higher average and marginal costs,
2.
higher costs lead to a higher equilibrium price of the final product,
3.
an increase in the price of the final product results in a reduction in the quantity of the product demanded,
4.
the reduction in quantity sold results in a reduction in the quantity of output produced
(and in the amount of inputs needed to produce this output).
When the price elasticity of demand for the final product is relatively high, the increase in the price of the product occurring in the 3rd step results in a larger reduction in the quantity of output demanded. If output falls by more, then the firm will reduce its employment of labor (and all other inputs) by a larger amount. Therefore, a given change in the wage will result in a larger reduction in the quantity of labor demanded when the price elasticity of demand for the final product is relatively high. Since a wage change results in a larger reduction in employment when the price elasticity of demand for the final product is relatively high, we can see that labor demand is more elastic in this situation.
This law explains why the demand for labor will be more elastic at the level of the labor market than at the level of an individual firm. It also explains why labor demand will be less elastic in industries that are characterized by an imperfectly competitive output market.

Another implication of this law is that labor demand will be more elastic in the long run than in the short run (since the demand for final products is more elastic in the long run than in the short run).
Second Hicks-Marshall law
The second Hicks-Marshall law states that own-wage elasticity of labor demand is relatively high when it is relatively easy to replace labor with other factors of production. This law, obviously, works through the substitution effect associated with a wage change. If it is relatively easy to substitute other factors for this category of labor, a wage increase will result in a larger reduction in the quantity of labor demanded.
Third Hicks-Marshall law
The third Hicks-Marshall law states that own-wage elasticity of labor demand will be relatively high when the supply of other factors of production is relatively elastic. This law works through the substitution effect associated with a wage change. The diagram below illustrates how the price elasticity of supply for capital may affect the amount of substitution that actually occurs when the wage rate rises. When the wage rate rises, firms will attempt to substitute other factors for labor. As they do so, the demand for these factors will rise (as illustrated by the shift from D to D' in the diagram below). When the supply of capital is relatively elastic, this increase in demand results in a relatively large increase in the use of capital and a relatively small increase in the price of capital. When the supply of capital is relatively inelastic, however, the increase in the demand for capital drives up the price of capital by a relatively large amount but has a relatively small effect on the quantity of capital employed by the firm. When this occurs, the increase in the price of capital limits the amount of additional capital that will be used as a substitute for labor.
Thus, when the supply of other factors is relatively elastic, the substitution effect will be larger and labor use will fall by a larger amount. Since labor use falls by a larger amount in response to a wage increase when the supply of other factors is more elastic, own-wage elasticity will be relatively high.
Fourth Hicks-Marshall law

The fourth Hicks-Marshall law states that own-wage elasticity is relatively large when this category of labor accounts for a relatively large share of total costs. This law works through the scale effect associated with a wage increase. If labor costs account for 1% of total costs, a doubling of labor costs will only increase total costs by 1%. If labor costs account for 50% of total costs, though, a doubling of labor costs will increase a firms total costs by 50%. When labor costs are a larger share of total costs, a wage increase will have a greater effect on the firm's costs and therefore a greater effect on the price of output. If output prices rises by more, the scale effect will be larger and the reduction in labor use will be greater. Therefore, an increase in a given category of labor's share of total costs will result in a higher own-wage elasticity of demand for this type of labor.
Unions attempt to increase the incomes of their members. When labor demand is relatively inelastic, a given wage increase will result in a smaller impact on employment. If labor demand is relatively elastic, however, a wage increase results in a relatively large reduction in employment. Clearly, unions would prefer to be operating in a labor market in which labor demand is more inelastic. This results in a few interesting results concerning union strategies:
 unions will be more successful in receiving wage increases in markets in which labor demand is relatively inelastic,
 unions will attempt to reduce the own-wage elasticity of demand for their workers, and
 unions might prefer to organize those labor markets in which labor demand is relatively inelastic.
Let's see how each of the Hicks-Marshall laws apply to these strategies.
First law and union strategy
Since labor demand is more inelastic when the demand for output is more inelastic, labor unions will receive larger wage increases when labor demand is more inelastic. This may explain why labor unions in the U.S. were relatively successful in the relatively concentrated industries of automotive manufacturing, steel production, and similar industries. Unions may attempt to apply this law by engaging in advertising campaigns ("Buy American" and "look for the union label") to attempt to reduce the elasticity of demand for the final product. These campaigns, if successful, also have the desirable effect (from the union's viewpoint) of increasing the demand for union labor.
Second law and union strategy
Unions consisting of skilled workers were historically the first successful unions. One of the reasons for this is that skilled workers are harder to replace than unskilled workers in many production processes. An examination of a typical union contract indicates that a great deal of effort goes into negotiating job descriptions and job titles that carefully delineate job duties for each employee. One of the reasons for the use of such careful language in contracts is that this limits the ability of firms to substitute lower-cost workers for more highly paid workers. By reducing the ease of substitution among workers, unions are able to reduce the own-wage elasticity of demand for each type of worker. An extreme form of this practice occurs in the case of "featherbedding." Featherbedding occurs when contracts are negotiated that require firms to hire workers whose jobs are no longer needed as a result of technological change.

Unions generally favor restrictions on immigration and were active supporters of mandatory education and child labor laws. One of the reasons for this support is that immigrant workers and children serve as low-cost substitutes to union workers. By reducing the availability of immigrant and child labor, unions are able to face a more inelastic demand curve for labor.
Third law and union strategy
Unions advocate child labor laws and laws restricting immigration partly to limit the supply of substitutes and also to reduce the elasticity of supply of substitute labor. By raising the penalties associated with illegal immigration or with violations of child labor laws, the supply of these other sources of labor is reduced, but also becomes more inelastic (since a larger wage increase is required to induce a given increase in the supply of illegal labor).
Fourth law and union strategy
Of course, it is unlikely that unions will actively attempt to reduce the share of labor costs in total costs. Unions, however, have been relatively more effective historically in capital-intensive industries in which labor costs are a relatively small share of total costs. As your text notes, airline pilots have been able to achieve relatively high wages, in part, because they account for a relatively small share of total costs (the 2nd law also applied as well here). One of the reasons for the limited success of unions in the service sector is that labor costs are a relatively large share of total costs in this sector.
The cross-wage elasticity of labor demand (also known more generally as the cross-price elasticity of demand) is a measure of the effect of the change in the price of one factor of production on the demand for another factor of production. It is defined as:
A positive cross-price elasticity of demand between two inputs indicates that the two inputs are gross substitutes . As noted in the notes to the previous chapter, this will occur only if the substitution effect outweighs the scale effect. Two inputs are gross complements if the crossprice elasticity is negative. A negative cross-price elasticity occurs when the scale effect is larger than the substitution effect.
Cross-wage (cross-price) elasticities provide evidence on a variety of policy issues such as: the effect of a lower subminimum wage for teenagers on adult employment and the effect of an investment tax credit on employment.
Empirical studies suggest that:

 labor and energy are substitutes,
 labor and materials are substitutes, skilled workers are more likely to be gross complements with capital than are unskilled workers, and
 there is little complementarity or substitution between immigrant and native workers.

One factor that should be kept in mind when analyzing the minimum wage is that the minimum wage is specified in nominal terms, not real terms. Once a new higher minimum wage is passed, its real value begins to decline as a result of inflation. Most of the increases in the minimum wage over time have been designed to restore the real minimum to its past higher real values.
As noted earlier, the introduction of a minimum wage law that covers all employees into a perfectly competitive labor market will be expected to result in a reduction in employment.
Let's examine what happens in perfectly competitive labor markets when some workers are not covered by the minimum wage law. The first national attempt at a federal minimum wage law during the Great Depression relied on the National Industrial Recovery Act, an attempt to have firms in major industries form trade association agreements that set minimum wages for labor and minimum prices for commodities. This effort was ruled unconstitutional by the U.S.
Supreme Court (this was one of the cases that lead to FDR's attempt to expand the size of the
Supreme Court). A second, and successful attempt at a national minimum wage was provided by the Fair Labor Standards Act of 1938. Since the constitutional justification for the minimum wage was that the federal government could only regulate firms engaged in "interstate commerce" less than half of the labor force was initially covered by the minimum wage law. The coverage of the minimum wage law has expanded substantially over time.
While nearly 90% of nonsupervisory workers are legally covered by the minimum wage law, workers who are working "off the books" in the underground economy sometime receive a wage that is below the minimum wage. The diagram below illustrates the effect of having a "noncovered" sector of the economy. In the absence of a minimum wage law, the equilibrium wage would equal Wo in both sectors of this market. The introduction of a minimum wage in covered firms result in an increase in the wage (to Wm) and a reduction in employment in the covered sector of the economy. Workers who cannot find work in the covered sector have the option of shifting to firms that are not covered by the minimum wage law. This will result in an increase in supply in the non-covered sector. In response to this increase in supply, employment in the noncovered sector will increase, but wages in this sector will decline.
Notice that an increase in the minimum wage need not result in increased employment as long as the workers who lose their jobs in the covered sector are able to shift to work in non-covered firms. Despite this, however, there is still an efficiency cost for society since the marginal revenue product of the last worker hired in the covered sector will exceed the marginal revenue

product of the last worker hired in the non-covered sector. Society would have been able to produce more total output if the MRP were the same in both sectors. An example might help to illustrate this efficiency cost. Suppose that the minimum wage is $5.10 and the wage in the noncovered sector is $4.50. The loss of one hour of labor in the non-covered sector results in a loss of $4.50 in output in this sector. If this hour was transferred to the covered sector, nearly
$5.10 in additional output can be produced, resulting in a net gain to society of $.60 an hour.
The analysis that was applied above to the effect of a minimum wage can also be used to explain the effects resulting from the introduction of an industrial union into some, but not all, of the firms in an industry.
In general, the theories that we have discussed suggest that a minimum wage law (or union) will result in:
 unemployment and economic inefficiency if the labor market is perfectly competitive and there is complete coverage,
 economic inefficiency if the labor market is perfectly competitive and there is a non-
 covered sector, and an ambiguous effect on the level of employment if firms possess some degree of monopsony power.
Since theory offers mixed predictions, empirical evidence must be used to determine the effects of the minimum wage on employment. The results here are somewhat mixed. Early studies found negative employment consequences for teenagers when the minimum wage increases.
More recent, more carefully designed, and more comprehensive studies have found little or no employment effects associated with increases in the minimum wage.
There is substantial evidence, though, that the minimum wage is not the most effective method of reducing policy. Only a very small proportion of minimum wage workers (approximately
22%) live in poor households.
Technological change results in lower cost and higher quality products. Changes in product demand resulting from technological change will result in changes in the demand for the labor used to produce these commodities. The invention of steam engines, internal combustion engines, cathode ray tubes, and computers all resulted in substantial shifts in the pattern of demand for output and for labor.
A second effect involves the introduction of automation. Roughly speaking, this type of technological change is equivalent to a reduction in the price of capital. The effect of this change in any given labor market depends upon whether this type of labor is a complement to or a substitute for capital.
There is no evidence that suggests that technological change results in an overall increase in unemployment.

The focus of this chapter is on nonwage labor costs, those costs that do not directly vary with the number of hours worked by the worker. These nonwage labor costs include hiring costs, training costs, and employee benefits.
Hiring costs include all of the costs associated with the hiring process. These costs include the costs associated with:





 placing advertisements, selecting candidates for interviews, interviewing candidates, selecting candidates for job offers, negotiating job offers, and processing the worker's employment (filling out W4 forms, I9 forms, and adding the worker to the company's insurance and pension plans) in the human resources department of the firm.
In the secondary labor market, hiring costs are generally relatively low. Hiring costs in the primary labor market, however, can be very substantial, particularly when the firm is operating in a national labor market.
The costs of training include:
 the explicit cost of hiring trainers and using materials (such as manuals, videotapes, and
 capital equipment) for training purposes, the implicit cost of using other workers, raw materials, and capital during informal onthe-job training, and
 the opportunity cost of the trainee's time during training (the trainee could have been assigned to a task at which they would have been more immediately productive).
Firms may affect the level of their training costs by the wage offers that they make. Firms that offer low wages will have higher turnover rates and lower quality applicants. This tends to increase the firm's training costs. A high-wage strategy results in a larger applicant pool, allowing the firm to be more selective. High-wage workers also tend to stay with the firm for longer periods of time, reducing the firm's overall training expense.
Employee benefits include both legally mandated social insurance programs (such as social security and unemployment compensation) and privately provided benefits such as health insurance, vacation pay, and pension plans.
Quasi-fixed costs are costs that vary with the number of workers hired by the firm, but not with hours worked per employee. Hiring costs, training costs, and many employee benefit programs

are quasi-fixed costs. For example, if it requires 5 hours to train a worker to operate a given piece of equipment, this cost will be the same per worker regardless of whether the worker uses the machine 1, 2, 5 or 40 hours a week. This cost varies only with the number of workers that must be trained, not with the number of hours worked per employee. The cost of providing health insurance to a worker is the same regardless of whether the worker works 35, 40, 60, or more hours per week.
Up to this point, we have been using L to denote the quantity of labor demanded by a firm. We have not explicitly taken into account the fact that firms may increase their use of labor by:


 adding additional workers, increasing the length of the workweek, or some combination of increases in hours and increases in the number of workers.
A simple way to describe this process is using a production function of the form:
Q=f(M,H) where: Q = quantity of output
M = number of workers
H = length of average work week
This simple production function is a short-run production function in which capital is held constant. In this case, the marginal product of M is the additional output that is produced when an additional worker is hired. It is expected that, ceteris paribus , the marginal product of M declines as more workers are added (this is just the usual law of diminishing returns). The marginal product of H is the additional output that results when the length of the workweek is increased by one hour. It is expected that the marginal product of H will decline as the length of the workweek rises (since people become less productive as they become tired....).
An optimal mix of M and H occurs at the point at which the marginal product per dollar of spending is the same for each input. This occurs when:
(Your text uses the reciprocal of these conditions. While the two conditions are equivalent, the method of expression used above is more consistent with the coverage in Chapter 3. It also seems a bit more intuitive.) This condition is analogous to the cost minimization condition derived in Chapter 3 for the optimal mix of labor and capital. The only difference is that this more general specification refers to the marginal expense of each input rather than the factor price. (A formal proof of this condition requires mathematical tools beyond the scope of this course.) Note that the marginal expense of hours is affected by the mandated overtime premium

that exists under the Fair Labor Standards Act. Once workers work more than 40 hours per week, they must be paid one and a half times their base rate of pay for each additional hour of work.
This indicates that the mandated overtime premium raises the marginal expense of labor once the workweek exceeds 40 hours. The marginal expense of M includes quasi-fixed costs in addition to direct wage payments.
Congress periodically considers an increase in the mandated overtime premium to twice the base pay rate. The rationale for this change is a belief that such a policy would reduce unemployment by encouraging firms to hire additional workers rather than use overtime work. Let's first examine the substitution and scale effects associated with such a change.
An increase in the mandated overtime premium is equivalent to an increase in the marginal expense of H. The substitution effect resulting from this change involves an increase in M and a reduction in H. This is consistent with the goal of this proposed policy. The scale effect, however, would reduce both M and H. The net effect depends on whether the substitution or scale effect is larger.
In a more complete model, though, a number of other factors have to be considered. If the overtime premium increased, we'd also expect to see:
 a substitution of capital and other inputs for labor (the cost of both M and H rise as the overtime premium rises),

 increased noncompliance with the Fair Labor Standards Act, only limited substitution of less skilled unemployed workers for the skilled workers who
 tend to work overtime hours (since these inputs are not perfect substitutes),
 increased moonlighting, and a decline in the base rate of compensation in those industries that use significant amounts of overtime, so that the total compensation of workers remains unchanged.
Each of these factors tends to reduce the effect of an increase in the overtime premium on unemployment.
The quasi-fixed costs associated with full-time employees is usually higher than the quasi-fixed costs associated with part-time employees. Studies have shown that employment of ratio of parttime/full-time employment is very sensitive to the part-time/full time wage ratio. In recent years, there have been proposals to require that firms provide mandatory health-insurance to all workers (including part-time workers). This would be expected to have a serious adverse effect on the proportion of part-time employment available since the hourly cost of part-time workers would rise substantially more than the hourly cost of full-time employees (especially since many full-time employees already receive this insurance while few part-time workers are covered by such health plans).
In earlier chapters, we used a single period model to describe the optimal level of employment.
In practice, of course, most workers tend to work for their firms for relatively long periods of time. In considering multi-period employment models, we should note that firms may lose

money while they are training a worker as long as they make a high enough return later on to justify the cost of the training.
A comparison of benefits and costs over time requires the use of the present value concept that was discussed in your introductory economics classes. If you wish to review this concept, you can jump over to some notes on present value from my micro principles class. In any case, the present value of $K received T years in the future is equal to: when the interest rate is r. As this equation suggests, the present value of a future payment is lower when:

 the payment is received in the more-distant future, and/or the interest rate is relatively high.
Let's apply this concept to the analysis of a two-period employment model. In this model, the worker is employed for an initial training period and then a post-training period of known duration. Let's first define a few terms:
Wo = wage during training
W1 = post-training wage
W* = wage if no training is received (the same in each period)
Z = hiring and training cost (paid during the training period)
MPo = marginal product during training
MP1 = marginal product after training
MP* = marginal product if no training is received (assumed to be the same in each period)
The relationships among these MP curves is illustrated in the diagram below.
As this diagram illustrates, a worker is less productive while being trained than if he or she were to work in a job that did not require training. After the completion of the training, though, a worker's productivity rises above that of an untrained worker.

The MRP=MFC condition discussed earlier is appropriate for a single-period model of labor demand, In the multi-period model, this condition generalizes to:
PV(MRP) = PV(MFC) where: PV(MRP) is the present value of the marginal revenue product stream associated with an additional worker, and PV(MFC) is the present value of the marginal factor cost stream associated with an additional worker.
Your text uses the abbreviation PVP for the PV(MRP) and the abbreviation PVE for the
MV(MFC).
In this model:
 PVP = MPo + MP1/(1+r), and
 PVE = Wo + Z + W1/(1+r).
(Note that it is implicitly assumed that the output market is perfectly competitive and that the price of final output is equal to 1. These simplifying assumptions are necessary if we are to use
MP instead of MRP in computing the PVP.)
Thus, an optimal level of employment occurs at the level of labor use at which:
PVP=PVE or:
MPo + MP1/(1+r) = Wo + Z + W1/(1+r)
This condition is illustrated in the diagram below. An optimal level of employment (L*) occurs at the level at which the present value of the stream of marginal revenue product is just equal to the marginal product of the stream of marginal factor costs over the worker's period of employment with the firm.

With a little bit of algebraic manipulation, the equilibrium condition stated above can be expressed as:
Wo + Z - MPo = (MP1 - W1) / (1 + r)
In your text, the term on the left-hand side of this expression is called NEo, the net expense to the firm during the training period. This is a measure of the amount by which the costs to the firm during training exceeds the value of the worker's output. The right-hand side of this expression is referred to as G, the present value of the expected gain in the post-training period.
The equilibrium condition requires that the net cost during training must be equal to the present value of the expected gain in the post-training period. In mathematical terms, the condition above can be simply stated as::
NCo = G
One implication of this result is that the firm will cover some of the costs of training (NCo > 0) only if it can realize a gain in the post-training period. This occurs, only if MP1 > W1. In other words, a firm will pay a worker more than he or she is worth to the firm during training only if it can pay the worker a wage that is less than the worker's worth to the firm after the training is completed. If a worker is paid a wage equal to his or her MP after training is completed, then the net cost that will be borne by the firm during training is zero.
General training is training that raises a worker's productivity in more than one firm. Firmspecific training increases the worker's productivity only in the current firm. The type of training provided by a formal education involves general training. Learning how to operate a forklift, a lathe, or a copy machine also involves general training. Learning to use software or production procedures that are unique to a specific firm, though, is an example of firm-specific training. Let's examine who will bear the costs of each type of training.
Since general training raises a worker's productivity in more than one firm, a worker possessing general training has increased his or her productivity in firms other than the one in which he or she is employed. This means that the worker is now more productive in other firms as well as in the current firm. If the current firm pays for the worker's training expecting that the worker will work for a wage below his or her MP after the training is completed, the firm is likely to be disappointed. Since the worker could receive a wage of MP1 in other firms, the current firm must pay the worker this wage or risk losing the worker. In other words, G is expected to be zero when workers receive general training. Since firms are not able to receive a benefit from this training, they will not bear the cost of the training. This means that the workers receiving general training will be expected to bear all of the cost of training by receiving a wage equal to:
Wo = MPo - Z during the training period, and a wage equal to:
W1 = MP1 after the training is completed. Thus, workers are expected to bear all of the costs of and receive all of the benefits from general training. The only exceptions occur when the firm is able to tie the worker to the firm for some period after the training is complete. Reserve clauses in professional sports and military contracts, for example, are able to force athletes and military

employees to remain in the current employment for some period of time after the completion of training investments.
The result is somewhat different in the case of firm-specific training. If workers bore all of the costs by accepting an initial wage equal to MPo - Z, there is no reason for the firm to keep that worker after the training is completed (since the firm did not invest anything in the worker's training). Since the training is valuable only in the current job, workers would be reluctant to pay for training that will not benefit them if the firm lays them off. On the other hand, if firms pay for all of the costs of training by offering a wage equal to W* (=MP*) in the hopes of receiving a benefit in the future, there is no particular reason for workers to stay with the firm. So, workers will not cover all of the costs because firms might terminate their contracts after the training is complete while firms would not pay all of the costs because workers might leave and the firm would lose its investment in training.
A solution to this problem is for the costs and benefits from firm-specific training to be shared between the worker and the firm. The costs are shared by paying the worker a wage greater than the worker's MP, but less than the worker's wage elsewhere. This occurs by paying a wage in the following range:
MPo - Z < Wo < MP*
If the costs are shared, the benefits can also be shared by paying workers a wage greater than could be received elsewhere, but less than their worth to the firm. In this case:
MP* < W1 < MP1
If workers and firms share the costs and the benefit, they both have a stake in maintaining the employment relationship. This reduces the risk to both parties to this transaction.
One implication of this model is that firms will be more reluctant to lay off workers who have received training investments paid for by the firm. Similarly, they'd be more likely to rely on overtime rather than using additional employees in those markets in which firms pay a substantial share of training costs. Thus, we'd expect to see smaller changes in employment over the course of the business cycle in those labor markets in which there is a relatively high level of firm-specific training, This results in a reduction in labor productivity during a recession (since employment changes by a smaller percentage than does output), but higher productivity during periods of economic expansion.
Another implication of this model is that increases in the minimum wage may reduce the amount of training that occurs. For workers to bear part or all of the cost of their training, they must be paid less during the training period. The minimum wage sets a floor on this wage that limits the ability of workers to bear the costs of such training by accepting a lower wage. Firms faced with such a system may respond by providing less training, thereby limiting the rate of growth of earnings for workers who would have experienced increased future productivity and wage offers if they had received more training.

In a more complete model, we would have to take into account the fact that firms do not know how long a given worker will work for a firm. Because firms face an uncertain environment, though, they don't know how long a given worker will remain with a firm. They may observe, though, from past experience that workers with particular credentials (such as a college degree or
3 years of work experience) or other observable signals (age, race, gender, etc) have stayed with the firm longer than workers with other credentials and signals. Firms will use these credentials or signals to guide their decisions concerning hiring and promotion if this reduced their overall training costs. Such a policy, though, results in statistical discrimination , in which workers are judged by the characteristics of the groups to which they belong rather than based on their individual characteristics.
Two common forms of statistical discrimination associated with hiring and promotions involve age and gender discrimination. Firms often observe that females and older workers, on average, are less likely to remain employed with the firm for long periods of time. In consequence, they may engage in statistical discrimination by providing preferential employment and promotion decisions for younger males. By doing this, firms will make some mistakes, but may receive higher levels of expected profits.
As female labor force participation rates continue to rise and as female quit rates continue to decline, it might be expected that gender based statistical discrimination will be less common.
The use of internal labor markets is expected to reduce statistical discrimination in promotion decisions since firms have more information about the motivation and likelihood of long-term employment of workers who are already working in the firm.
This week, we'll examine the determinants of labor supply. The framework for this discussion relies on the basic neoclassical model in which individuals are assumed to face a trade-off between labor and leisure time. In this model, it is assumed that there are only two possible uses of time: labor and leisure. Each individual is assumed to select the mix of time and purchased inputs that maximizes his or her level of satisfaction (utility).
During the past century, the labor force participation rate for males has declined, primarily for relatively young males and males aged 65 and older. These changes are primarily the result of increased education attainment (delaying entry into the labor force) and earlier retirement. (In fact, retirement is a relatively recent phenomenon, induced in part by the introduction of the
Social Security system and increases in private pension plans.)
The labor force participation rate for females, on the other hand, have increased rather dramatically over the past century. This increase is most pronounced for married females (partly because this group began the century with very low labor force participation rates). Among the reasons for the increase in female labor force participation rates are:
 World War II,

 rising real wages,
 reduced fertility,

 increased educational attainment,
 rising divorce rates, and changing societal norms.
Since there are only two uses of time in the basic neoclassical model, the opportunity cost of an additional hour of leisure time is the wage payment that is given up by choosing to not work.
Individuals choose to not work an additional hours if the value of leisure time exceeds the market wage rate. Individuals will work an additional hour if the value of the products that can be purchased with the wage outweigh the benefits of an additional hour of leisure time.
A change in the wage results in two effects on an individual's labor supply:

 a substitution effect, and an income effect.
As the wage rate rises, the opportunity cost of leisure time rises. In response to this higher wage, individuals consume less leisure time and spend more time at work. This is the substitution effect resulting from a higher wage.
An increase in the wage, however, also raises an individual's real income. This leads to an increase in the consumption of all normal goods. Since leisure is expected to be a normal good for most individuals, a higher wage will generally induce individuals to consume more leisure time (and reduce hours of work). Individuals who receive a higher wage can afford to take more time off from work. This is the income effect resulting from a wage increase.
If we assume that leisure is a normal good, an increase in the wage will cause the quantity of labor supplied to:

 increase if the substitution effect is larger than the income effect, and decrease if the income effect is larger than the substitution effect.
This may result in a backward-bending labor supply curve (as illustrated below).

In the diagram above, it is suggested that, at relatively low wages, individuals respond to an increase in the wage by working additional hours (since the substitution effect exceeds the income effect). Eventually, though, when the wage becomes sufficiently high, individuals will begin to work less in response to a higher wage rate. (In practice, it appears that most labor supply curves are either upward sloping or vertical.)
Let's examine how indifference curves and budget constraints may be used to illustrate the optimal combination of labor and leisure. An indifference curve is a graph of alternative combinations of goods that provide a given level of satisfaction (utility). In the simple neoclassical model of labor supply, it is assumed that the individual's utility level is a function of two goods: real income (Y), and leisure time (L). In mathematical terms, this utility function may be expressed as:
U = U(Y,L) where U = the level of utility associated with alternative combinations of L and Y. In this case, an indifference curve provides a graph of all of the combinations of income and leisure that provides a given level of utility to an individual. The diagram below illustrates a possible indifference curve.

This indifference curve is downward sloping because an individual is willing to give up some income to receive additional leisure (or vice versa).
A few points have been added to the diagram below. Due too the definition of the indifference curve, this individual would be just as happy with the combination of real income and leisure represented by point A as he or she would be with the combination of Y and L represented by point B. Points that lie above and to the right of the indifference curve, such as point C, provide a higher level of utility.
Each point in this diagram provides a particular level of utility. The indifference curve that passes through point C provides a higher level of utility. This means that U' corresponds to a higher level of utility in the diagram below.

Individuals attempt to achieve the highest possible level of utility. The choice among alternative levels of Y and L, however, is restricted due to two constraints:
 a time constraint, and
 a goods constraint.
The time constraint is given by:
H + L = T where: w = wage rate
H = hours of work
P = price index for real income
Y = real income
This time constraint simply notes that time spent at work plus time spent at leisure must add up to the total time available (since these are the only two uses of time in this model).
Using the definitions above, the goods constraint is given by: pY = wH
This equation states that total spending (pY) must equal earnings (= wH). (Since this is a oneperiod model, saving and lending do not occur. More complex models that include this possibility have results that do not differ substantially from those derived below in this simpler model. The analysis of more complex multi-period models, however, requires mathematical tools that are beyond the scope of this course.)
Thus, the two equations that must be satisfied are:
1.
H + L = T
2.
pY = wH

Rewriting equation (1) as: H = T - L and substituting this into equation (2) results in: pY = WT - wL
With a little algebraic manipulation, this becomes:
3. wT = pY + wL
This equation is called a "full-income constraint." Economists define full income as an individual's maximum earnings potential (= wT in this case). This equation states that full income equals the total explicit costs of goods and services (pY) plus the total implicit cost of leisure time (wL).
An alternative form of equation (3) is given by:
3'. Y = -(w/p)L + (w/p)T
This equation describes the relationship that exists between hours of leisure and real income.
Equation (3') is the individual's budget constraint .
The intercept of the budget constraint on the horizontal axis equals T. This is the maximum amount of leisure time that an individual can receive. This is illustrated by the highlighted point in the diagram below. Notice that both H and L can be measured along the horizontal axis. The level of work effort decreases from T to 0 as the level of leisure time rises from 0 to T.
Noting that the budget constraint contained in equation (3') is expressed in slope-intercept form, the intercept of the budget constraint on the vertical axis equals wT/p (= the real value of full income). Using the slope-intercept form of the budget constraint in equation (3'), we can also see that the slope of the budget constraint equals -w/p. The diagram below illustrates the budget constraint facing this individual.

In the diagram below, three indifference curves have been added to the diagram containing the budget constraint. Each point on the budget constraint is a feasible combination of income and leisure. It is assumed that the individual will select the combination of income and leisure that provides the highest possible level of utility. As indicated by the diagram below, this optimal combination of L and Y occurs at a point of tangency between the budget constraint and an indifference curve. In the diagram below, this optimal point occurs when real income equals Y* and hours of leisure equals L*. At this point, the individual chooses to work H* hours.
The absolute value of the slope of an indifference curve is a measure of the opportunity cost of time at that point. Note that the absolute value of the slope of an indifference curve serves as a measure of the amount of income that is required to induce the worker to give up an hour of leisure time. A steep indifference curve indicates that a large change in income is required to induce an additional hour of work; a relatively small increase of income can induce an additional hour of work when indifference curves are relatively flat. Thus, indifference curves are relatively

steep when the value of time in nonmarket activities is relatively high. The diagram below contains a set of indifference curves for an individual who places a high value on nonmarket time.
A corner solution occurs when the indifference curve is steeper than the budget constraint at the point corresponding to zero hours of work. This possibility is illustrated in the diagram below. A careful inspection of this diagram should indicate that the highest possible level of utility (given this budget constraint and these preferences) occurs at zero hours of work. An individual chooses to remain out of the labor force when a corner solution such as this occurs.
A corner solution at zero hours of work will occur when the value of leisure time is relatively high and/or the market wage is relatively low. To see this, note that the absolute value of the slope of the indifference curve is a measure of the opportunity cost of leisure time while the absolute value of the slope of the budget constraint is the real wage. A corner solution occurs only if the value of leisure time (the absolute value of the slope of the indifference curve) exceeds the real wage (the absolute value of the slope of the budget constraint).

The absolute value of the slope of the indifference curve at the point corresponding to zero hours of work is the individual's reservation wage (expressed in real terms. This is illustrated in the diagram below.
If the real wage in the labor market exceeds the reservation wage, the individual chooses to work. This possibility is illustrated in the diagram below. Notice that when the real wage exceeds the reservation wage, there are feasible points on the budget constraint that provides a higher level of utility than would occur at zero hours of work.
If the real wage in the labor market is less than the reservation wage, the individual chooses to remain out of the labor force and a corner solution occurs. This possibility is illustrated in the diagram below.

So, whenever the wage exceeds the reservation, an individual will chose to work. An individual will not work if the wage is below the reservation wage. The individual is indifferent between not working and working when the wage equals the reservation wage (since the opportunity cost of leisure time is just equal to the wage at this point).
Up to this point, we have assumed that all income is received in the form of labor income.
Individuals, however, also receive income in the form of nonlabor income. As we noted at the beginning if this semester, income from nonlabor sources is referred to as "unearned income."
This nonlabor income may be received in the form of interest payments, rent, dividends, profits, alimony payments, transfer payments, lottery winnings, lawsuit settlements, or as any other income that does not vary with hours worked.
Using the definition:
A = total amount of nonlabor income the time and goods constraints that we derived above become:
1.
Time constraint: H + L = T
2.
Goods constraint: wH + A = pY
Note that the time constraint is the same as that discussed earlier (those with more nonlabor income do not have any additional hours in the day....). The goods constraint is modified to account for two source of income: earned income (wH) and unearned income (A).
Solving equation (1) for H:
H = T-L
Substituting this for Y in equation (2) results in:
Y = -(w/p)L + (wT+A)/p

An inspection of this budget constraint equation indicates that the slope equals -w/p (as in the simpler model) and the intercept on the vertical axis equals (wT+A)/p
Three budget constraints corresponding to alternative levels of nonlabor income (A) appear in the diagram below. As the level of nonlabor income rises, the budget shifts vertically in an upward direction. The slope remains constant at -w/p.
Notice that the slope of the budget constraint stays the same when nonlabor income changes.
While the budget constraint shifts upward as nonlabor income rises, it still terminates at T hours of leisure. No matter how wealthy you are, there are still only 24 hours in your day.
If leisure is a normal good, an increase in nonlabor income results in an increase in leisure time and a reduction in hours worked (as illustrated below).
The change in hours worked that results from a change in real income, holding relative prices constant, is called a "pure income effect." When leisure is a normal good, this income effect reduces hours worked when income rises.

As the wage rate rises from wo to w', the budget constraint pivots upward. The diagram below illustrates this possibility. In response to this increase in the wage, the equilibrium shifts from point A to point C. In this example, the quantity of labor supplied has decreased in response to this higher wage. As noted earlier, this suggests that the income effect must be larger than the substitution effect for this individual (i.e., this person is operating on the backward-bending portion of his or her labor supply curve).
In the diagram below, the effect of the wage increase has been decomposed into separate substitution and income effects. The substitution effect is the change in the mix of L and Y that results from a change in the relative price of leisure (the real wage), holding utility constant. This is represented by the movement from point A to point B in this diagram. The budget constraint that is tangent to the indifference curve at point B is a hypothetical budget constraint. It is constructed so that it has a slope equal to the slope of the new budget constraint (-w'/p) and is tangent to the initial indifference curve. Notice that, as expected, the quantity of leisure consumed declines when the relative price of leisure rises.

The shift from point B to C is a pure income effect (and is equivalent to the pure income effect discussed above). Since leisure is a normal good for this individual, the quantity of leisure consumed rises (and hours worked declines) as real income rises in response to the higher wage.
When the income effect is smaller than the income effect, an increase in the wage will result in an increase in hours worked and a reduction in leisure time (as illustrated below). In this example, the substitution effect is again illustrated by the shift from point A to B; the shift from
B to C is the income effect. The net effect in this case is an increase in hours worked and a reduction in leisure time.
It is important to note that we never observe separate income and substitution effects when the wage rate changes. Instead, we only observe the combined substitution and income effects
(represented by a movement from point A to point C). The decomposition of this change into substitution and income effects, however, explains why a backward-bending labor supply curve may exist.
The diagram below represents an optimal combination of leisure and work for an individual facing a wage rate equal to w. This individual will work Ho hours (leisure time = Lo) and will receive an income of Yo.

Suppose that an unemployment compensation program is introduced that provides a replacement for all lost income. If this individual becomes unemployed, he or she would shift from point A to point B (as illustrated in the diagram below).
Since point B lies above the original indifference curve, however, this individual would receive a higher level of utility if he or she were unemployed. This occurs because leisure time is valued by the worker. For this reason, unemployment compensation systems do not generally provide complete replacement of lost income.
To maintain the worker at the original level of utility, an appropriate level of compensation would be equal to Y' in the diagram below. The problem, of course, is that Y' cannot be determined by the government. In the U.S., unemployment benefits are typically equal to approximately 1/2 of an individual's lost income.

A similar argument can be applied to disability insurance programs. If disable workers receive the same level of income after an injury as before and receive more leisure time, their level of utility would increase (assuming that "pain and suffering" and medical expenses are fully compensated). Disability insurance programs require medical examinations by approved physicians to reduce the possibility that workers will file fraudulent disability claims.
A work-related injury that results in a partial disability reduces the wage that the affected worker will receive. This reduction in the wage generates both substitution and income effects on the quantity of labor supplied. If the goal is to adequately compensate the worker, however, an appropriate income replacement scheme would be to provide a payment that is just large enough to offset the income effect resulting from the reduction in the wage (since it is only the income effect that involves a loss is utility).
Let's examine the effect of the U.S. welfare system on labor supply.
The first major national attempt at providing aid to low-income households in the U.S. occurred during the Great Depression. Most of the relief programs developed during this period, however, were temporary programs designed to deal with the problems resulting from the Depression.
The modern U.S. welfare system was introduced in the early 1960s as part of the War on Poverty during the Johnson administration. Under this welfare system, a poverty level was established based upon studies that attempted to determine the amount of income needed to provide households with an adequate level of nutrition and basic necessities. Under this system, it is assumed that a household of a given size in a particular geographical area must receive an appropriate level of income (Yt) to ensure that these basic needs could be satisfied. (This level of income is higher for larger households and for residents in geographical regions where the cost of living is higher.)
Under this welfare system, the government provides welfare benefits to those households in which the level of income falls below the target level (Yt). These welfare benefits may take the form of monetary payments or subsidies for food, housing, medical care, or other basic

commodities. The goal is to provide a level of welfare benefits that brings the level of household income up to the target level.
The diagram below illustrates the budget constraint that results from the introduction of such a welfare system. If the individual does not work at all, the level of welfare benefits equals Yt. If the individual is working, but receives a level of income that falls below Yt, the government provides enough welfare benefits to provide a total income of Yt.
Thus, as illustrated above, the budget constraint becomes horizontal at an income level of Yt. In this portion of the budget constraint, the marginal wage (the additional income resulting from an additional hour of work) equals zero. If a welfare recipient works an additional hour and receives a wage of $6, welfare benefits are reduced by $6, leaving total income unchanged.
In the situation illustrated below, it can be seen that an individual who, in the absence of a welfare system, has a level of income that lies below the target level of income would always prefer to leave the labor force when such a welfare system is available (since the level of income and leisure both increase in this case).

Some individuals who, in the absence of this welfare system, would have received a level of income that exceeds Yt, would also choose to leave the labor force (as illustrated below).
Note that the substitution effect that results from lowering the marginal wage to zero reduces the quantity of labor supplied, as does the income effect resulting from the provision of welfare benefits.
Because of the labor supply disincentives effects resulting from this type of welfare system, this system was replaced in 1967 with a welfare system that allowed individuals to keep a small amount of monthly earned income ($30) without giving up any welfare benefits. Beyond this point, welfare benefits were reduced by $2 for every $3 earned (as compared to a $1 reduction for every $1 earned under the earlier system). This system reduced the labor supply disincentive effects resulting from the earlier system.
This revised system remained in effect until the early 1980s. During the Reagan administration, the welfare system was restored to a form that was essentially equivalent to that of the early
1960s. The reason for this change was a desire to reduce welfare benefits for higher income welfare recipients while preserving benefits for the "truly needy."
With the restoration of a system that provides a marginal wage of zero, the number of "working poor" declined and a larger share of welfare recipients left the labor force.
To deal with the labor supply disincentives that were reintroduced during the Reagan administration, a "workfare" system has been adopted. Under this system, welfare recipients are required to work a minimum number of hours to qualify for welfare benefits. Welfare benefits are zero unless welfare recipients work the minimum number of hours (or are engaged in approved job training or educational programs). Individuals are also restricted to receiving welfare benefits for a maximum of five years under this system.
The budget constraint below illustrates the effect of a workfare requirement. Individuals receive no benefits if they work fewer than the minimum number of hours (Hm) in this example). If they work Hm or more hours, they receive the same level of benefits as under the earlier system.

Under such a system, it would be expected that welfare recipients would choose to work Hm hours. If they work more than this, the marginal wage falls to zero (until they work enough hours so that all benefits are eliminated). This outcome us illustrated in the diagram below.
The earned-income tax credit is an alternative method of providing increased income to lowincome households. Under an earned-income tax credit, a tax credit is provided that rises with income up to a point and then gradually declines as income rises beyond this point. The earnedincome tax credit generates a smaller labor supply disincentive effect than the current welfare system. The diagram below illustrates how an earned-income tax credit alters the shape of an individual's budget constraint.

The household production model is based on the assumption that utility is derived from the consumption of N final commodities (Z i
, i = 1,N). Each of these commodities is produced and consumed within the household by combining time and purchased inputs. As an example of this, note that an individual derives utility from the act of watching a movie, not from purchasing a ticket to the movie. The final commodity that we think of as "watching a movie" requires the use of both time and purchased inputs (tickets, transportation expenses, etc.).
In the very beginning of this course, it was noted that the cost of acquiring a college degree requires not only the payment of tuition, but also the use of time that could have been spent on alternative activities. This is another example of the household production model.
The full cost of any activity involves the cost of both time and purchased inputs. The full cost of watching a movie includes the opportunity cost of time as well as the opportunity cost of tickets.
The full cost of acquiring a college degree includes the opportunity cost of time as well as the direct costs of tuition, books, supplies, etc.
College enrollments often increase during recessions because the full cost of a college degree is lower during a recession, since the expected opportunity cost of time (forgone earnings) is typically lower during a recession.
Consider the following assumptions and definitions:
U = U(Z
1
, Z
2
, Z
3
, ..., Z
N
), where: U = level of utility, and
Z i
is the level of production and consumption of activity i .

It is assumed that Z i
is produced according to the production function given by:
The time constraint in this model is given by:
This time constraint simply states that the sum of the time spent in all household production activities and time spent at work must add up to the total time available.
The goods constraint is given by:
This goods constraint states that the sum of the nominal expenditures on purchased inputs must equal nominal income. (As before, we're working with a single period model for simplicity so there are no borrowing or lending possibilities.)
Solving the time constraint for time at work, results in:
Substituting this result into the goods constraint results in:

With a little bit of algebraic manipulation, this can be expressed as a full-income constraint:
As in the basic neoclassical model of labor supply, full income is defined as the individual's maximum earnings potential (= wT). The first term in the summation on the right-hand side of the equation is the explicit cost of goods and services used to produce the Zi. The second term is the opportunity cost of the time used in household production.
An alternative way of expressing this full-income constraint is: where FC i
is defined as the full cost of commodity i :
Individuals are assumed to select a mix of time and purchased inputs that minimizes the full cost of producing and consuming a given level of Z i
. Before examining the details associated with this model, consider how it might explain such phenomena as:
 the growth of the fast-food industry,

 why convenience stores can survive while charging higher prices than grocery stores,
 the decline in fertility, and why many people do not use coupons in grocery stores.
The diagram below contains an isoquant that illustrates the alternative combinations of time and purchased inputs that result in the production of a given number of meals of a given quality
(assuming efficient production).

In this model, an isoquant curve is also an indifference curve since the production and consumption of a given level of Z i
results in a constant level of utility.
Consider point A in the diagram below. At this point, an individual prepares meals using basic ingredients such as flour, vegetables, meat, etc. In this case, the individual is using a relatively large amount of time, but a relatively low level of purchased inputs.
At point B (illustrated below), the individual prepares meals of the same quality using prepackaged mixes, frozen meals, and other preprocessed ingredients. This requires a larger expenditure on purchased inputs but less time than the method of production used at point A.

This individual uses less of his or her own time and more purchased ingredients when producing and consuming at point C (illustrated below). This may involve the consumption of meals in restaurants or of meals delivered to the home from restaurants.
Points that lie above an isoquant correspond to the production of a higher level of Zi. Point D in the diagram below illustrates such a possibility.

Isocost curves have a slope equal to -w/p (the negative of the real wage). The level of total costs increases as more time and purchased inputs are used. The diagram below illustrates a set of possible isocost curves.
The least costly combination of time and purchased inputs occurs at the point of tangency between the isoquant curve and an isocost curve. This occurs at point E in the diagram below.

An increase in the wage results in two types of substitution effects. The diagram below illustrates one of the substitution effects resulting from a higher wage. As the wage rate increases, the relative price of time rises and households substitute purchased inputs for time in the production and consumption of a given level of each commodity. This is represented by the shift from point
A to point B in the diagram below. As the diagram below indicates, this substitution effect reduces time spent in household production (resulting in more time spent at work) when the wage rate rises.
Let's consider the second type of substitution effect.
Some activities are inherently more time-intensive than other activities. When the wage rate rises, the relative price of time-intensive activities increases. In response, goods-intensive activities will be substituted for time-intensive activities. This substitution effect will also result in the use of more purchased inputs and less time spent in household production.

Under both of the substitution effects described above, a higher wage reduces the quantity of time used in household production and increases the amount of time spent in paid market labor.
An increase in the wage, though, also increases the quantity of final commodities (Z i
) consumed.
This income effect tends to increase the amount of time required for the production and consumption of these commodities (as illustrated in the diagram below).
Thus, the labor supply curve is upward sloping if the substitution effects resulting from a wage increase are larger in magnitude than the income effect. An individual operates on a backwardbending portion of his or her labor supply curve if the income effect is larger than the substitution effects.
If a household wishes to produce output efficiently, each individual should specialize in those tasks in which he or she possesses a comparative advantage. (As you learned in your micro principles course, a household member possesses a comparative advantage in an activity if the opportunity cost of the activity is lower for this individual than it is for any other member of the household. If you wish to review the concept of comparative advantage, you may wish to review some notes I use for my microeconomics class on this topic.)
A comparative advantage may exist because an individual is more productive in an activity than other members of the household (in this case an "absolute advantage" is said to occur), or because the individual's time is relatively less valuable in alternative activities.
Historically, married women have tended to specialize in household production and married males have tended to specialize in market production. It can be argued that, in past decades, married women tended to have a comparative advantage in household production due to:


 high completed fertility rates, high infant mortality rates (resulting in the need for higher fertility levels to achieve a given level of desired completed fertility), and labor market discrimination.

As infant mortality and completed fertility rates decline and as female wage rates rise, it is expected that this division of labor between spouses will be altered. In recent years, married women have substantially increased the amount of time spent in the paid labor market and have spent slightly less time in household production). Married men now spend slightly more time in household production than in the past.
Both spouses will tend to work together in household production tasks in which their time is complementary and will tend to specialize when one spouse's time is a substitute for the time of the other spouse.
Earlier, it was noted that the labor force participation rate declines during recessions as a result of an increase in the number of discouraged workers. In a household, however, one spouse may increase his or her labor supply (or enter the labor force) if the other spouse becomes unemployed. This "additional worker effect" partly offsets the "discouraged worker effect" discussed earlier. Empirical evidence, however, suggests that the additional worker effect is smaller in magnitude than the discouraged worker effect.
One reason for the small magnitude of the "additional worker effect" is that the expected wage received in the labor market declines during a recession. The expected wage is equal to:
As the unemployment rate rises during a recession, the probability of being unemployed declines, leading to a reduction in the expected wage. For those who are not currently working, this reduces the incentive to enter the labor market.
Married women tend to increase their labor supply when a divorce becomes more likely. This is partly to prepare for the reduction in the division of labor that occurs after a divorce. Empirical evidence suggests that the level of per capita consumption declines by a larger amount in the splitoff household headed by divorced women. This is one reason for the relatively high labor force participation rate of divorced females.
The productivity of time spent in the paid labor market varies over the course of an individual's lifetime. The diagram below illustrates how the market real wage received by an individual is likely to change over time in response to these productivity changes. As this diagram suggests, wages increase relatively rapidly in the early stages of the work life as individuals acquire human capital through both formal training and informal on-the-job training. Beyond some point, though, worker productivity may decline in response to aging and the obsolescence of job skills
(and the reduced incentive to invest in new skills later in the worklife).

In response to this lifecycle pattern of wages, individuals are expected to spend more time working in the paid labor market (and less time in household production) during those periods of time when market wage rates are relatively high. This pattern is illustrated in the diagram below.
Many married females chose to reduce the quantity of labor supplied or leave the labor force during childbearing years. The diagram below illustrates why such a departure from the labor force may occur.

As fertility levels have declined and market wage rates have increased, however, a smaller proportion of married working mothers exit the labor force during childbearing years today, as compared to previous decades. This change in illustrated in the diagram below.
The diagram below illustrates the effect of a increase in the level of social security benefits on the choice of retirement age. Note that an increase in the level of retirement benefits induces individuals to retire earlier.

A large share of welfare payments are received by households headed by single mothers. As noted in our earlier discussion of the welfare system, the current welfare system provides incentives for many such household heads to remain out of the labor force (as illustrated in the diagram below).
Many states have introduced "child support enforcement programs" that help to ensure that absent parents contribute to the support of their children. This causes the budget constraint facing the custodial parent to shift vertically upward. In some cases, this program will have no effect on labor supply, but will reduce welfare expenditures (since the absent parent will provide a larger share of household income). This possibility is illustrated in the diagram below.

This program will also encourage some single parents to leave welfare and enter the labor force
(as indicated in the diagram below).
In households in which the custodial parent is initially working, however, this program is expected to reduce the labor supply of the custodial parent (due to a pure income effect).

The theory of compensating wage differentials provides one explanation of wage differences across individuals and across occupations. This theory suggests that wage differentials exist, in part, to compensate workers for nonpecuniary characteristics of alternative types of employment.
The theory of compensating wage differentials was first expressed in detail in 1776 by Adam
Smith in the Wealth of Nations , (Book I: Chapter X).
Let's consider an example to illustrate this concept. Suppose that two occupations (X and Y) are initially perceived as being equivalent in all attributes ( e.g.
, educational requirements, job stress, working conditions, and other characteristics). In this case, it would be expected that labor supply adjustments would equate wages between these two occupations (as illustrated below).

Suppose, though, that it is discovered that workers in occupation Y face a greater risk of suffering a fatal on-the-job injury than workers in occupation X (a perfectly safe occupation).
This will induce some workers to migrate from occupation Y to occupation X. Migration continues until the wage difference between the two jobs is large enough to induce workers to stay in their current occupations. The diagram below illustrates this possibility.
The wage differential w"-w' is the amount that a worker must be compensated to accept the additional risk associated with employment in the risky occupation. This compensating wage differential can be thought of as the risk premium associated with employment in occupation Y.
The left-side diagram below illustrates the magnitude of this compensating wage differential.

Ceteris paribus , it would be expected that a similar compensating wage differential would exist for differences in working conditions, job stress, educational requirements, and other characteristics of jobs that make them either more or less desirable. It is expected that more pleasant jobs will offer lower wages than less pleasant jobs, holding all other job characteristics constant.
Compensating wage differentials will reflect the market value of non-wage job characteristics if:
1.
workers attempt to select an occupation that maximizes their utility levels, not their income,
2.
workers have perfect information about all job characteristics, and
3.
sufficient labor mobility exists.
We will use a hedonic pricing model to explain the existence and magnitude of compensating wage differentials. Under a hedonic pricing model, a commodity is sold that possesses a set of characteristics that vary across the products that are offered in a particular market. The bundle of characteristics that describe a particular commodity is observed by both buyers and sellers of the commodity, as is the price of each particular object. The market price of each individual characteristic, however, is not directly observed, but may be imputed using econometric techniques.
In the labor market, each job can be described as consisting of a set of characteristics ( e.g.
, the level of education required, the amount of risk associated with the job, the level of job stress, and so on) and an associated wage offer. As noted earlier, it is assumed that wage differentials across jobs (under the conditions listed above) compensate for differences in non-wage job characteristics.
Let's examine how firms and workers may jointly establish a market value for differences in the risk of injury faced on alternative jobs.

The diagram below contains a representative indifference curve relating alternative levels of the wage and the risk of a work-related injury for individual A. The convex shape of this indifference curve indicates that this individual must receive progressively larger wage increases to compensate for additional risk as the level of risk rises. Point that lie on an indifference curve
(such as points A, B, C, and D) provide the same level of utility. Points that lie above and to the left of the indifference curve (such as point E) are preferred to points on the indifference curve.
(The reason for this is that utility rises when the wage rises and/or the level of risk declines.)
An indifference curve passes through each possible combination of wage rate and level of risk.
In the diagram below, the highest level of utility for person A occurs on the indifference curve labeled U2.

Individuals with steeper indifference curves are more "risk averse" than individuals with flatter indifference curves. In the example below, person A is more risk averse than person B since person A requires a larger wage increase to compensate for an increase in risk (as can be seen when the level of risk rises from ro to r').

To understand the tradeoff between wages and risk that faces firms, it is useful to introduce the concept of an isoprofit curve. In the model that we are examining, an isoprofit curve is a graph of all combinations of wage rates and levels of risk that result in a given level of economic profits.
An isoprofit curve slopes upward because a reduction in risk (a leftward movement along the curve) raises a firm's cost; wages must be reduced to offset the cost of risk reduction if profits are to be held constant. The diagram below contains a zero-profit isoquant for firm X.

The concave shape of the isoprofit curve indicates that the marginal cost of reducing risk rises as the level of risk is reduced.
The diagram below contains a set of three isoprofit curves for Firm X. Notice that an isoprofit curve that lies above the zero-profit isoprofit curve corresponds to a negative level of profits
(since wages are higher at each level of risk). Similarly, an isoprofit curve that lies below the zero-profit isoprofit curve corresponds to a positive level of profits.

Economic profit, however, will equal zero in a long-run equilibrium in any market in which there are no substantial barriers to entry (perfectly competitive, monopolistically competitive, and perfectly contestable oligopoly markets). Thus, the long-run equilibrium tradeoff between wage rates and job risk must occur along the zero-profit isoprofit curve.
Firms that face a higher marginal cost of reducing risk (at any given level of risk) will have a steeper isoprofit curve. In the example below, the marginal cost of reducing risk is higher for
Firm Y than for Firm X.

At any given level of risk, workers will always select the job that offers the highest wage rate, assuming that other job characteristics are held constant. In the simplified diagram below, a worker can choose to work at either Firm X or Firm Y. A worker who selects a level of risk of ro or r1 will choose to work at Firm X (since Firm X provides a higher wage at these levels of risk.
A worker who is willing to accept higher levels of risk (such as r2 or r3), however, will choose to work at Firm Y.

In a more realistic environment in which there are a large number of firms, a wage-risk offer curve exists that serves as an envelope curve to the zero-profit isoprofit curves for all of the firms in a particular labor market. This curve traces out the highest wage offer that workers can receive at each possible level of job risk.

Under the assumptions of this model, workers will select the combination of wage rates and job risk that maximizes their utility levels, given the constraint that all available job offers lie on the wage-risk offer curve. As the diagram below indicates, the optimal choice lies on a point of tangency between an indifference curve and the wage-risk offer curve.

As the diagram below indicates, individuals who are less risk averse will select more risky jobs that offer higher wages.

Notice also that, in this optimal sorting, the level of risk is the lowest in those firms in which the marginal cost of risk reduction is relatively low.

OSHA requirements are designed to reduce the level of risk that workers face in the workplace.
For our purposes, it will be helpful to assume that OSHA requirements establish a maximum level of risk that is allowed at any job. Let's examine the impact of such requirements using the hedonic pricing model.
In the diagram below, rmax is the maximum level of risk allowed by OSHA. As this diagram illustrates, individuals who are initially working at jobs that have a level of risk below rmax are not affected by OSHA requirements.

In the absence of OSHA requirements, person B would find it optimal to receive a wage of wB and to accept a level of risk equal to rB. Since this level of risk exceeds the maximum allowable level, OSHA requirements will result in a reduction in the level of risk (to rmax) and a reduction in the wage (to wmax).

This is the primary argument against OSHA requirements. If the assumptions of the hedonic pricing model are satisfied, OSHA requirements:

 have no affect on the wellbeing of workers who are already working in safe jobs, and lower the level of utility received by workers who prefer high-risk/high wage jobs.
Supporters of OSHA, however, argue that OSHA requirements may be justified on either of the following grounds:
 workers systematically underestimate the amount of risk that they face in the workplace, and/or
 there are externalities that are not taken into account when workers compare alternative combinations of risk and wage rates.
Let's examine each of these arguments.
If workers systematically underestimate the amount of risk that they are facing on the job, the perceived wage offer curve lies to the left of the actual relationship between wages and job risk.
This is illustrated in the diagram below. (Notice that the perceived level of risk is less than the actual level of risk at any given wage rate.)

Workers maximizing utility subject to this perceived wage offer curve will select a point of tangency between an indifference curve and the perceived wage offer curve. This blissfully ignorant person believes that he or she is at point P (as illustrated below).

While this person mistakenly believes that he or she is at point P, the actual combination of wages and risk occurs at point A. If this person were to be informed of the risk that is actually faced, he or she will receive the lower level of utility associated with point A (as illustrated above). When this person becomes aware of the actual risk associated with this job, he or she would move to the combination of wages and risk that provides the highest level of utility given the actual wage-risk offer curve. In the diagram below, this occurs at point B.

While one solution to the problem of imperfect information is to provide workers with additional information about the actual risks faced in alternative occupations, this is a costly process. Some supporters of OSHA argue that it is more cost-effective to mandate a reduction of risk to a level that is consistent with the maximum risk a worker would accept under conditions of perfect information.

Other supporters of OSHA note that work-related injuries and deaths generate negative externalities to family members who would be harmed if a worker were killed or seriously injured on the job. Workers making decisions based only on their own costs and benefits would not take these external costs into account and would accept a level of risk that exceeds the socially optimal level.
The existence of worker compensation programs also result in a similar problem since workers who are insured against the financial effects of a disabling injury would accept a level of risk that exceeds the socially optimal level. The problem in this case is akin to the externality problem above in that the cost of the injury to the worker is less than the social cost of the injury.
The positive relationship between the level of education and the level of earnings is one of the most robust relationships observed by labor economists. Typically, this relationship is explained using the human capital model. Human capital, in this model, can be thought of as a measure of an individual's productive capacity. Under the human capital model, it is assumed that the level of an individual's earnings is determined by the individual's stock of human capital. An individual can increase his or her human capital by investments in:

 education, training, or

 health care.
For now, we'll focus on the first of these types of investment. Most economic models of educational attainment are based on the assumption that individuals select the level of educational attainment that results in the highest expected present value of lifetime earnings (net of educational costs). Simply stated, this means that a person will attend college only if the present value of the expected benefits exceeds the present value of the expected costs associated with this choice.
There are three types of costs associated with a college education:


 direct costs such as tuition, books, and supplies, forgone earnings (the opportunity cost of time), and psychic costs.
Notice that the direct costs include only those direct expenditures that a student would make only if he or she attends college. The costs of meals, dorm fees, etc., would not generally be a cost of education since these individuals would face costs of meals and lodging if they had been engaged in some alternative use of time (such as working). Room and board fees would partially enter as a cost only if these costs are higher than they would have been under the next-best alternative use of time.
As noted earlier, the forgone earnings associated with being a full-time student is usually the largest cost associated with acquiring a college or advanced degree.
The psychic costs associated with attending college include the stress, anxiety, and sometimes boredom associated with classes, exams, assignments, papers, etc.
The benefits associated with acquiring a college degree include:
 higher expected earnings,
 more pleasant jobs,
 lower expected unemployment rates, and
 psychic benefits.
In general, college graduates receive not only higher pay, they also receive jobs that are more secure and involve less tedious work, less physical work, more pleasant work environments, better working conditions, higher social status, and so forth. The psychic benefits associated with education include the enjoyment that may be received by being in the college environment.
An individual will acquire additional education as long as the present value of the marginal benefits from this additional education outweighs the present value of the marginal costs. Those individuals who have higher benefits and/or lower costs will acquire more education. The diagram below illustrates the effect of changes in MC and MB on the optimal level of human capital investment.

The costs and benefits associated with deciding to acquire a bachelors degree are represented in the diagram below. This diagram illustrates two possible earnings streams facing an 18-year old high school graduate. The costs associated with college attendance includes both forgone earnings (the upper portion of the area shaded in red in the diagram) and the direct costs of college (the lower rectangle that is shaded in red in the diagram below. Note that this diagram suggests that a 22-year old college graduate earns less than they would have at this age if they had gone to work directly after high school. On average, it takes approximately 6-7 years for the earnings of a college graduate to catch up to the earnings of a high school graduate with identical observable characteristics. The area shaded in light blue represents the increase in earnings that a college graduate would be expected to receive over the rest of his or her worklife. (These earnings streams, of course would differ across individuals due to differences in individual ability and costs.)
It is expected that an individual would attend college if the present value of the costs (the red area above) is less than the present value of the benefits (the light blue area above).

The human capital model suggests that the level of human capital investment is affected by:
 interest rates,

 the age of the individual,
 the costs of education, and the wage differential between high school and college graduates.
Since most of the benefits associated with a college degree occur relatively later in the lifecycle while the costs are borne more immediately, an increase in the interest rate facing an individual will be expected to lower the net benefit of education. (This occurs because an increase in the interest rate lowers the present value of more distant benefits and costs by more than it lowers the benefits of short-term benefits and costs.) Government subsidized student loan programs are designed to reduce interest rate differentials across households. (In the absence of these subsidized interest rates, low-income households would face substantially higher interest rates, resulting in a lower probability that children from such households will attend college.)
It is expected that individuals will tend to invest more in education at an earlier stage of their lifecycle because this results in a larger period over which the increased earnings may be realized. (Exceptions to this often occur when individuals change careers.)
The theory discussed above, of course, directly predicts that more people will attend college when the costs are lower and/or the benefits are higher.
As your text notes, age-earnings profiles, for a given level of educational attainment, are generally concave. This means that earnings increase at a progressively slower rate as the individual ages (holding constant the level of educational attainment). The simplest explanation for this is that individuals invest in a larger quantity of on-the-job training at earlier stages of their worklife. Evidence also suggests that those who invest in more education also invest in a larger amount of on-the-job training (for similar reasons). This results in a widening in the gap in earnings across educational levels as individuals age.
One of the reasons for the historically lower level of educational attainment for females is that females tended to have significantly shorter expected worklives than males. In recent years, however, increases in female labor force participation have narrowed the gap in expected worklife between males and females. This increase in expected worklife is one of the reasons for the rather dramatic increase in female college enrollment rates in recent decades.
Estimates of the rate of return to education are determined by comparing the expected lifetime earnings streams that an individual could receive under alternative levels of educational attainment. Roughly speaking, estimates of this rate of return to a bachelors degree are derived by comparing the earnings streams of college graduates with the earnings streams of high school graduates who have equivalent observable characteristics. Estimates derived in this manner suggest a rate of return to investment in education in the range of 5-12%. Numerous studies suggest that this rate of return has increased in recent years.
There are, however, a few potential sources of bias in these estimates.

If college graduates differ from high school graduates in terms of unobservable differences in ability or motivation, those who attend college might have received higher earnings even if they had not attended college. The same argument suggests that high school graduates would not earn as much as college graduates do if they had instead chosen to attend college. In this case, the return to education would overstate the increase in earnings that would be received by individuals. This type of bias, called "ability bias," suggests that the observed difference in earnings between high school and college graduates overstates the return to education that would be received by a given individual.
The return to education, however, may be understated by a comparison of the earnings of high school and college graduates as a result of the non-pecuniary returns received from education.
Some of the benefits from education involve increased productivity in non-market activities.
College graduates also receive more pleasant jobs. These nonpecuniary benefits from education result in a smaller wage difference between high school and college graduates than would have been received if their jobs were equivalent in all dimensions except for the wage. (To see this, recall the theory of compensating wage differentials discussed in Chapter 8).
Still another possibility involves the existence of selectivity bias. Willis and Rosen (1979) found that those who attend college perform relatively well in the types of jobs that college graduates receive while those who do not attend college perform relatively well in the types of jobs that high school graduates receive. This suggests, for example, that a good lawyer may be a poor carpenter while a good carpenter may be a poor lawyer. In this case, the return to college is relatively large for those who attend college for two reasons: they do well in the types of jobs that college graduates receive while they would have received relatively low wages if they had not gone to college. Their results also suggest that the return to education is relatively low for those who choose to not attend college. Similar results in a later study were found by Kane
(1986).
While there is substantial evidence that higher education provides a good investment for individuals, it is less clear that the level of educational spending is socially optimal. Education in the most countries is heavily subsidized by the government (at least through the secondary level).
In the U.S., public education is free through high school and higher education is subsidized in both public and private institutions. Subsidies of this sort will result in an optimal level of investment only if the marginal subsidy equals the value of the marginal external benefits associated with education. Evidence on this is somewhat mixed. There is, however, substantial evidence that economies that invest more in education tend to experience higher rates of economic growth.
The signaling model, however, raises substantial questions about social returns to education.
Under the signaling model, education does not raise any worker's productivity. Instead, it allows firms to sort workers according to their productivity. The signaling model suggests that firms cannot directly measure the productivity of individual workers (at least not when they are initially hired). Over time, though, firms observe that college graduates are more productive than high school graduates. This results in higher pay for college graduates and lower pay for high school graduates (as compared to a situation in which this educational "signal" did not exist).
Under this model, the benefits to a college degree are the same for all workers (since all workers with a college degree receive the higher pay). Low ability individuals, however, are assumed to face higher costs of education (it requires more time and effort for a low ability worker to make it through a bachelors degree). Thus, only high ability find it profitable to attend college in an equilibrium in this model.

Since education does not raise any individual's productivity under the pure signaling model, society as a whole does not benefit from higher education under this model. If this model is correct, total output would increase if institutions of higher education were shut down.
It should be noted that, among economists, the human capital model is much more widely accepted than the signaling model.
The cobweb model is used to explain the behavior of price and quantity over time when a lagged supply response occurs. This model is appropriate in labor markets in which the minimum educational qualifications for a job include several years of college or technical training. The diagram below represents such a market. The supply curve in this market represents the quantity of labor that will be supplied at each wage after workers have enough time to complete the educational requirements. Initially, this market is assumed to be in a state of long-run equilibrium at a wage of w and a level of employment equal to L.
Suppose the demand for labor increases to D'. In the short run, the quantity of labor available in this market is fixed at L (since it takes time for new workers to receive the training necessary to enter this labor market). Thus, the short-run effect of an increase in labor demand is an increase in the wage rate to w' (with no change in the quantity of labor employed). This short-run change in the wage (at the initial level of employment) is represented by the arrow in the diagram below.

In response to this higher wage, however, a relatively large number of workers will chose to acquire training in this field. As the diagram below indicates, the quantity of labor supplied will ultimately increase to L' at a wage of w'.
Once all of these newly trained workers enter this market, however, the short-run labor supply curve will be fixed at a quantity of L'. Given this new short-run labor supply curve, the equilibrium wage will fall to w''.

At this new lower wage of w'', however, students entering college will choose to major in other fields and the number of workers in this market will ultimately fall to L''.
Now that the short-run supply curve has fallen to L'', however, the wage rate will increase to w'''
(as illustrated below).

This process continues until a new long-run equilibrium is reached at w* and L* (assuming, of course, that there are no further shifts in either labor demand or supply....).
(The diagram above should suggest why this model is referred to as a "cobweb model.")
Worker mobility involves a movement from one job to another. This may involve geographic changes (within or across national borders) as well as movement from one employer to another.

It is assumed that workers will leave one job to accept another only if the expected present value of the net benefits associated with this choice is positive. Since the costs are generally borne at the time of the move, the level of net benefits associated with a move is given by:
Note that the benefits and costs associated with a move include psychic benefits and costs as well as direct costs and benefits. Friendship with co-workers, family ties, working environment, nonpecuniary benefits associated with the job, and the characteristics of the old and new geographical locations (for geographical moves) must be taken into account as well as pay differences and the direct costs of moving.
Individuals will be more likely to move when:

 the difference in wages or salaries is large,
 the worker is unhappy in his current job or location, the direct costs associated with moving are low, and
 when there is a longer time period (T) over which benefits can be realized.
As your text notes, there is a relatively high level of geographic mobility within the United
States. In recent years, a relatively large share has been from the northeast and midwest to the south. Empirical studies have found that geographical movement is more strongly affected by the
"pull" of strong labor market conditions at the destination than by the "push" of poor labor market conditions at the original site.
Young workers are significantly more likely to move than older workers. As your text notes, approximately 12% of workers between the ages of 20-24 move across county or state boundaries in a given year. Only 4% of 47 year old workers do so. One reason for this is that young workers have a higher expected return to moving because they have a longer expected worklife over which benefits can be realized. A second reason is that ties to the community increase as individuals become older and begin to raise families. Married individuals, especially when children are present, are less likely to move across county or state boundaries than are single individuals.
Individuals with higher levels of educational attainment are also more likely to move (holding age constant). Individuals with low levels of education generally work in local labor markets and are less likely to engage in national search. National labor markets involve workers with higher levels of education. Since individuals in national labor markets will generally search over large geographical regions, it is not surprising that individuals with more education are more likely to move.

Distance is also another factor in mobility decisions. Individuals and households are much more likely to move within a county than across counties. There is also much more mobility within states than across states. One reason for this is that individuals have lower costs of acquiring information of labor market opportunities locally than over large distances. Moves over shorter distances also reduces the cost of leaving friends and family members behind. More highly educated individuals are more likely to migrate over larger distances.
A frequently observed phenomena is the existence of chain migration , migration to areas where friends or relatives have located. This reduces the psychic and information costs associated with migration.
One of the major factors that determines the mix of skills of immigrants is the degree of inequality in the distributions of income and earnings. If the income distribution in a foreign country is more compressed (more equal) than in the U.S., the rate of return to human capital in the foreign country is less than in the U.S. This will encourage more highly educated individuals in such an economy to emigrate to the U.S.
Countries that have a greater variation in earnings generally provide a higher return to human capital investment. Immigrants to the U.S. from such countries will, on average, tend to be less skilled.
In recent decades, immigrants to the U.S. have possessed lower levels of education and training than immigrants in earlier time periods. A major reason for this is that recent waves of immigration have been from countries, such as Mexico, that have a greater level of income inequality.
Most evidence suggests that international migration provides substantial returns to those families that migrate as compared to the increase in earnings of domestic families with similar characteristics. Wives in such families, however, generally experience a reduction in earnings. It is likely that this occurred because the choice of location has often been based on alternative earnings prospects for husbands (the dominant earner in most immigrant households). As women's wages rise internationally, it would be expected that this adverse effect on wive's income would be weakened over time.
New immigrants generally earn substantially less than domestic workers, but experience a more rapid growth in earnings. The lower initial wage is frequently the result of language issues. The more rapid rate of growth in earnings is likely to be the result of improvement in language skills and other forms of human capital investment.
Recent waves of immigrants have experienced lower rates of growth in earnings over time. This is presumably due to changes in the skill mix of immigrants.
A substantial amount of both internal and international migration involves a return to a previous area of residence. This is partly the result of planned returns after spending time living in a highwage area. It is also sometimes the result of unrealized expectations, cases in which migrants received lower than anticipated returns to migration.

Until 1921, the U.S. had relatively limited restrictions on immigrations. The Quota Law of 1921, however, established limitations on the number of individuals who could immigrate from each country. Initially, this law restricted immigration from eastern and southern Europe. Further restrictions on immigrants from southeastern Europe were imposed in 1924 and 1929.
The Immigration and Naturalization Act of 1965 replaced this quota system with a total cap on the number of immigrants from all countries. Most of the spots were reserved for individuals who immigrated for the purpose of family reunification. There are no restrictions on the number of political refugees (they must, though, meet specific criteria to fall into this category).
Illegal immigration occurs in response to the restrictions on immigration. There are two categories of illegal immigrants: those who enter on student or tourists and overstay the time specified on their visa and those who enter the country illegally. The large number of illegal immigrants resulted in the passage of the Immigration Reform and Control Act of 1986. This act provided amnesty for illegal immigrants who had been in the U.S. for at least 5 years or who had worked in agriculture for over 90 days per year; it also imposed substantial penalties on employers of illegal immigrants. Supporters of this act believed that illegal immigrants were taking jobs away from domestic workers. As we'll see below, the evidence for this is, at best, mixed.
Those who favor restrictive immigration laws believe that each immigrant worker takes one job away from a domestic worker. At the other extreme, some argue that immigrants take jobs that domestic workers would not be willing to do. As your text notes, both of these arguments are incorrect.
Immigrant workers increase the supply of labor in all of the labor markets in which they participate. This supply shift lowers wages and reduces the number of domestic workers employed in these markets. This labor supply shift is the basis for immigration restrictions. As shown in your text, the actual reduction in domestic employment is less than the number of new workers added to the market, but there would still be lower wages and reduced employment in these labor markets, if this is the only effect that occurs.
Immigrants, though, not only supply labor; they also buy groceries, clothing, TVs, stereos, take vacations, receive hair cuts, etc. An increase in immigration raises the demand for final goods and services, thereby increasing the demand for the labor that produces these goods and services.
In some markets, demand will increase by more than supply and wages will rise, benefiting domestic workers. Wages will fall, harming domestic workers, in those labor markets in which immigration increases labor supply by more than labor demand. Thus, some domestic workers gain, while some lose as a result of immigration. Most studies suggest that immigration has, at most, a very small effect on domestic wage rates.
To the extent to which immigrants provide low-cost labor, consumers benefit from lower product prices.
The overall effect of immigration on the U.S. economy appears to be positive for two reasons:
 immigrants pay more in taxes than they consume in government services, and

 immigrants bring their human capital investments with them when they immigrate, providing the U.S. with the benefits of their enhanced productivity without having to cover the cost of providing the human capital.
Ironically, illegal immigrants are more likely to provide a net gain for the domestic economy.
They cannot generally evade payroll taxes, yet are very unlikely to apply for government assistance (to avoid the risk of detection).
Labor mobility also involves changes in jobs without a change in place of residence. Employee turnover is the result of job quits and layoffs. Workers are expected to engage in a voluntary job quit only if the expected benefits of changing jobs outweigh the expected costs. To the extent that voluntary job quits are the result of imperfect initial matches between workers and firms, economic efficiency is improved by the movement of workers to firms in which their skills, talents, and abilities are more productively employed. Economic efficiency also improves when workers are fired from jobs for which they are not well suited. These workers have an incentive to seek jobs that more appropriately match their mix of skills and abilities.
Workers who receive a lower wage than they could receive elsewhere are more likely to quit a given job. Firms that pay lower than average wages, ceteris paribus , have higher quit rates.
Large firms tend to have lower quit rates. This could be the result of the higher wages that are usually paid by large firms. It may also be the result of the use of internal labor markets in these firms that provide more opportunities for promotion and advancement within the firm.
Women have historically had higher quit rates. This is partly the result of departures from the labor force during childbearing years. It is also partly the result of the lower level of firmspecific human capital investments received by women. It is likely that this phenomena will decline over time in response to more continuous labor force attachment for married females.
Job quits rise during economic expansions and fall during recessions (due to changing alternative job prospects). Layoffs increase during recessions and fall during expansions.
Younger workers are more likely to quit a job than are older workers. This is partly the result of the longer period of time over which young workers receive benefits from a job change, but is also partly the result of improvements in the quality of job matches with age.
Workers are less likely to quit a job when the cost of quitting is higher. This explains why there is higher turnover in areas and time periods in which there are more extensive alternative job prospects.
If there are no costs of mobility, the law of one price would apply in labor markets. Workers would shift from job to job until the wage rate was the same everywhere for workers with a given mix of skills and abilities. Mobility costs, however, give firms some degree of monopsony power in labor markets.

This week, we'll examine the effect of gender, race, and ethnicity on labor market outcomes.
The average weekly earnings of full-time female employees is significantly less than the average weekly earnings of full-time male employees. Most of this difference, however, can be explained by gender-related differences in:
 educational attainment,
 prior work experience,
 average weekly hours of work (on average, full-time male employees work approximately 10% more hours than full-time female employees), and
 occupational choice.
Some studies have found that these factors account for all of the gender wage gap, while others suggest that up to 1/4 of the wage gap cannot be explained using these variables. Even if these factors account for all of the wage gap, it is still possible that discrimination may be the sources of the differences in education, employment, and occupational choice.
(A summary of the major issues concerning the gender wage gap can be found on the web site I constructed on this topic for South-Western College Publishing.)
Economists say that discrimination occurs if workers with identical productive characteristics experience receive different wages or employment opportunities due to demographic characteristics unrelated to productivity. If there is no discrimination, workers with the same mix of skills and abilities will receive the same pay. Discrimination occurs when factors other than worker productivity affects pay and employment decisions.
As noted above, much of the gender wage gap is due to differences in occupational choice.
Those occupations that are disproportionately filled by women offer lower wages, on average, than those occupations that are disproportionately filled by men. One issue that is not easy to resolve is whether this difference in occupational choice is due to differences in preferences and planned lifetime labor force activities or whether it is due to discriminatory employment practices in higher paid occupations.
The index of dissimilarity provides a method of measuring the degree of gender inequality in the mix of occupations. This index provides a measure of the proportion of one gender that would have to change occupations, holding employment of the other gender constant, in order to achieve gender equality in employment. This index equals 100 if there is complete gender segregation and equals zero if there is no difference in the gender mix of occupations. While the index of dissimilarity has declined in recent decades, a substantial amount of occupation segregation remains. This occupational segregation explains a substantial component of the gender wage gap.

The wage gap between black and white males is larger than the gender wage gap. Among the causes of this are difference in employment, labor force participation, and unemployment rates between black and white workers. Black males have lower employment rates, lower labor force participation rates, and higher unemployment rates than do white workers. Black women, on the other hand, have higher employment rates, higher labor force participation rates, and higher unemployment rates than white workers. Much of the decline in the labor force participation rate for black males in recent decades is due to an increasing number of discouraged workers. Only a relatively small portion of these differences can be explained by differences in education, work experience, or occupational choice. The evidence suggests that most of these differences are the result of either discrimination or unobserved differences in the quality of education. Much of the gap can be explained by differences in standardized test scores, such as the Armed Forces
Qualifying Test (AFQT). (This test is mentioned frequently in studies of this sort because it was administered to all participants in several large longitudinal data collections that are used to analyze these issues.) This is suggestive of differences in the quality of education.
There is less occupational segregation between white and black workers than occurs between men and women.
Census data indicates that Russian, Italian, and Japanese male immigrants who work full time earn more than the U.S. average. Mexican, Puerto Rican, and Native American workers earn less than the U.S. average. Most of these differences, however, can be explained by differences in human capital. The level of language proficiency also plays a role in explaining earnings differentials for recent immigrants.
Economists argue that labor market discrimination may be the result of:
 employer discrimination,
 customer discrimination,
 employee discrimination, or
 statistical discrimination.
Employer discrimination occurs when employers are willing to pay a premium to employ workers that they favor. Women and minorities are hired only if the wage is sufficiently low to compensate for the prejudice. Under such a system, wages for the groups that are discriminated against will be lower than that of the favored groups. This means that the wages of the victims of this prejudice will be below the value of their output. In such a situation, firms that do not discriminate can increase their profit by hiring those workers who are the targets of this form of discrimination. In a competitive market, non-discriminating firms will have higher profits than those firms that discriminate. Thus, firms that discriminate do so at a cost to their profit. In the long run, it would be expected that this form of discrimination would be eliminated as a result of competition.
Customer prejudice occurs when customers are willing to pay a higher price to buy goods and services from members of a favored group. In such a situation, segregated workplaces are likely to appear, at least for those employees that interact with customers. The significantly lower wages of black self-employed males is likely to be largely the result of customer prejudice.
Customer discrimination raises product costs for those customers that discriminate and lowers the wages of the groups that are the targets of the discrimination.

Employee discrimination occurs when workers avoid employment that involves interaction with those groups that are the target of their prejudice. In competitive markets, it would be profitable for firms to hire only the targets if such discrimination (due to their lower wages). As your text notes, however, in many occupations, there are insufficient numbers of minority or women workers available to fill such positions. The majority status of white males in some of these occupations allows for the continued existence of this form of discrimination.
The topic of statistical discrimination was discussed several weeks ago (in the discussion accompanying Chapter 5). Firms rely on statistical discrimination when they have imperfect information about a potential employee's productivity. If firms cannot reliably predict the level of a worker's productivity based upon only the worker's observed characteristics, they may take into account group characteristics that are good predictors of individual productivity. When this occurs, workers with the same individual characteristics will receive different wage and employment offers as a result of the groups to which they belong. This results in observed discrimination against members of groups that have lower average levels of human capital and lower levels of lifetime labor force participation. This type of discrimination lowers a firm's costs and is profitable for firms. It is not the result of prejudice, but instead a reaction to the existence of imperfect information.
There are two closely related noncompetitive models that are used to explain discrimination
(primarily gender-based discrimination)

 crowding, and dual labor markets.
The crowding hypothesis is based on the assumption that too many women are "crowded" into some occupations. Male dominated occupations offer higher wages because they are less crowded.
The dual labor market hypothesis refers to the distinction between the primary and secondary labor markets that we discussed in the early stages of this course. Primary sector employment involves high wages and stable employment relationships. Low wages and unstable employment relationships characterize the jobs available in the secondary sector.
Both of these models are based on the assumption that workers in alternative labor markets are in noncompeting groups. Under this assumption, relatively high wages in one market will not cause a significant migration of workers to shift from the low-wage sector to the high-wage sector.
A search-related monopsony model provides another explanation for the existence of gender or racial wage differentials. In this model, the existence of some discriminatory employers raises the expected cost of job search for members of groups that are the targets of discrimination. The existence if these higher search costs results in an upward sloping labor supply curve for affected workers in their existing firms. This upward sloping labor supply curve provides the firm with some degree of monopsony power in establishing wages for affected workers.

A Marxist analysis of discrimination often relies on an assumption of collusive behavior on the part of all firms in a labor market. It is argued that discriminatory behavior creates divisions among workers and reduces the likelihood of successful unionization efforts. A major problem with this argument is that any firm could increase its profits by violating the collusive agreement.
The Equal Pay Act of 1963 made it illegal to offer different pay to men and women performing the same tasks. It did not, however, prohibit discrimination in hiring or promotion. Title VII of the Civil Rights Act of 1964 filled in this gap by prohibiting discriminatory hiring practices.
Discriminatory memberships practices by unions were also prohibited by Title VII.
Court interpretation of these acts have relied on two different criteria for measuring discriminatory behavior: disparate treatment and disparate impact . Disparate treatment occurs when individuals are treated differently based on their race, gender, religion, or ethnicity.
Employment policies result in a disparate impact if they have a different impact on different groups even if the same standard is applied to all workers. The disparate treatment standard requires an intent to discriminate. Disparate impact can occur even if there was not a clear intent to engage in discriminatory behavior; it may be simply the result of policies that continue the effect of past discrimination.
Seniority rules are allowed under Title VII, even though they perpetuate the effects of past discrimination.
A comparable worth pay system attempts to provide equal pay for "equivalent" worth. As described in the web site referenced above, such pay schemes result in economic incentives that encourage an oversupply of labor in "crowded" occupations and a shortage in those occupations that are not initially subject to crowding.
The Federal Contract Compliance Program was created in 1965 to ensure that firms doing business with the federal government engage in nondiscriminatory employment behavior. Firms doing business with the federal government are required to maintain a mix of workers that is proportionate to their representation in the relevant labor market. Unfortunately, the definition of the relevant labor market is not generally obvious.