Applied Microeconomics
Winter 20/21
Chapter 1: Preliminaries
Microeconomics
- deals with the behaviour of individual economic units:
o Consumers, investors, owner of land, business firms
o Markets that these units comprise
- explains how and why these units make economic decisions
o how many workers to hire, how workers decide where & how much work to do
Macroeconomics
- deals with aggregate economic quantities:
o level & growth rate of national output, interest rates, unemployment, inflation
- also involves the analysis of markets
The themes of Microeconomics
- Limits and ways to make the most of these limits: allocation of scarce resources
Trade-Offs:
- Consumers:
o Consumer theory describes how consumers, based on their preferences, maximizes their
well-being by trading off the purchase of less of others
o Trading off current consumption for future consumption
- Workers:
o Trade off working now (immediate income) for continued education (hope of earning a
higher future income)
o Choice of employment
o Labour for leisure
- Firms:
o Variety of products and resources to produce them
o Theory of the firm describes how these trade-offs can best be made
Prices and Markets:
- All of the trade-offs are based on the prices they are faced
- In centrally planned economies, prices are set by the government
- In a market economy, prices are determined by interactions
Theories and Models:
- Explanation and prediction are based on theories
- Theories are developed to explain observed phenomena in terms of a set of basic rules and
assumption
- It explains how choices depend on the prices of inputs & the prices received for the outputs
- Statistics & econometrics:
o theories used to construct models from which quantitative prediction can be made
o measures accuracy of predictions
- Model = mathematical representation, based on economic theory
- The usefulness and validity of a theory depend on whether it succeeds in explaining &
predicting the set of phenomena
Positive versus Normative Analysis:
- Positive analysis = analysis describing relationships of cause & effect
o Use of economic theory for prediction is important for managers of firms & public policy
- Normative analysis = analysis examining questions of what ought to be
o Also important for managers and public policy
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It’s concerned with alternative policy options & design of particular policy choices
Often supplemented by value judgements: weighing equality against economic efficiency
1.2 What is a Market?
-
Market = collection of buyers & sellers that, through their actual or potential interactions,
determine the price of a product or set of products
- Markets includes more than an industry (= supply side of market)
- Industry = collection of firms that sell the same or closely related products
- Market definition = determination of the buyers, sellers and range of products that should
be included in a particular market
- Potential interactions can be as important as actual ones
- Significant differences in the price of a commodity create a potential for arbitrage
- Arbitrage = practice of buying at a low price at one location & selling at a higher price in
another
Competitive versus Noncompetitive Markets:
- Perfectly competitive market has many buyers & sellers, so that no single buyer or seller has
any impact on price  most agricultural markets
- Noncompetitive market = individual firms can jointly affect the price
Market Price:
- Market price = price prevailing in a competitive market
- In markets that are not perfectly competitive, different firms might charge different prices
for the same product  market price = the price averaged across brands or supermarkets
- Market prices of most goods will fluctuate over time, & for some goods the fluctuations can
be rapid
Market Definition – The Extent of a Market:
- Extent of a market = boundaries of a market, both geographical & in terms of range of
products produced & sold within it
- Market definition is important for 2 reasons:
o A company must understand who its actual & potential competitors are for the various
products that it sells or might sell in the future. It must also know the product
boundaries & geographical boundaries of its market in order to set price, determine
advertising budgets, & make capital investment decisions
o Public policy decisions: should the government allow a merger or acquisition involving
companies that produce similar products, or should it challenge it? The answer depends
on the impact of that merger or acquisition on future competition & prices; often this
can be evaluated only by defining a market
1.3 Real versus Nominal Prices
-
Real price = price of a good relative to an aggregate measure of prices; price adjusted for
inflation
Nominal price = absolute price of a good, unadjusted for inflation
Consumer Price Index (CPI) = measure of the aggregate price level
Percentage changes in the CPI measure the rate of inflation in the economy
Producer Price Index (PPI) = measure of the aggregate price level for intermediate products
& wholesale goods
Percentage changes in the PPI measure cost inflation & predict future changes in the CPI
Product or service normally purchased by consumers  CPI
Product or service normally purchased by businesses  PPI
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𝑟𝑒𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛 𝑋1 =
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𝐶𝑃𝐼𝑋0
× 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛 𝑋1
𝐶𝑃𝐼𝑋1
𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑟𝑒𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 =
𝑟𝑒𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛 𝑋1 − 𝑟𝑒𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛 𝑋0
𝑟𝑒𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛 𝑋0
Chapter 2: The Basics of Supply and Demand
2.1 Supply and Demand
-
Helps us understand why and how prices change, & what happens when the government
intervenes in a market
The supply-demand model combines two important concepts: supply curve & demand curve
The Supply Curve:
- = Relationship between the quantity of a good that producers are willing to sell and the price
of the good
𝑄𝑆 = 𝑄𝑆 (𝑃)
- The supply curve in the Figure slopes upwards:
 the higher the price, the more that firms are able & willing to
produce & sell
 if production costs fall, firms can produce the same quantity at
a lower price or a larger quantity at the same price (supply curve
shifts to the right: S to S´)
- A higher price may also attract new firms to the market  they
face higher costs because of their inexperience in the market &
would therefore have found entry uneconomical at a lower price
Other Variables that affect Supply:
- Production costs, including wages, interest charges, & the costs of raw materials
- The supply curve in the Figure was drawn for particular values of these other variables: a
change in the values of one or more of these variables translates into a shift in the curve
- When production costs decrease, output increases  entire supply curve shifts to the right
- Economists use the phrase ‘change in supply’ to refer to shifts in the supply curve, while
reserving the phrase ‘change in the quantity supplied’ to apply to movements along the
supply curve
The Demand Curve: = Relationship between the quantity of a good that consumers are willing to buy
& the price of the good
𝑄𝐷 = 𝑄𝐷 (𝑃)
- the demand curve in the Figure is downward sloping:
 consumers are usually ready to buy more if the price is lower
- The quantity of a good that consumers are willing to buy can also
depend on weather, the prices of other goods & income: the
quantity demanded increases when income rises  shift of
demand curve to the right (D to D’)
Shifting the Demand Curve:
- Increase of income levels would result in the shift of the entire
demand curve to the right
- The phrase ‘change in demand’ is used to refer to shifts in the demand curve, whereas the
phrase ‘change in the quantity demanded’ refers to movements along the demand curve
Substitute & Complementary Goods:
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Substitutes = two goods for which an increase in the price of one leads to an increase in the
quantity demanded of the other
o Aluminium – copper: the quantity of copper demanded will increase if the price of
aluminium increases
Complements = two goods for which an increase in the price of one leads to a decrease in
the quantity demanded of the other
o Automobiles – gasoline: a decrease in the price of gasoline increases the quantity
demanded for automobiles
2.2 The Market Mechanism
-
= the tendency for supply & demand to equilibrate, so
that there is neither excess demand nor excess supply
equilibrium (or market-clearing) price = price that
equated the quantity supplied to the quantity demanded
surplus = quantity supplied > quantity demanded
shortage = quantity demanded > quantity supplied
2.3 Changes in Market Equilibrium
-
shift in the supply curve (decrease in the price of raw
materials)  market price drops & the total quantity produced increases
shift in the demand curve (increase in income)  higher price & greater quantity
shift to the right of both curves  slightly higher price & a much larger quantity
2.4 Elasticities of Supply and Demand
-
elasticity = percentage change in one variable resulting from a 1-percent increase in another
price elasticity of demand = percentage change in quantity demanded of a good resulting
from a 1-percent increase in its price
𝐸𝑝 =
-
-
∆𝑄/𝑄
∆𝑃/𝑃
=
𝑃∆𝑄
𝑄∆𝑃
𝐸𝑝 > 1 in magnitude = price elastic; 𝐸𝑝 < 1 = price inelastic
the steeper the slope of the curve, the less elastic is demand
o Infinitely elastic: consumers will buy as much as they
can at a single price; for even the smallest increase in
price, quantity demanded increases without limit
o Completely inelastic: consumers will buy a fixed
quantity, no matter the price
Income elasticity of demand = % change in the quantity
demanded resulting from a 1% increase in income: 𝐸𝐼 =
-
∆𝑄/𝑄
∆𝐼/𝐼
𝐼 ∆𝑄
= 𝑄 ∆𝐼
Cross-price elasticity of demand = % change in the quantity demanded of a good resulting
∆𝑄 /𝑄
from a 1% increase in the price of another: 𝐸𝑄𝑏 𝑃𝑚 = ∆𝑃 𝑏/𝑃 𝑏 =
𝑚
𝑚
𝑃𝑚 ∆𝑄𝑏
𝑄𝑏 ∆𝑃𝑚
-
Price elasticity of supply = % change in quantity supplied at a 1% increase in price
-
Arc elasticity: 𝐸𝑝 =
∆𝑄
∆𝑃
=
𝑃̅
𝑄̅
2.5 Short-run versus Long-Run Elasticities
-
Elasticities pertain to a time to time frame, & for most goods it is important to distinguish
between short-run & long-run elasticities
o For most goods: demand is more elastic in the long run  it takes time to change
consumption habits
o Durable goods: demand is more elastic in the short run  total stock of each good
owned, is large relative to annual production
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We can use supply-demand diagrams to see how shifts in the supply &/or demand curve can
explain changes in the market price & quantity
2.6 Understanding and Predicting the Effects of Changing Market Conditions
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If we can estimate, at least roughly, the supply & demand curves for a particular market, we
can calculate the market-clearing price by equating the quantity supplied with the quantity
demanded. Also, if we know how supply & demand depend on other economic variables,
such as income or the prices of other goods, we can calculate how the market-clearing price
& quantity will change as these other variables change. This is a means of explaining or
predicting market behaviour.
Simple numerical analysis can often be done by fitting linear supply & demand curves to
data on price & quantity & to estimates of elasticities. For many markets, such data &
estimates are available, & simple “back of the envelope” calculations can help us understand
the characteristics & behaviour of the market.
1. Demand: Q = a – bP
Supply: Q = c + dP
∆𝑄
2. E = P/Q ∗ ∆𝑃
demand: E = -b(P*/Q*)  solve for b
supply: E = d(P*/Q*)  solve for d
3. Rewrite equation  a = Q* + bP*
2.7 Effects of Government Intervention – Price Controls
When a government imposes price controls, it keeps the price
below the level that equates supply & demand. A shortage
develops; the quantity demanded exceeds the quantity supplied.
Chapter 3: Consumer Behaviour
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= explanation of how consumers allocate incomes among different goods & services to
maximize their well-being
3 steps: consumer preferences, budget constraint, consumer choices
3.1 Consumer Preferences
-
Market basket (or bundle) = list with specific quantities of one or more goods
Consumers usually select market baskets that make them as well off as possible
As the method of measurement is largely arbitrary, we will describe the items in a market
basket in terms of the total number of units of each commodity
Some Basic Assumptions about Preferences:
1. Completeness: consumers can compare and rank all possible baskets  a consumer will
prefer A to B, B to A or will be indifferent between two (costs are ignored)
2. Transitivity: if a consumer prefers basket A to basket B and basket B to basket C, then the
consumer also prefers A to C
3. More is better than less: consumers always prefer more of any good to less; more is always
better, even if just a little better (“bads” ignored)
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Indifference Curves:
= curve representing all combinations of market baskets that
provide a consumer with the same level of satisfaction
Describing individual preferences:
- because more of each good is preferred to less, we can compare
market baskets in the shaded areas. Basket A is clearly preferred to
basket G, while E is clearly preferred to A
- A can’t be compared with B, D, or H without additional information
Indifference curve:
- the curve that passes through market basket A shows all baskets
that give the consumer the same level of satisfaction as does A
- The consumer prefers basket E, which lies above U1, to A, but
prefers A to H or G, which lie below U1
Indifference Maps:
= graph containing a set of indifference curves showing the market
baskets among which a consumer is indifferent
- Any market basket on indifference curve U3 (A…), is preferred to any
basket on curve U2 (B…), which in turn is preferred to any basket on U1
- Indifference curves cannot intersect  violates 2. assumption
Shape of Indifference Curves:
= describes how a consumer is willing to substitute one good for
another
- The more food a person possesses, the less clothing he will give up for more food
The Marginal Rate of Substitution:
= Maximum amount of the good on the vertical axis that a consumer is willing to give up in
order to obtain one additional unit of the good on the horizontal axis
- = the value that the individual places on 1 extra unit of a good in terms of another
- 𝑀𝑅𝑆 = −∆𝐶/∆𝐹
- To understand how the decline in the MRS reflects a characteristic of consumer preferences,
an additional assumption will be added:
4. Diminishing MRS: indifference curves are usually convex  the slope of the curve
increases as we move down along the curve  indifference curve is convex, if the MRS
diminishes along the curve
Perfect Substitutes & Perfect Complements:
- Perfect substitutes = 2 goods for which the MRS of one for the other is a constant
- Perfect complements = 2 goods for which the MRS is 0 or infinite; the indifference curves are
shaped as right angles
- Bads = good for which less is preferred rather than more  redefine the product under
study so that consumer tastes are represented as a preference for less of the bad  good
Utility:
= numerical score representing the satisfaction that a consumer gets from a market basket
-
Utility function = formula that assigns a level of utility to individual market baskets
𝑢(𝐹, 𝐶) = 𝐹 ∗ 𝐶
The utility function is a way of ranking different market baskets; the magnitude of the utility
difference between any 2 market baskets doesn’t really tell us anything  we do not know
how much one is preferred to the other
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Ordinal utility function = utility function that generates a ranking of market baskets in order
of most to least preferred
Cardinal utility function = describes by how much one market basket is preferred to another
It attaches to market basket numerical values that can’t arbitrarily be doubled or tripled
without altering the differences between the values of various market baskets
3.2 Budget Constraints
The Budget Line:
= all combinations of goods for which the total amount of money spent is equal to income
- 𝑃𝑋1 𝑋1 + 𝑃𝑋2 𝑋2 = 𝐼
 solve for 𝑋2 
C = (I/𝑃𝑋2 ) - (𝑃𝑋1 /𝑃𝑋2 ) 𝑋1
- slope of the budget line - (𝑃𝑋1 /𝑃𝑋2 ) = the negative of the ratio of the prices of the two goods
- the magnitude of the slope = rate at which the 2 goods can be substituted for each other
without changing the total maximum amount of money spent
- (I/𝑃𝑋2 ) = maximum amount of 𝑋2 that can be purchased with income I
- (I/𝑃𝑋1 ) = how many units of 𝑋1 can be purchased if all income were spent on 𝑋1
The Effects of Changes in Income and Prices:
- Income changes: alteration to the vertical intercept of the budget line, but not the slope:
o Income increase  budget line shifts outward (parallel)  can double purchase
o Income decrease  budget line shifts inward
- Price changes:
o Price of good on the horizontal intercept is halved  vertical intercept of the budget
line remains unchanged, the slope changes  outward rotation of budget line
o Price doubled  inward rotation of budget line
o Prices of both goods change: both intercepts shift, slope is unchanged:
 Outward shift if prices are halved
3.3 Consumer Choice
-
-
Maximizing market basket must satisfy 2 conditions:
1. It must be located on the budget line:
a. market baskets to the left of and below the budget
line leaves some income unallocated
b. market baskets to the right of and above the budget
line can’t be purchased with available income
2. It must give the consumer the most preferred
combination of goods & services
A maximizes satisfaction  budget line & indifference curve
are tangent  no higher level of satisfaction can be attained
At A, the MRS between the two goods equals the price ratio
B, however, because the MRS is greater than the price ratio, satisfaction is not maximized
-
satisfaction is maximized, when marginal benefit is equal to marginal cost
marginal benefit = benefit from the consumption of one additional unit of a good  MRS
marginal cost = cost of one additional unit of a good  price ratio
-
Corner Solution:
- = situation in which the MRS of one good for another in a chosen market basket is not equal
to the slope of the budget line
𝑀𝑅𝑆 ≥ 𝑃𝑋1 /𝑃𝑋2
…
𝑋1 = good that is consumed, 𝑋2 = not consumed at all
- Satisfaction maximized by consuming only one of the two goods
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If the MRS of 𝑋1 for 𝑋2 is substantially greater than the price ratio, then a small decrease in
the price of 𝑋2 will not alter the consumer’s choice
If the price of 𝑋2 falls far enough, the consumer could quickly choose to consume a lot of it
3.4 Revealed Preference
If a consumer chooses one market basket over another, & if the chosen market basket is more
expensive than the alternative, then the consumer must prefer the chosen market basket
Two Budget Lines:
- If an individual facing budget line l1 chose market basket A
rather than market B, A is revealed to be preferred to B.
- The individual facing line l2 chooses market basket B, which is
then revealed to be preferred to market basket D
- A is preferred to all market baskets in the blue-shaded area,
all baskets in the pink-shaded area are preferred to A
4 Budget Lines:
- Facing budget line l3 the individual chooses E, which is
revealed to be preferred to A
- Facing line l4, the individual chooses G which is also
revealed to be preferred to A
- Whereas A is preferred to all market baskets in the blueshaded area, all market baskets in the pink-shaded area are
preferred to A
-
Revealed preference approach is valuable as a means of
checking whether individual choices are consistent with the assumption of consumer theory
It can help us understand the implications of choices that consumers must make in particular
circumstances
3.5 Marginal Utility and Consumer Choice
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-
Marginal utility (MU) = additional satisfaction obtained from consuming one additional unit
of a good
Diminishing marginal utility = principle that as more of a good is consumed, the consumption
of additional amounts will yield smaller additions to utility
[F = X1; C = X2]



 tells us that utility maximization is achieved when the budget is
allocated so that the marginal utility per dollar of expenditure is the same for each good
Equal marginal principle = principle that utility is maximized when the consumer has
equalized the marginal utility per dollar of expenditure across all goods
Rationing:
- Under a market system, those with higher incomes can outbid those with lower incomes to
obtain goods that are in scarce supply
- When a good is rationed, less is available than consumers would like to buy
- Everyone will have an equal chance to purchase a rationed good
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Some consumers will be worse off, but others may be better off with rationing
3.6 Cost-of-Living Indexes
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-
-
-
= ratio of the present cost of a typical bundle of consumer goods and services compared
with the cost during a base period
Ideal cost-of-living index = cost of attaining a given level of utility at current prices relative to
the cost of attaining the same utility at base-year prices
Laspeyres price index (LI) = amount of money at current year requires to purchase a bundle
of goods and services chosen in a base year divided by the cost of
purchasing the same bundle at base-year prices
Paasche Index (PI) = amount of money at current-year prices that an
individual requires to purchase a current bundle of goods and services
divided by the cost of purchasing the same bundle in a base year
Both LI and PI are fixed-weight indexes. For the LI, however, the
quantities’ unchanged at base-year levels; for the Paasche at current-year levels
The Laspeyres index is much higher than the ideal price index  always overstate the true
cost-of-living index  assumes that consumers do not alter their consumption patterns as
prices change
The Paasche index understates the ideal cost of living  assumes that the individual will buy
the current-year bundle in the base period
In actuality, facing base-year prices, consumers would have been able to achieve the same
level of utility at a lower cost by changing their consumption bundles
Overstating the cost of the base-year bundle will cause the Paasche index itself to be
understated
Chapter 4: Individual and Market Demand
4.1 Individual Demand
Price Change:
o a reduction in the price of food, with income & the price of
clothing fixed, causes the consumer to choose a different
market basket
o in (a), the baskets that maximize utility for various prices of
food trace out the price-consumption curve
o part (b) gives the demand curve, which relates the price of
food to the quantity demanded
- Price-consumption curve = curve tracing the utility-maximizing
combinations of 2 goods as the price of one changes
- Individual demand curve = curve relating the quantity of a good
that a single consumer will buy to its price
- The level of utility that can be attained changes as we move along the curve  the lower the
price, the higher the level of utility
- At every point in the demand curve, the consumer is maximizing utility by satisfying the
condition that the MRS of food for clothing equals the ratio of the prices of food and
clothing  as the price of food falls, the price ratio of food & MRS also fall
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Income Changes:
- Income changes appear as changes in the budget line
- Income-consumption curve = curve tracing the utility-maximizing
combinations of 2 goods as consumer’s income changes
o An increase in income, with the prices of all goods fixed, causes
consumers to alter their choice of market baskets
o In part (a), the baskets that maximize consumer satisfaction for
various incomes trace out the income-consumption curve
o The shift to the right of the demand curve in response to the
increases in income is shown in part (b)
- Any change in income must lead to a shift in the demand curve itself
Normal versus Inferior Goods:
- Normal: consumers want to buy more goods as their incomes increase:
o Income-consumption curve has a positive slope, quantity
demanded increases with income  income elasticity of demand is positive
- Inferior: consumption falls when income rises:
o Income elasticity of demand is negative  income-consumption curve bends backward
Engel Curves:
= relates the quantity of a good consumed to income
- (a): food is a normal good  Engel curve is
upward sloping
- (b): income < $20  hamburger = normal
good; income > $20  inferior good
Substitutes and Complements:
- A way to see whether 2 goods are complements or substitutes is to examine the priceconsumption curve
o Downward sloping  substitutes
o Upward sloping  complements
4.2 Income and Substitution Effects
1. Substitution Effect: Consumers will tend to buy more of the good that has become cheaper
& less of those that are now relatively more expensive
2. Income Effect: Because one of the goods is now cheaper, consumers
enjoy an increase in real purchasing power
o The substitution effect F1E changes the relative prices of food &
clothing but keeps real income constant
o The income effect EF2 keeps relative prices constant but increases
purchasing power
- Total Effect (F1F2) = Substitution Effect (F1E) + Income Effect (EF2)
- Substitution effect = change in consumption of a good associated with
a change in its price, with the level of utility held constant
o Always leads to an increase in the quantity demanded
- Income effect = change in consumption of a good resulting from an increase in purchasing
power, with relative prices held constant
o Can move demand in either direction, depending on whether the good is normal or
inferior  positive = normal; negative = inferior
- Even with inferior goods, the income effect is rarely large enough to outweigh the
substitution effect  when the price falls, its consumption almost always increases
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Special Case: The Giffen Good = good whose demand curve slopes upward because the
(negative) income effect is larger than the substitution effect
o Decrease in the price of food  lower quantity demanded
o 𝐸𝐷 ≥ 0  inferior good
4.5 Market Demand
-
Market demand curve = curve relating the quantity of a good that all consumers in a market
will buy to its price
o It’s obtained by summing consumers’ demand curves
o At each price, the quantity demanded by the market is the sum of the quantities
demanded by each consumer
o Though each of the individual demand curves is a straight line, the market demand
curve need not be
1. The market demand curve will shift to the right as more consumers enter the market
2. Factors that influence the demands of many consumers will also affect market demand
Elasticity of Demand:
- Inelastic demand: quantity demanded is relatively unresponsive to changes in price  total
expenditure on the product increases when the price increases
- Elastic demand: total expenditure on the product decreases as the price goes up
- Isoelastic demand: the price elasticity of demand is constant all along the demand curve
o Unit-elastic demand curve: demand curve with price elasticity always equal to -1 
total expenditure remains the same after a price change
- Speculative demand: demand driven not by the direct benefits one obtains from owning or
consuming a good but instead by an expectation that the price of the good will increase
o It’s possible to profit by buying the good and then reselling it later at a higher price
4.4 Consumer Surplus
= difference between what a consumer is willing to pay for a good & the amount actually paid
- Consumer surplus can be calculated easily if we know the demand
curve  adding the excess values or surpluses for all units purchased
o aggregate consumer surplus in a market area below the
market demand curve & above the price line
- Consumer surplus (figure) = ½ * ($20 - $14) * 6500 = $19.500
- When combining surplus with the aggregate profits that producers
obtain, we can evaluate both the costs & benefits not only of
alternative market structures, but of public policies that alter the
behaviour of consumers & firms in those markets
4.5 Network Externalities
= situation in which each individual’s demand depends on the purchases of other individuals
- Positive network externality: quantity of a good demanded by a typical consumer increases
in response to the growth in purchases of other consumersdemand curve relatively elastic
o E.g., Bandwagon effect = consumer wishes to possess a good in part because others do
- Negative network externality: quantity demanded decreases market demandless elastic
o E.g., snob effect = consumer wishes to own an exclusive or unique good
Appendix to Chapter 4: Demand Theory – A Mathematical Treatment
Utility Maximization:
- Marginal utility  as utility change resulting from a very small increase in consumption
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Suppose the utility function is given by U (X, Y) = log X + log Y, then the marginal utility
associated with the additional consumption of X is given by the partial derivative of the
utility function with respect to good X
𝜕𝑈(𝑋, 𝑌) 𝜕(log 𝑋 + log 𝑌) 1
𝑀𝑈𝑋 =
=
=
𝜕𝑋
𝜕𝑋
𝑋
While the level of utility is an increasing function of the quantities of goods consumed,
marginal utility decreases with consumption
When there are 2 goods (X, Y), the consumer’s optimization problem may be written as
𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑈 (𝑋, 𝑌)
Subject to the constraint that income is spent on the 2 goods:
𝑃𝑋 𝑋 + 𝑃𝑌 𝑌 = 𝐼
The technique of constrained optimization can be used to describe the conditions that must
hold if the consumer is maximizing utility
The Method of Lagrange Multipliers:
= technique to maximize or minimize a function subject to one or more constraints
1. Stating the Problem: write the Lagrangian (= function to be maximized or minimized, plus a
variable multiplied by the constraint):
- Budget constraint is written as:
- This sum is then inserted into the Lagrangian
2. Differentiating the Lagrangian: maximizing will be equivalent to maximizing U (X, Y)
𝑀𝑈𝑋 (𝑋, 𝑌) = 𝜕𝑈(𝑋, 𝑌)/𝜕𝑋 … exchange in utility from a
very small increase in X’s consumption
3. Solving the Resulting Equations: the three equations above can be written as:
-
The resulting values of X & Y are the solution to the consumer’s optimization problem
The Equal Marginal Principle:
- The third equation above is the consumer’s budget constraint
- The first two equations tell us that each good will be consumed up to the point at which the
marginal utility from consumption is a multiple of the price of the good
 combining the first 2 conditions to obtain the equal marginal principle:
- The consumer must get the same utility from the last dollar spent by consuming either X or Y
- The ratio of the marginal utilities is equal to the ratio of the prices:
Marginal Rate of Substitution:
- An indifference curve represents all market baskets that give the consumer the same level of
utility  if U* is a fixed utility level, then the indifference curve = U (X, Y) = U*
- The total change in utility must equal zero:
Rearranged:
- When the individual indifference curves are convex, the tangency of the indifference curve
to the budget line solves the consumer’s optimization problem
Marginal Utility of Income:
- Lagrangian multiplier = extra utility that results from an extra dollar of income
- Totally differentiating utility function U (X, Y) with respect to I:
- Any increment in income must be divided between the goods:
- Substituting equal marginal principle into the 1. equation:
- Substituting the 2. equation into the 3.:
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An Example:
- Cobb-Douglas utility function:
or
- The demand for each good
depend
only on the price of that good and on income, not on the price of the other good  crossprice elasticities of demand are 0
Duality in Consumer Theory:
- Duality = alternative way of looking at the consumer’s utility maximization decision: rather
than choosing the highest indifference curve, the consumer chooses the lowest budget line
that touches a given indifference curve
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑃𝑋 𝑋 + 𝑃𝑌 𝑌
- Subject to the constraint that:
𝑈(𝑋, 𝑌) = 𝑈 ∗
- The corresponding Lagrangian:
- 𝜇 = Lagrange multiplier;
differentiating 𝜑 with respect to X, Y and 𝜇 & setting the derivatives equal to 0:
𝑈(𝑋, 𝑌) = 𝑈 ∗
-
-
Solving the first 2 equations:
It is also true that:
the cost-minimizing choice of X & Y must occur at the point of tangency of the budget line &
the indifference curve that generates utility U*
The dual expenditure-minimization problem yields the same demand function that are
obtained from the direct utility-maximization problem
Income and Substitution Effects:
- Demand function tells us how any individual’s utility-maximizing choices respond to changes
in both income & the prices of goods
- We must differentiate the portion of any price change that involves movement along an
indifference curve & from the portion which involves movement to a different indifference
curve
- The change in demand can be divided into a substitution effect and an income effect
- We denote the change in X that results from unit change in the price of X, holding utility
𝑑𝑋
constant: 𝑑𝑃 = 𝜕𝑃
𝑋
-
𝑋|𝑈=𝑈∗
+ (𝜕𝑋/𝜕𝐼)(𝜕𝐼/𝜕𝑃𝑋 )
1. term on the right = substitution effect; 2. term = income effect
From consumer’s budget constraint 𝐼 = 𝑃𝑋 𝑋 + 𝑃𝑌 𝑌  differentiation  𝜕𝐼/𝜕𝑃𝑋 = 𝑋
The equation tells us how much additional income the consumer would need in order to be
as well off after price change as they were before  income effect is negative:
𝑑𝑋
𝑑𝑃𝑋
-
𝜕𝑋
= 𝜕𝑃
𝜕𝑋
𝑋|𝑈=𝑈∗
− 𝑋(𝜕𝑋/𝜕𝐼) … Slutsky equation = formula for decomposing the effects of a
price change into substitution & income effects
1. term = substitution effect; 2. = income effect
Alternative way to decompose a price change into substitution & income effects, does not
involve indifference curves  Hicksian Substitution
o The individual initially consumes market basket A
o Price decrease of food  shift of budget line from RS to RT
o If a sufficient amount of income is taken away to make the
individual no better off than A, 2 conditions must be met:
1. New market basket must lie on segment BT’ of budget line R’T’
2. Quantity of food consumed must be greater than at A
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Quantity of food demanded increases whenever there is a decrease in the price of food with
utility held constant
The negative substitution effect holds for all price changes & doesn’t rely on the assumption
of convexity of indifference curves
Chapter 5: Uncertainty and Consumer Behaviour
5.1 Describing Risk
Probability = likelihood that a given outcome will occur
- Can depend on: nature of the uncertain event, beliefs of the people involved, or both
- Objective interpretation relies on the frequency with which certain events tend to occur
- Subjective probability is the perception that an outcome will occur  based on a person’s
judgement or experience, but not necessarily on the frequency with which a particular
outcome has actually occurred in the past
Expected value = probability-weighted average of the payoffs or values associated with all possible
outcomes  measures the central tendency
𝐸(𝑋) = 𝑃𝑟1 𝑋1 + 𝑃𝑟2 𝑋2 + ⋯ + 𝑃𝑟𝑛 𝑋𝑛

X = payoffs; Pr = probabilities
Variability = extent to which possible outcomes of an uncertain event differ
- Variability of the possible payoffs is different  deviations = difference between expected
payoff and actual payoff  can be positive or negative
- Standard deviation: square root of the weighted average of the squares of the deviations of
the payoffs associated with each outcome from their expected values
o The greater the spread (standard deviation) of possible payoffs, the riskier it is
𝑉(𝑋) = 𝑃𝑟1 (𝑋1 − 𝐸)2 + 𝑃𝑟2 (𝑋2 − 𝐸)2 + ⋯ + 𝑃𝑟𝑛 (𝑋𝑛 − 𝐸)2
5.2 Preferences Toward Risk
-
-
-
Expected utility = sum of the utilities associated with all possible outcomes, weighted by the
probability that each outcome will occur
o (a): consumer’s marginal utility diminishes as income
increases. The consumer is risk averse  prefers a certain
income of $20000 (utility 16) to a gamble with a .5
probability of $10000 & a .5 probability of $30000 (u=14)
o (b): consumer is risk loving  prefers the same gamble
(expected utility 10.5) to the certain income (u=8)
o (c): consumer is risk neutral & indifferent between certain &
uncertain events with the same expected income
Risk premium = maximum amount of money that a
risk-averse person will pay to avoid taking a risk 
magnitude depends on the risky alternatives that the
person faces [4th figure]
The extent of an individual’s risk aversion depends on
the nature of the risk & on the person’s income
o Highly risk averse: an increase in the standard
deviation of income requires a large increase in expected
income if they are to remain equally well off
o Slightly risk averse: an increase in the standard deviation
of income requires only a small increase in expected
income if they are to remain equally well off
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5.3 Reducing Risk
1. Diversification:
- = practice of reducing risk by allocating resources to a variety of activities whose outcomes
are not closely related
- Positively correlated variables = variables having a tendency to move in the same direction
- Negatively correlated variables = variables having a tendency to move in opposite directions
The Stock Market:
- Mutual fund = organization that pools funds of individual investors to buy a large number of
different stocks or other financial assets  reduce risk through diversification
- Not all risk is diversifiable
2. Insurance:
- Buying insurance assures a person of having the same income whether or not there is a loss
 insurance cost = expected loss  this income = expected income from the risky situation
- For a risk-averse consumer, the guarantee of the same income regardless of the outcome
generates more utility than would be the case if that person had a high income when there
was no loss & a low income when a loss occurred
- Law of Large Numbers: tells us that although single events may be random & largely
unpredictable, the average outcome of many similar events can be predicted
- Actuarial Fairness: characterizing a situation in which an insurance premium is equal to the
expected payout
- Catastrophic disasters are so unique & unpredictable that they can’t be viewed as
diversifiable risks  companies don’t feel that they can determine actuarially fair rates
3. The Value of Information:
- The value of complete information = difference between the expected value of a choice
when there is complete information & the expected value when information is incomplete
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑤𝑖𝑡ℎ 𝑐𝑜𝑚𝑝𝑙𝑒𝑡𝑒 𝑖𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 − 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑤𝑖𝑡ℎ 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦
= 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑜𝑚𝑝𝑙𝑒𝑡𝑒 𝑖𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛
- More information is a good thing, although it isn’t always the case
Chapter 6 – Production
The Production Decisions of a Firm:
- Are analogous to the purchasing decisions of consumers  3 steps:
1. Production Technology:
o Describes how an input can be transformed into outputs
o Firms produce a particular level of output by using different combinations of inputs
2. Cost Constraint:
o Firms take prices of inputs into account  minimizing production cost
3. Input Choices:
o How much of each input should a firm use in producing its output?
- Theory of the firm: explanation of how a firm makes cost-minimizing production decisions &
how its cost varies with its output
6.1 Firms and Their Production Decisions
Why Do Firms Exist?
- They offer a means of coordination that is extremely important & would be sorely missing if
workers operated independently
- They estimate the need for every worker to negotiate every task that he or she will perform,
& bargain over the fees that will be paid for those tasks
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They can avoid this kind of bargaining by having managers that direct the production of
salaried workers
- The theory of firms has positive aspects (explaining why managers & workers behave the
way they do) & normative aspects (explaining how firms can be best organized so that they
operate as efficiently as possible)
- Firms exist because they allow goods & services to be produced far more efficiently than
would be possible without them.
The Technology of Production:
- Firms take inputs & turn them into outputs  essence of what firms do
- Factors of production: Inputs into the production process
- Input can be categorized into:
o Labour: skilled & unskilled workers, entrepreneurial efforts of managers
o Materials: steel, plastics, electricity, water; any goods required to produce output
o Capital: land, buildings, machinery, other equipment, investors
The Production Function:
- = function showing the highest output that a firm can produce for every specified
combination of inputs
𝑞 = 𝐹(𝐾, 𝐿)
- The equation relates the quantity of output to the quantities of the 2 inputs (capital, labour)
& applied to a given technology
- Inputs & outputs are flows
- Production functions describe what’s technically feasible when the firms operate efficiently
The Short Run versus the Long Run:
- It takes time for a firm to adjust its inputs to produce its product with differing amounts of
labour & capital
- Short run: period of time in which the quantities of one or more production factors can’t be
changed  at least one factor can’t be varied = fixed input
o Firms vary the intensity with which they utilize a given plant & machinery
- Long run: amount of time needed to make all inputs variable
o The size of the plant is varied
- All fixed inputs represent the outcomes of previous long-run decisions based on estimates of
what a firm could profitably produce & sell
- We assume that capital is the fixed input, & labour is variable
6.2 Production with One Variable Input (Labour)
Cost on an incremental basis  focusing on the additional output that results from an
incremental addition to an input
- Average basis  considering the result of substantially increasing an input
- To make the decision, it’s important to know how the amount of output q increases as the
input of labour L increases
o L = 0, then q = 0
o Q increases as L is increased
o Beyond a certain point, total output declines  additional labour is no longer useful
Average and Marginal Products:
- Average product (𝐴𝑃𝐿 ) = output per unit of a particular input
𝐴𝑃𝐿 = 𝑞/𝐿
 measures the productivity of the firm’s workforce in terms of how much output each
worker produces on average  increases then falls
- Marginal product (𝑀𝑃𝐿 ) = additional output produced as an input is increased by one unit
-
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𝑀𝑃𝐿 = ∆𝑞/∆𝐿
 change in output resulting from a 1-unit increase in labour input  increases then falls
- The Slopes of the Product Curve:
o When 𝑀𝑃𝐿 is greater than 𝐴𝑃𝐿 , 𝐴𝑃𝐿 is increasing
o When 𝑀𝑃𝐿 is less than 𝐴𝑃𝐿 , 𝐴𝑃𝐿 is decreasing
- The Average Product of Labour Curve:
o 𝐴𝑃𝐿 is given by the slope of the line drawn from the origin to the
corresponding point on the total product curve
- The Marginal Product of Labour Curve:
o 𝑀𝑃𝐿 at a point is given by the slope of the total product at point
- Relationship between the Average and Marginal Products:
o At A, 𝑀𝑃𝐿 > 𝐴𝑃𝐿  𝐴𝑃𝐿 increases as we move from A to B
o At B, 𝐴𝑃𝐿 = 𝑀𝑃𝐿  𝐴𝑃𝐿 = slope of the line from the origin 0B,
𝑀𝑃𝐿 = tangent to the total product curve at B (at D  𝑀𝑃𝐿 =𝐴𝑃𝐿 )
o From B to C, 𝑀𝑃𝐿 < 𝐴𝑃𝐿  slope of the tangent to the total
product curve is lower than the slope of the line from the origin
The Law of Diminishing Marginal Returns:
= principle that as the use of an input increases with other inputs fixed, the resulting
additions to output will eventually decrease
- Usually applies to the short run, but it can also apply to the long run
- It results from limitations in the use of other fixed inputs
- It describes a declining marginal product but not necessarily a negative one
- It applies to a given production technology
- Overtime, inventions & other improvements in technology may allow the entire total
product curve to shift upward  the more output can be produced with the same inputs
Labour Productivity:
= average product of labour for an entire industry or for the economy as a whole
- It helps to illustrate one of the links between micro- & macroeconomics
- It determines the real standard of living that a country can achieve for its citizens
- Productivity & the standard of living:
o aggregate value of goods & services produced by an economy = payments made to all
factors of production, including wages, rental payments to capital, profit to firms
o consumers in the aggregate can increase their rate of consumption in the long run only
by increasing the total amount they produce
- Sources of growth in labour productivity:
o Growth in stock of capital = total amount of capital available for use in production
o Technological change = development of new technologies allowing factors of
production to be used more effectively
- Levels of labour productivity have differed considerably across countries, as have rates of
growth of productivity
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6.3 Production with Two Variable Inputs
- Long run  both labour & capital are variable
Isoquants = curve showing all possible combinations of inputs that
yield the same output
- Output increases as labour inputs are increased, while
capital inputs remain fixes
- Output also increases as capital inputs are increased,
while labour inputs remain fixed
- Isoquant map = graph combining a number of isoquants,
used to describe a production function
- Input Flexibility: firms can usually obtain a particular
output by substituting one input for another  managers can choose input combinations
that minimize cost & maximize profit
Diminishing Marginal Returns:
- Adding one factor while holding the other factor constant eventually leads to lower & lower
incremental output  isoquant must become steeper as more capital is added in place of
labour & flatter when labour is added in place of capital
- Diminishing marginal returns to capital  labour fixed, then 𝑀𝑃𝐾 decreases as K is increased
Substitution Among Inputs:
- The slope of each isoquant indicates how the quantity of one input can be traded off against
the quantity of the other, while output is held constant
- Marginal rate of technical substitution (MRTS) = amount by which the quantity of one input
can be reduced when one extra unit of another input is used, so that output remains
constant  always a positive quantity
𝑀𝑅𝑇𝑆 = −∆𝐾/∆𝐿 (𝑓𝑜𝑟 𝑎 𝑓𝑖𝑥𝑒𝑑 𝑙𝑒𝑣𝑒𝑙 𝑜𝑓 𝑞)
- Diminishing MRTS:
o isoquants are convex
o Productivity of input is limited  production needs a balanced mix of both inputs
𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑓𝑟𝑜𝑚 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑢𝑠𝑒 𝑜𝑓 𝑙𝑎𝑏𝑜𝑢𝑟 = (𝑀𝑃𝐿 )(∆𝐿)
𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑜𝑢𝑡𝑝𝑢𝑡 𝑓𝑟𝑜𝑚 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑢𝑠𝑒 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 = (𝑀𝑃𝐾 )(∆𝐾)
-
Total change in output must be 0: (𝑀𝑃𝐿 )(∆𝐿) + (𝑀𝑃𝐾 )(∆𝐾) = 0 
(𝑀𝑃𝐿 )
𝑀𝑃𝐾
∆𝐾
= − (∆𝐿) = 𝑀𝑅𝑇𝑆
- MRTS between two inputs is equal to the ratio of the marginal products of the inputs
Production Functions – Two Special Cases:
- Perfect substitutes:
o MRTS is constant at all points
o Same output can be produced with mostly capital, with mostly labour, or with a
balanced combination of both
- Fixed-proportions production function/Leontief production function:
o Production function with L-shaped isoquants, so that only one combination of
labour & capital can be used to produce each level of output
o Describes situations in which methods of production are limited
6.4 Returns to Scale
- In the long run, with all inputs variable a firm must consider the best way to increase output
= rate at which output increases as inputs are increased proportionately  3 cases:
o Increasing returns to scale = situation in which output more than doubles when all
inputs are doubled  large firms rather than many small firms
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Constant return to scale = situation in which output doubles when all inputs are
doubled  size of the firm’s operation does not affect the productivity
o Decreasing returns to scale = situation in which output less than doubles when all
inputs are doubled  applies to some firms with large-scale operations
Describing Returns to Scale:
- Returns to scale need not be uniform across all possible levels of output
- Increasing return to scale:
o Isoquants come closer together as we move away from the origin
 less than twice the amount of both inputs is needed to
increase production
o decreasing returns  isoquants are increasingly distant form one
another as output levels increase proportionally
o The opposite would be true for decreasing returns to scale
- Constant return to scale: when both inputs double, output doubles
Chapter 7 – The Cost of Production
7.1 Measuring Cost: Which Costs Matter?
Economic Cost versus Accounting Cost:
- Accounting cost = actual expenses + depreciation charges for capital equipment
- Economic cost = cost to a firm of utilizing economic resources in production
Opportunity cost = cost associated with opportunities forgone when a firm’s resources are not put to
their best alternative use
- Economic cost & opportunity cost actually boil down to the same thing
- Accountants & economists also differ in their treatment of depreciation:
o Economists & managers are concerned with the capital cost of plant & machinery 
monetary outpay for buying & then running the machinery + cost associated with wear
& tear  estimates future profitability
o Accountants use tax rules that apply to broadly defined types of assets to determine
allowable depreciation in their cost & profit calculationsevaluates past performance
Sunk costs = expenditure that has been made & can’t be recovered
- Always ignored when making future economic decisions  because it has no alternative
use, its opportunity cost is zero
- Prospective sunk cost = investment  firm must decide whether that investment in
specialized equipment is economical (if the equipment hasn’t been bought yet)
Fixed Costs & Variable Costs:
- Total cost (TC or C) = total economic cost of production, consisting of fixed & variable costs
- Fixed cost (FC) = costs that does not vary with the level of output & that can be eliminated
only by shutting down
- Variable cost (VC) = cost that varies as output varies
Amortizing Sunk Costs:
- Amortization = policy of treating a one-time expenditure as an annual cost spread out over
some number of years
- Amortizing large capital expenditures & treating them as ongoing fixed costs can simplify the
economic analysis of a firm’s operation
Marginal & Average Cost:
- Marginal cost (MC) = increase in cost resulting from production of one extra unit of output
∆𝑉𝐶 ∆𝑇𝐶
𝑀𝐶 =
=
∆𝑞
∆𝑞
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Average total cost (ATC) = firm’s total cost divided by its level of output = TC/q
o It’s used interchangeably with AC & has 2 components:
o Average fixed cost (AFC) = fixed cost divided by the level of output = FC/q
 Declines as the rate of output increases
o Average variable cost (AVC) = variable cost divided by the level of output = VC/q
7.2 Cost in the Short Run
The Determinants of Short-Run Cost:
- Suppose a firm can hire as much labour as it wishes at a fixed wage 𝜔
- Marginal cost is the change in variable cost for a 1-unit change in output  change in
variable cost is the per-unit cost of the extra labour 𝜔 times the amount of extra labour
needed to produce an extra output:
∆𝑉𝐶 𝜔∆𝐿
𝑀𝐶 =
=
∆𝑞
∆𝑞
- The marginal product of labour is the change in output resulting from a 1-unit change in
labour input  extra labour needed to obtain an extra unit of output is ∆L/∆q = 1/𝑀𝑃𝐿 
𝑀𝐶 = 𝜔/𝑀𝑃𝐿
- If 𝑀𝑃𝐿 decreases, then MC increases & vice versa
Diminishing Marginal Returns & Marginal Cost:
- Diminishing marginal returns  𝑀𝑃𝐿 declines as the quantity of labour employed increases
- When there are diminishing marginal returns, marginal cost will increase as output increases
The Shapes of the Cost Curves:
- VC = 0, when q = 0 & increases continuously as output increases
- FC does not vary with output
- TC is determined by vertically adding the fixed cost curve to the variable cost curve
- AFC falls continuously when output is 1, toward 0 for large output
- Shapes of the remaining curves are determined by the relationship between the marginal &
average cost curves
- Whenever marginal cost lies above average cost, the average cost curve falls
- When average cost is at a minimum, marginal cost equals average cost
The Average-Marginal Relationship:
- ATC curve shows the average TC of production
- Average TC = average VC + average FC & AFC curve declines
everywhere  vertical distance between ATC & AVC curves
decreases as output increases
- AVC cost curve reaches its minimum point at a lower output
than the ATC curve
- Minimum point of the ATC curve must lie above & to the
right of the minimum point of the AVC curve
- Tangent to the VC curve at A is the marginal cost of
production  marginal cost = average variable cost because
average cost is minimized at this output
Total Cost as a Flow:
- If the firm is currently producing at a level of output at which marginal costs is sharply
increasing, & if demand may increase in the future, management might want to expand
production capacity to avoid higher costs.
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7.3 Cost in the Long Run
Firms have much more flexibility  can choose its combination of inputs to minimize cost of
producing a given output
The User Cost of Capital = annual cost of owing & using a capital asset, equal to economic
depreciation plus forgone interest
- It would be useful to treat capital as though it were rented
- For economic purposes the purchase price can be allocated or amortized  revenues &
costs can be compared on an annual flow basis
- Amortized cost can be viewed as the annual economic depreciation
- User cost of capital = sum of the economic depreciation & the interest that could have been
earned had the money been invested elsewhere
𝑢𝑠𝑒𝑟 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 = 𝑒𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝑑𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 + (𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒)(𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙)
- As the purchase depreciates over time, its value declines, as does the opportunity cost of the
financial capital invested in it
- User of capital can also be expressed as a rate per dollar of capital:
𝑟 = 𝑑𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 + 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
The Cost-Minimizing Input Choice:
- The amount of variable inputs that a firm uses will depend on the prices of these inputs
- competitive markets for both inputs  prices are unaffected by what the firm does
- price of labour is simply the wage rate 𝜔
- price of capital: capital expenditure is expressed as a flow  expenditure must be amortized
by spreading it over the lifetime of the capital & forgone interest must be taken into account
o price of capital = user cost, given by r = depreciation rate + interest rate
- rental rate of capital = cost per year of renting one unit of capital
o competitive market  rental rate = user cost r
- Capital that is purchased can be treated as though it were rented at a rental rate equal to
the user cost of capital.
The Isocost Line = graph showing all possible combinations of labour & capital that can be purchased
for a given total cost
- Total cost C of producing any output is given by the sum of the firm’s labour cost ωL &
capital cost rK: C = 𝜔L + rK
- Isocost line 𝐶0 : all possible combinations of labour & capital that cost a total of 𝐶0 to hire 
equation for a straight line  K = C/r – (ω/r)L
- Slope: ∆K/∆L = -(ω/r)  ratio of the wage rate to the rental cost of capital
- If the firm gave up a unit of labour to buy ω/r units of capital at a cost of r dollars per unit, its
total cost of capital would remain the same
- Choosing Inputs:
o point of tangency of the isoquant & the isocost line gives us the cost-minimizing choice
o at this point, the slopes of the isoquant & the isocost line are just equal
o when the expenditure on all inputs increases, the slope of the isocost line does not
change because the prices of the inputs have not changed; interest increases
o if the price of one of the inputs (labour) were to increase, the slope of the isocost line (ω/r) increases in magnitude & the isocost line becomes steeper
o in this case, the firm minimizes its cost of producing output by substituting capital for
labour in the production process
𝑀𝑅𝑇𝑆 = −∆𝐾/∆𝐿 = 𝑀𝑃𝐿 /𝑀𝑃𝐾
o isocost line has a slope of ∆K/∆L = - ω/r  𝑀𝑃𝐿 /𝑀𝑃𝐾 = ω/r  𝑀𝑃𝐿 /𝜔 = 𝑀𝑃𝐾 /𝑟
o 𝑀𝑃𝐿 /𝜔 = additional output that results from spending an additional dollar for labour
-
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o
o
𝑀𝑃𝐾 /𝑟 = additional output that results from spending an additional dollar for capital
Cost-minimizing firms choose their quantities of inputs so that the last dollars’ worth of
any input added to the production process yields the same amount of extra output
o Because a dollar spent for capital is 5x more productive than a dollar spent for labour,
the firm will want to use more capital & less labour  marginal product of labour will
rise & marginal product of capital will fall
o Eventually, the point will be reached at which an additional production of an additional
unit of output costs the same regardless of which additional input is used  firm is
minimizing its cost
Cost Minimization with Varying Output Levels:
- We determine the cost-minimizing input quantities for each output level & then calculate
the resulting cost
- The curve passing through the points of tangency between the firm’s isocost lines & its
isoquants is its expansion path
- Expansion path = curve passing through points of tangency between a firm’s isocost lines &
its isoquants
- As long as the use of both labour & capital increases with output, the curve will be upward
sloping  expansion path is a straight line with a slope equal to ∆K/∆L
The Expansion Path & Long-Run Costs:
- To move from the expansion path to the cost curve:
o Choose an output level represented by as isoquant. Then find the point of tangency of
that isoquant with an isocost line.
o From the chosen isocost line, determine the minimum cost of producing the output
level that has been selected.
o Graph the output-cost combination.
- The shape of the expansion path provides information about
how costs change with the scale of the firm’s operation.
7.4 Long-Run versus Short-Run Cost Curves
- Short-run average cost curves are U-shaped
- Long-run average cost curves can also be U-shaped
The Inflexibility of Short-Run Production:
- In the long run, the firm’s planning horizon is long enough to
allow for a change in plant size  added flexibility allows the firm to produce at a lower
average cost than in the short run
- The firm’s long-run expansion path is the straight line from the origin
- Short-run: If the capital is fixed, the firm is forced to increase its output by using capital K1
and labour L3 (P)  cost of production is higher  expansion path: line from the origin &
then becomes a horizontal line when the capital input reaches K1
Long-Run Average Cost:
- Constant returns to scale: average cost is the same for all levels of output
- Increasing returns to scale: average cost falls with output
- Decreasing returns to scale: average cost increases with output
- Constant average cost means a constant marginal cost
- Long-run average cost curve (LAC) = curve relating average cost of production to output
when all inputs are variable  U-shaped (increasing & decreasing returns to scale)
- Short-run average cost curve (SAC) = curve relating average cost of production to output
when level of capital is fixed  U-shaped
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Long-run marginal cost curve (LMC) = curve showing the change in long-run total cost as
output is increased incrementally by 1 unit
o Lies below LAC when LAC is falling & above it when it’s rising
o The two curves intersect, where LAC achieves its minimum
o LAC constant, then LAC = LMC
Economies & Diseconomies of Scale:
- As output increases, the firm’s average cost of producing that output is likely to decline:
o If the firm operates on a larger scale, workers can specialize in the activities at which
they are most productive.
o Scale can provide flexibility. By varying the combination of inputs utilized to produce the
firm’s output, managers can organize the production process more effectively.
o The firm may be able to acquire some production inputs at lower cost because it is
buying them in large quantities & can therefore negotiate better prices. The mix of
inputs might change with the scale of the firm’s operation if managers take advantage
of lower-cost inputs.
- At some point, the average cost of production will begin to increase with output:
o At least in the short run, factory space & machinery may make it more difficult for
workers to do their jobs effectively.
o Managing a larger firm may become more complex & inefficient as the number of tasks
increases.
o advantages of buying in bulk may disappear once certain quantities are reached. At
some point, available supplies of key inputs may be limited, pushing their costs up
- Economies of scale = output can be doubled for less than a doubling of cost
- Diseconomies of scale = doubling of output requires more than a doubling of cost
- Difference between returns to scale & economies of scale:
o Returns to scale: inputs are used in constant proportions as output is increased
o Economies of scale: input proportions are variable  𝐸𝐶 = (∆C/C)/(∆q/q) 
𝐸𝐶 = (∆C/C)/(∆q/q)=MC/AC
- 𝐸𝐶 = 1, when marginal = average cost  costs increase proportionately with output, & there
are neither economies nor diseconomies of scale
- When there are economies of scale, marginal cost is less than average cost & 𝐸𝐶 < 1
- When there are diseconomies of scale, marginal cost is greater than average cost & 𝐸𝐶 > 1
The Relationship between Short-Run & Long-Run Cost:
- The long-run average cost curve is the envelope of the short-run average cost curves – it
envelops or surrounds the short-run curves
- The long-run average cost curve exhibits economies of scale initially but exhibits its
diseconomies at higher output levels
- The LAC never lies above any SAC
- Because there are economies & diseconomies of scale in the long run, the points of
minimum average cost of the smallest & largest plants do not lie on the LAC
- The LMC is not the envelope of the SMC  SMC apply to a particular plant; LMC apply to all
possible plant sizes
7.5 Production with Two Outputs – Economies of Scope
Production Transformation Curves = shows the various combinations of two
different outputs that can be produced with a given set of inputs
- Negative slope: to get more of one output, the firm must give up some
of the other output
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O2 lies twice as far from the origin as the curve O1, signifying that this firm’s production
process exhibits constant returns to scale in the production of both commodities
- If O1 were a straight line, joint production would entail no gains
Economies & Diseconomies of Scope:
- Economies of scope = joint output of a single firm is greater than output that could be
achieved by 2 different firms when each produces a single product
- Diseconomies of scope = joint output of a single firm is less than could be achieved by
separate firms when each produces a single product
- No direct relationship between economies of scale & economies of scope
The Degree of Economies of Scope (SC) = percentage of cost savings resulting when 2 or more
products are produced jointly rather than individually
𝐶(𝑞1 ) + 𝐶(𝑞2 ) − 𝐶(𝑞1 , 𝑞2 )
𝑆𝐶 =
𝐶(𝑞1 , 𝑞2 )
- 𝐶(𝑞1 ) = cost of producing only output 𝑞1
- 𝐶(𝑞2 ) = cost of producing only output 𝑞2
- 𝐶(𝑞1 , 𝑞2 ) = joint cost of producing both outputs  physical units of output  𝐶(𝑞1 + 𝑞2 ) 
sum of the individual costs  SC > 0
- The larger the value of SC, the greater the economies of scope
Appendix: Production & Cost Theory – A Mathematical Treatment:
Cost Minimization:
-
Marginal product of capital: 𝑀𝑃𝐾 (𝐾, 𝐿) =
-
Marginal product of labour: 𝑀𝑃𝐿 (𝐾, 𝐿) =
- Minimize C = 𝜔L + rK
- F(𝐾, 𝐿) = 𝑞0
Step 1:
Step 3:
𝑀𝑃𝐾 (𝐾,𝐿)
𝑟
=
𝜕𝐹(𝐾,𝐿)
𝜕2 𝐹(𝐾,𝐿)
>
0,
<0
𝜕𝐾
𝜕𝐾2
2
𝜕𝐹(𝐾,𝐿)
𝜕 𝐹(𝐾,𝐿)
> 0, 𝜕𝐿2 < 0
𝜕𝐿
Step 2:
𝑀𝑃𝐿 (𝐾,𝐿)
𝜔
-
Rewrite 1. & 2. conditions in Step 2:
r/𝑀𝑃𝐾 (𝐾, 𝐿) measures additional input cost of producing an additional unit of output by
increasing capital
- 𝜔/𝑀𝑃𝐿 (𝐾, 𝐿) measures additional cost of producing a unit of output using additional labour
as an input
- The Lagrange multiplier = marginal cost of production
Marginal Rate of Technical Substitution:
- F(𝐾, 𝐿) = 𝑞0 represents a production isoquant
- 𝑀𝑃𝐾 (𝐾, 𝐿)𝑑𝐾 + 𝑀𝑃𝐿 (𝐾, 𝐿)𝑑𝐿 = 𝑑𝑞 = 0
 – dK/dL= 𝑀𝑅𝑇𝑆𝐿𝐾 = 𝑀𝑃𝐿 (𝐾, 𝐿)/𝑀𝑃𝐾 (𝐾, 𝐿)
𝑀𝑃 (𝐾,𝐿)
-
Rewrite condition in Step 3: 𝑀𝑃 𝐿 (𝐾,𝐿) = 𝜔/𝑟
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At the point of tangency of the isoquant & the isocost line  MRTS = ratio of the input
prices  𝑀𝑃𝐿 / 𝜔 = 𝑀𝑃𝐾 /𝑟
Marginal products of all production inputs must be equal when these marginal products are
adjusted by the unit cost of each input
-
𝐾
Applied Microeconomics
Duality in Production & Cost Theory:
- Maximize F(𝐾, 𝐿) subject to 𝜔𝐿 + 𝑟𝐿 = 𝐶0
Step 1:
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Step 2:
Step 3: combine first 2 equations
The Cobb-Douglas Cost & Production Functions:
- Cobb-Douglas production function = production function of the form q = 𝐴𝐾 𝛼 𝐿𝛽 , where q is
the rate of output, K is the quantity of capital, and L is the quantity of labour, and where A, 𝛼,
and 𝛽 are positive constants
- 𝛼<1, 𝛽<1
- If 𝛼 + 𝛽 = 1, the firm has constant returns to scale, because doubling K & L doubles F
- If 𝛼 + 𝛽 > 1, the firm has increasing returns to scale
- If 𝛼 + 𝛽 < 1, it has decreasing returns to scale
Applied Microeconomics
Winter 20/21
Chapter 8 – Profit Maximization & Competitive Supply
8.1 Perfectly Competitive Markets
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Three basic assumptions:
1. Price taking: Firm that has no influence over market price & thus takes the price as given
2. Product homogeneity:
o products of all of the firms in a market are perfectly substitutable with one another
o homogeneous products = commodities
o single market price, consistent with supply-demand analysis
o products heterogeneous  each firm has the opportunity to raise its price above
that of its competitors without losing all of its sales
3. Free entry & exit:
o Condition under which there are no special costs that make it difficult for a firm to
enter or exit an industry
o Buyers easily switch suppliers, & suppliers easily enter/exit a market
When is a Market Highly Competitive?
- Although firms may behave competitively in many situations, there is no simple indicator
that tell us when a market is highly competitive
8.2 Profit Maximization
Do Firms Maximize Profit?
- A manager’s freedom to pursue goals other than long-run profit maximization is limited
- Firms that survive in competitive industries make long-run profit maximization one of their
highest priorities
Alternative Forms of Organization:
- Some forms have objectives that are quite different from profit maximization  cooperative
- Cooperative = association of businesses or people jointly owned & operated by members for
mutual benefit
o Food cooperative: provides members with food & other groceries at the lowest possible
cost; prices are set to avoid losing money, any profits are incidental & are returned to
the members (usually in proportion to their purchases)
o Housing cooperatives/co-ops: members own shares in the corporation, accompanied by
a right to occupy a unit; members can participate in the management of their building
- Condominium = housing unit that is individually owned but provides access to common
facilities that are paid for & controlled jointly by an association of owners
o they share in the payment for the maintenance or operation of those common facilities
8.3 Marginal Revenue, Marginal Cost, & Profit Maximization
profit = difference between total revenue & total cost: 𝜋(q) = R(q) - C(q)
to maximize profit, the firm selects the output for which the difference between revenue &
cost is the greatest
- marginal revenue = change in revenue resulting from a one-unit increase in output  slope
of the revenue curve  firms can sell a greater level of output only by lowering its price
- marginal cost = measures additional cost of producing one additional unit of output  slope
of total cost curve  positive when output = 0 because there’s a fixed cost in the short run
- profit declines from its maximum when output increases above q*
- profit is maximized, when marginal revenue = marginal cost
Demand & Marginal Revenue for a Competitive Firm:
- market price is determined by the industry demand & supply curves
- competitive firm is a price taker
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Q & D for market output & demand; q & d for firm’s output & demand
Demand curve D is downward sloping  horizontal
The demand curve d facing an individual firm in a competitive market is both its average
revenue curve and its marginal revenue curve. Along this demand curve, marginal revenue,
average revenue, and price are all equal.
Profit Maximization by a Competitive Firm:
- A perfectly competitive firm should choose its output so that marginal cost equals price:
𝑀𝐶(𝑞) = 𝑀𝑅 = 𝑃
8.4 Choosing Output in the Short Run
Short-Run Profit Maximization by a Competitive Firm:
- Marginal revenue equals marginal cost at a point at which the marginal cost curve is rising
- Output Rule: if a firm is producing any output, it should produce at the level at which
marginal revenue equals marginal cost
- At the profit-maximizing output q*, the price P is less than average cost
8.5 The Competitive Firm’s Short-Run Supply Curve
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Supply curve = portion of the marginal cost curve for which marginal cost is greater than
average variable cost
Slope upward  increase in the market price will induce those firms already in the market
to increase the quantities they produce  total profit also increases
The Firm’s Response to an Input Price Change: output needs to be reduced
8.6 The Short-Run Market Supply Curve
- = amount of output that the industry will produce in the short run for every possible price
- = sum of the supply curves of the individual firms
Elasticity of Market Supply:
- Price rises  output expands  increases demand for inputs to production & may lead to
higher input prices
- Increasing prices shifts the marginal cost curve upward
- Price elasticity measures sensitivity of industry output to market price  always positive
-
∆𝑄
𝑄
∆𝑃
𝑃
𝐸𝑆 = ( )/( )  percentage change in Q in response to a 1-unit change in P
-
Perfectly inelastic supply = rises, when the industry’s plant & equipment are so fully utilized
that greater output can be achieved only if new plants are built
- Perfectly elastic supply = arises when marginal cost is constant
Producer Surplus in the Short Run:
- Producer surplus = sum over all units produced by a firm of differences between the market
price of a good & the marginal cost of production
- It measures the area above a producer’s supply curve & below the market price
- It’s the difference between the firm’s revenue & its total variable cost
Producer Surplus versus Profit:
- Producer surplus = revenue – variable cost  variable profit
- Total profit = revenue – fixed cost – variable cost
- When fixed cost is positive, producer surplus is greater than profit
- The area under the marginal cost curve from 0 to q* is TC(q*) - TC(0) = TC - FC = VC
- Producer surplus lies below the market price & above the supply curve between the output
levels 0 & Q*
8.7 Choosing in the Long Run
Long-Run Profit Maximization:
- Horizontal demand curve
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LAC = presence of economies of scale; at higher output levels  diseconomies of scale
LMC cuts LAC from below at the point of minimum of LAC
Long-run output of a profit-maximizing competitive firm is the point at which long-run
marginal cost equals the price
Long-Run Competitive Equilibrium:
- Accounting profit = difference between the firm’s revenues & its cash flows for labour, raw
materials, & interest plus depreciation expenses  R – 𝜔L  positive
- Economic profit takes opportunity costs into account  𝜋=R – 𝜔L – rK
- Zero economic profit = a firm is earning a normal return on its investment  it’s doing as
well as it could by investing its money elsewhere
- Entry & exit: a firm enters when it can earn a positive long-run & exits when it faces the
prospect of a long-run loss
- Long-run competitive equilibrium = all firms in an industry are maximizing profit, no firm has
an incentive to enter or exit, & price is such that quantity supplied = quantity demanded
- Economic rent = amount that firms are willing to pay for an input less the minimum amount
necessary to obtain it
o Zero economic profit tells a firm that it should remain in a market only if it is at least as
efficient in production as other firms.
o It also tells possible entrants to the market that entry will be profitable only if they can
produce more efficiently than firms already in the market.
Producer Surplus in the Long Run:
- Consists of economic rent that it enjoys from all its scarce inputs
-
8.8 The Industry’s Long-Run Supply Curve
-
Shape depends on the extent of which increases & decreases in industry output affect the
prices that firms must pay for input into the production process
- Economies of scale: input prices will decline as output increases
- Diseconomies: input prices may increase with output
- 3. Possibility: input costs may not change with output
- Output is increased by using more inputs
- It’s useful to distinguish between 3 types of industries:
1. Constant-cost industry = long-run supply curve is
horizontal, at a price = long-run minimum average
cost of production  figure 1
2. Increasing-cost industry = long-run supply curve is
upward sloping  figure 2
3. Decreasing-cost industry = long-run supply curve is
downward sloping
The Effects of a Tax:
1. output tax is imposed only on this firm & doesn’t affect
the market price of the product  the tax on output encourages the firm to reduce q
2. every firm in the industry is taxed & so has increasing marginal costs  each firm reduces its
output at the current market price, the total output supplied by the industry will also fall,
causing the price of the product to increase
Long-Run Elasticity of Supply:
- constant-cost industry: long-run supply curve is horizontal; long-run supply elasticity is
infinitely large
- increasing-cost industry: long-run supply elasticity is positive but finite
Applied Microeconomics
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Chapter 9 – The Analysis of Competitive Markets
9.1 Evaluating the Gains and Losses from Government Policies – Consumer and
Producer Surplus
Review if Consumer & Producer Surplus:
- Consumer Surplus = total benefit/value consumers receive beyond what they pay for
o Area between the demand curve & market price
o Measures total net benefit to consumers
- Producer Surplus = benefit lower-cost producers enjoy by selling at the market price
o Difference between market price the producer receives & marginal cost of producing
o Area between supply curve & market price
Application of Consumer & Producer Surplus:
- Welfare effects = gains & losses to consumers & producers
- Changes that result from the government price-control policy:
1. Change in Consumer Surplus:
- Those who are worse off  rationed out of the market due to
the reduction in production
- Better off  they can buy the good at a lower price  they
enjoy an increase in consumer surplus A reduction of price in
each unit times number of units that can be bought
- Net change = A – B  positive
2. Change in Producer Surplus:
- Producers that remain in the market: receive lower price for their output  A
- Additional loss for those who left & those who stayed but produce less  C
- Total change = – A – C
3. Deadweight Loss = net loss of total surplus:
- Total change in surplus = (A – B) + (–A – C) = –B – C
-
If demand curve is very inelastic, price controls can result in a net loss of consumer surplus
Because consumers value the good highly, those who are rationed out suffer a large loss
9.2 The Efficiency of a Competitive Market
-
-
Economic efficiency = maximization of aggregate consumer & producer surplus
Market Failure = situation in which an unregulated competitive market is inefficient because
prices fail to provide proper signals to consumers & producers
Market failure can occur:
1. Externalities = action taken by either a producer or consumer which affects other
producers or consumers but is not accounted for by the market price
2. Lack of Information: utility-maximizing purchasing decisions can’t be made
In the absence of externalities or a lack of information, an unregulated competitive market
does lead to the economically efficient output level.
o Price ceiling: lower quantity, producers & consumers in the aggregate are worse off
o Price is required to be above the market-clearing price: producers would like to produce
more at a higher price, consumers will buy less
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If producers produce only what can be sold, the market
output level is lower  there’s a net loss of total surplus
Some consumers are no longer buying  B
Some producers are no longer producing  C
This gives an optimistic assessment of the efficiency cost
of policies that force price above market-clearing levels
Some producers might increase their capacity & output
levels  unsold output
Or the government might buy up unsold output to
maintain production Q2 or close to it
In both cases, the total welfare loss will exceed the areas of B & C
9.3 Minimum Prices
-
-
-
One way to raise prices above market-clearing levels is by direct regulation
Pmin denotes a minimum price set by the government 
quantity supplied Q2 & quantity demanded Q3 
difference: unsold supply
Consumers who still purchase the good must pay a higher
price & suffer a loss of surplus  A
Consumers who dropped out  B
Total change in consumer surplus = ∆𝐶𝑆 = −𝐴 − 𝐵
Consumers are worse off
Producers receive a higher price for the units they sell  increase of surplus  A
Drop in sales results in a loss of surplus  C
If quantity produced increases from Q0 to Q2  because they only sell Q3, there is no
revenue to cover the cost in producing Q2 – Q3
The area under the supply curve from Q3 to Q2 is the cost of producing the quantity Q2 – Q3
 D  unless producers respond to unsold output by cutting production, the total change
in producer surplus = ∆𝑃𝑆 = 𝐴 − 𝐶 − 𝐷
This form of government intervention can reduce producers’ profits because of the cost of
excess production
Another example is the minimum wage law  higher than market-clearing wage  results
in unemployment
9.4 Price Supports & Production Quotas
Price support = price set by government above free-market level &
maintained by governmental purchases of excess supply
- Consumers: at Ps the quantity demanded falls, but the quantity
supplied increases
o To maintain the price & avoid having inventories pile up, the
government must buy the quantity excess
- Producers: gain  sell a larger quantity at a higher price Ps 
∆𝑃𝑆 = 𝐴 + 𝐵 + 𝐷
- Government: cost to the government must be paid for by taxes  cost to consumers
o Cost may be reduced if the government can dump some of its purchases  export
o This hurts the ability of domestic producers to sell in foreign markets
o Total change in welfare = ∆𝐶𝑆 + ∆𝑃𝑆 − 𝐶𝑜𝑠𝑡 𝑡𝑜 𝐺𝑜𝑣𝑡. = 𝐷 − (𝑄2 − 𝑄1)𝑃𝑠
Production Quotas:
- Government can raise the price by reducing supply  decree/quotas
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Supply curve becomes the vertical line S’ at Q1
Consumer surplus is reduced by A + B
Producers gain A but lose C
Deadweight loss: B + C
Incentive programs: acreage limitation programs give
farmers incentives to limit the planted acreage  supply
curve becomes inelastic at Q1 & market price is
increased from P0 to Ps
∆𝐶𝑆 = −𝐴 − 𝐵
∆𝑃𝑆 = 𝐴 − 𝐶 + 𝑃𝑎𝑦𝑚𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 𝑛𝑜𝑡 𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑛𝑔  = 𝐴 + 𝐵 + 𝐷
∆𝑊𝑒𝑙𝑓𝑎𝑟𝑒 = −𝐴 − 𝐵 + 𝐴 + 𝐵 + 𝐷 − 𝐵 − 𝐶 − 𝐷 = −𝐵 − 𝐶
9.5 Important Quotas & Tariffs
-
Import quota = limit on the quantity of a good that can be imported
Tariff = tax on an imported good
Imports are the difference between domestic consumption & domestic production Qd – Qs
Total change in consumer surplus = ∆𝐶𝑆 = −𝐴 − 𝐵 − 𝐶
Producer surplus = ∆𝑃𝑆 = 𝐴
Total surplus = –B – C  consumers lose more than producers gain
The effect of tariff collection on consumers & producers would be the same as with a quota
If tariff T is imposed on imports, then domestic price will rise to P*
o Domestic production will rise & domestic consumption will fail
o ∆𝐶𝑆 = −𝐴 − 𝐵 − 𝐶 − 𝐷
∆𝑃𝑆 = 𝐴
o ∆𝑊𝑒𝑙𝑓𝑎𝑟𝑒 = −𝐴 − 𝐵 − 𝐶 − 𝐷 + 𝐴 + 𝐷 = −𝐵 − 𝐶
9.6 The Impact of a Tax or Subsidy
-
The share of a tax borne by consumers depends on the shapes of the supply & demand
curves & on the relative elasticities
- Effects of a specific tax:
o Specific tax = tax of a certain amount of money per unit sold
o The price the buyer must exceed the net price the seller receives by t cents
- Market clearing requires four conditions to be satisfied after the tax:
1. Quantity sold & buyer’s price Pb must lie on the demand curve 𝑄 𝐷 = 𝑄 𝐷 (𝑃𝑏 )
2. Quantity sold & seller’s price Ps must lie on the supply curve  𝑄 𝑆 = 𝑄 𝑆 (𝑃𝑠 )
3. Quantity demanded must equal quantity supplied  𝑄 𝐷 = 𝑄 𝑆
4. Difference between the price the buyer pays & the price the seller receives must equal
the tax t  𝑃𝑏 − 𝑃𝑠 = 𝑡
- Tax results in a deadweight loss: ∆𝐶𝑆 = −𝐴 − 𝐵
∆𝑃𝑆 = −𝐶 − 𝐷
 −𝐵 − 𝐶
- If demand is relatively inelastic & supply is relatively elastic, the burden of the tax will fall
mostly on buyers
- If demand is relatively elastic & supply is relatively inelastic, the burden of the tax will fall
mostly on sellers
- A tax falls mostly on the buyer if 𝐸𝑑 /𝐸𝑠 is small, & mostly on the seller if 𝐸𝑑 /𝐸𝑠 is large
- Pass-through fraction = 𝐸𝑠 /(𝐸𝑠 − 𝐸𝑑 )
The Effects of a Subsidy:
- Subsidy = payment reducing the buyer’s price below the seller’s price, i.e., a negative tax
- The effect is the opposite of the effect of a tax  quantity will increase
- The benefit of a subsidy accrues mostly to buyers if 𝐸𝑑 /𝐸𝑠 is small & mostly to sellers if
𝐸𝑑 /𝐸𝑠 is large.
- 4 conditions needed for the market to clear:
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𝑄 𝐷 = 𝑄 𝐷 (𝑃𝑏 )
𝑄 𝑆 = 𝑄 𝑆 (𝑃𝑠 )
𝑄𝐷 = 𝑄 𝑆
𝑃𝑏 − 𝑃𝑠 = 𝑠
Chapter 10 – Market Power: Monopoly and Monopsony
Monopoly = market that has only one seller but many buyers
- Demand curve = market demand curve
o Demand curve relates the price received to the quantity offered for sale
o Quantity will be lower & its price higher than those of a competitive market
- Pure monopoly is rare
Monopsony = market with many sellers but only one buyer
- Monopsonist pay a price that depends on the quantity that maximizes its net benefit from
the purchase  value derived from the good less the money paid for it
- Pure monopsony is rare
- Buyers have monopsony power
Market power = ability of a seller or buyer to affect the price of a good
- E.g., monopoly & monopsony
10.1 Monopoly
-
To maximize profit, the monopolist must determine its cost & the characteristics of market
demand, then decide how much to produce & sell
Average Revenue and Marginal Revenue:
- Average revenue = price received per unit sold  market demand curve
- Marginal revenue = change in revenue resulting from a one-unit increase in output
- When positive  total revenue is increasing with quantity
- When negative  revenue is decreasing
- Demand curve is downward sloping  AR > MR (all units are sold at the same price)
- An increase by 1 unit in sales, price falls  all units sold will earn less revenue
- Demand curve is a straight line  marginal revenue curve has 2x the slope of demand curve
The Monopolist’s Output Decision:
- To maximize profit, a firm must set output so that marginal revenue is equal to marginal cost
∆𝜋/∆𝑄 = ∆𝑅/∆𝑄 − ∆𝐶/∆𝑄 = 0

MR – MC = 0 or MR = MC
∆𝑅/∆𝑄 = 𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑟𝑒𝑣𝑒𝑛𝑢𝑒
∆𝐶/∆𝑄 = 𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑐𝑜𝑠𝑡
- Q* is the output level at which MR = MC
- At Q1, firm sacrifices some profit  extra revenue (Q1-Q*) > cost
- At Q2: reduce profit  additional cost > additional revenue
A Rule of Thumb for Pricing:
-
Marginal revenue: MR =
∆𝑅
∆𝑄
=
∆(𝑃𝑄)
∆𝑄
o Producing 1 extra unit & selling it at P brings in revenue (1)(P) = P
o Downward sloping demand curve  producing & selling this extra unit results in a small
drop in price ∆𝑃/∆𝑄 which reduces the revenue from all units sold [Q(∆𝑃/∆𝑄)]
∆𝑃
𝑄
∆𝑃
-
So, 𝑀𝑅 = 𝑃 + 𝑄 ∆𝑄 = 𝑃 + 𝑃(𝑃 )(∆𝑄)
-
𝐸𝑑 = (𝑃/𝑄 )(∆𝑄/∆𝑃) 
-
Since MR = MC 
𝑃−𝑀𝐶
𝑃
1/𝐸𝑑 = (𝑄/𝑃)(∆𝑃/∆𝑄)
1
= −𝐸
𝑑
𝑀𝐶
 𝑃 = 1+(1/𝐸
𝑑)
1
 𝑀𝑅 = 𝑃 + 𝑃(𝐸 )
𝑑
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A monopolist charges a price that exceeds marginal cost, but by an amount that depends
inversely on the elasticity of demand
- If demand is extremely elastic, 𝐸𝑑 is a large negative number, & price will be very close to
MC  monopolized market will look much like a competitive one  little benefit
- A monopolist will never produce a quantity of output that is on the inelastic portion of the
demand curve, where 𝐸𝑑 < 1 in absolute value
- The firm will produce at the point where the elasticity of demand is exactly -1
Shifts in Demand:
- A monopolistic market has no supply curve  there is no one-to-one relationship between
price & quantity produced
- A monopolist’s output depends on MC & the shape of the demand curve
- Shifts in demand can lead to changes in price with no change in output, changes in output
with no change in price, or changes in both price & output
- Demand curve shifts down & rotates  quantity is unchanged, price falls
- Demand curve shifts up & rotates  larger quantity, price unchanged
The Effect of a Tax:
- Price can sometimes rise by more than the amount of the tax
- If tax t is levied, the firm’s marginal (& average) cost increases by t  MR = MC + t
- Marginal cost curve shifts upward by t
- Shifting marginal cost curve upwards results in a smaller quantity & higher price
The Multiplant Firm – 2 plants:
- Step 1: total output should be divided between the two plants so that marginal cost is the
same in each plant.
- Step 2: total output must be such that MR = MC  profit maximized: MR = MC at each plant
10.2 Monopoly Power
Production, Price, & Monopoly Power:
- Determining the elasticity of demand for a firm’s product is usually more difficult than
determining the market elasticity of demand
- If a firm had a good knowledge of its demand curve, then it could have monopoly power 
it can profitably charge a price greater than marginal cost
Measuring Monopoly Power:
- For a competitive firm, price equals marginal cost; for the firm with monopoly power, price
exceeds marginal cost
- A way to measure monopoly power, is to examine the extent to which the profit-maximizing
price exceeds marginal cost
- Lerner Index of Monopoly Power = measure of monopoly power calculated as excess of
price over marginal cost as a fraction of price  𝐿 = (𝑃 − 𝑀𝐶)/𝑃
o value between 0 & 1
o perfectly competitive: P=MC  L=0
o 𝐿 = (𝑃 − 𝑀𝐶)/𝑃 = −1/𝐸𝑑
 𝐸𝑑 elasticity of the firm’s demand curve
- Profit depends on average cost relative to price  more monopoly power ≠ higher profit
The Rule of Thumb for Pricing:
𝑀𝐶
1+(1/𝐸𝑑 )
-
𝑃=
-
But 𝐸𝑑 is the firm’s elasticity of demand, not that of the market
The manager must eliminate the percentage change in the firm’s unit sales that is likely to
result from a 1% change in the firm’s price
Given an estimate of the firm’s 𝐸𝑑 , the manger can calculate the proper markup
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If 𝐸𝑑 is large, markup will be small  very little monopoly power
𝐸𝑑 small, markup will be large  considerable monopoly power
10.3 Sources of Monopoly Power
- 3 factors determine a firm’s elasticity of demand:
1. The elasticity of market demand: firm’s own demand will at least be as elastic as market
demand; elasticity of market demand limits the potential for monopoly power
2. The number of firms in the market: if there are many firms, it is unlikely that any one form
will be able to affect price significantly
3. The interaction among firms: each firm is unable to profitably raise price very much if rivalry
among them is aggressive, with each firm trying to capture as much of the market as it can
The Elasticity of Market Demand:
- Several firms compete with each other  𝐸𝑑 of market sets a lower limit on the magnitude
of the elasticity of demand for each firm
- No matter how they compete, the 𝐸𝑑 for each firm could never become smaller in
magnitude than that of the market
The Number of Firms:
- Monopoly power for each firm will fall as the number of firms increases
- What matters is the number of major players  firms with significant market share
- Barrier to entry = condition that impedes entry by new competitors  competitive strategy
- Natural barriers: patent, copyright, government license
- Economies of scale may make it too costly for more than a few firms to supply the entire
market  natural monopoly might be more efficient
The Interaction Among Firms:
- Monopoly power is smaller when firms compete aggressively
- Monopoly power is larger when they cooperate
- Demand curve might be very inelastic in the short run but much more elastic in the long run
- Real or potential monopoly power in the short run can make an industry more competitive
in the long run  large short-run profits can induce new firms to enter an industry, thereby
reducing monopoly power over the longer term
10.4 The Social Costs of Monopoly Power
Monopoly power implies, that price exceed marginal cost  higher prices, lower quantity
Because of the higher price, those consumers who buy the good lose surplus  A
Consumers who do not buy the good at 𝑃𝑚 but at 𝑃𝑐 : lose surplus  B
Total loss of consumer surplus  A + B
Producer gains A by selling at a higher price, but loses C (additional
profit it would have earned by selling 𝑄𝑐 − 𝑄𝑚 at 𝑃𝑐 )
- Total gain in producer surplus  A – C
- Deadweight loss  B + C  social cost of inefficiency
Rent Seeking:
= spending money in socially unproductive efforts to acquire, maintain, or
exercise monopoly
- Social cost is likely to exceed the deadweight loss in B + C  rent seeking
- Rent seeking might involve lobbying activities to obtain government regulations that make
entry by potential competitors more difficult, …
- The larger the transfer from consumers to the firm (A), the larger the social cost
Price Regulation:
- Price regulation P can eliminate the deadweight loss that results from monopoly power
-
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If a firm cannot charge more than P, its new average revenue curve is a horizontal line at P
For output levels greater than Q, the new average revenue curve is identical to the old AR
curve  the firm will charge less than P & will be unaffected by the regulation
- The new marginal revenue curve corresponds to its new AR curve
- For output levels greater than Q, the new MR curve is identical to the original curve
- Complete MR curve now has 3 pieces: horizontal line at P for quantities up to Q; vertical line
at Q connecting the original AR & MR curves; original MR curve for quantities greater than Q
- At P & Q, the deadweight loss is reduced
Natural Monopoly:
- = firm that can produce the entire output of the market at a cost lower than what it would
be if there were several firms
- It usually arises when there are strong economies of scale
- If the firm represented by the figure was broken up into two competing firms, each
supplying half the market, the average cost for each would be higher than the cost incurred
by the original monopoly
- Minimum feasible price is found at the point at which average cost & demand intersect
Regulation in Practice:
- Rate-of-return regulation = maximum price allowed by a regulatory agency is based on the
(expected) rate of return that a firm will earn
- Difficulties:
o A firm’s capital stock is difficult to value
o A “fair” rate of return must be based on the firm’s actual cost of capital, that cost
depends in turn on the behaviour of the regulatory agency
o Often leads to delays in the regulatory response to changes in cost & other market
conditions  net result is regulatory lag
- Price caps: based on firms’ variable costs, past prices, & inflation & productivity growth
o More flexibility than rate-of-return regulation
10.5 Monopsony
-
Monopsony = market with a single buyer
Oligopsony = market with only a few buyers
Monopsony power = buyer’s ability to affect the price of a good (price < competitive market)
Marginal value = additional benefit derived from purchasing one more unit of a good
Marginal value schedule is the demand curve for the good  downward sloping
Marginal expenditure = additional cost of buying one more unit of a good
o Depends on  competitive or monopsony buyer
- Average expenditure = price paid per unit of a good  the same for all units
- Marginal expenditure = average expenditure = market price of the good
- Supply curve = average expenditure curve  upward sloping  marginal
expenditure curve must lie above it
Monopsony & Monopoly Compared:
- Monopolist produces where marginal revenue intersects marginal cost.
Average exceeds marginal revenue, so that price exceeds marginal cost
- Monopsonist purchases up to where marginal expenditure intersects
marginal value. Marginal expenditure exceeds average expenditure, so
that the marginal value exceeds price
10.6 Monopsony Power
-
= buyer’s ability to affect the price of a good
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A buyer with monopsony power can purchase a good at a price below marginal value 
extent depends on elasticity of supply facing the buyer
- Supply is very elastic  𝐸𝑆 is large, markdown is small, buyer has little monopsony power
- Supply inelastic  𝐸𝑆 is small, markdown is large, buyer has considerable monopsony power
Sources of Monopsony Power – depends on 3 things:
1. Elasticity of Market Supply:
- Upward-sloping supply curve  marginal expenditure exceeds average expenditure
- The less elastic, the greater the difference between marginal & average expenditure &
the more monopsony power
- Highly elastic  small monopsony power & little gain in being the only buyer
2. Number of Buyers:
- Large  no single buyer can have much influence over price  each buyer faces an
extremely elastic supply curve  almost competitive market
- Potential for monopsony power  number of buyers is limited
3. Interaction Among Buyers:
- Buyers compete aggressively  bid up price close to their marginal value of the
product, & will thus have little monopsony power
- Buyers compete less aggressively/collude  prices will not be bid up very much, buyers’
degree of monopsony power might be nearly as high as if there were only one buyer
The Social Costs of Monopsony Power:
- Monopsony power results in lower prices & lower quantities purchased
- Monopsonist’s net benefit is maximized by purchasing a quantity 𝑄𝑚 at 𝑃𝑚  MV = ME
- Lower price  producers lose A & C  reduced sales
- Total loss of producer surplus  A + C
- Consumers gain A  lower price & loses B  buy less
- Total gain in consumer surplus  A – B
- Deadweight loss from monopsony power  B + C
Bilateral Monopoly:
- = market with only one seller & one buyer
- Both the buyer & seller are in a bargaining situation
- Such situations are rare
- Monopsony power & monopoly power will tend to counteract each other
- In general, monopsony power will push price closer to marginal cost, & monopoly power will
push price closer to marginal value
-
10.7 Limiting Market Power: The Antitrust Laws
-
Excessive market power raises problems of equity & fairness: if a firm has significant
monopoly power, it will profit at the expense of consumers
- Natural monopoly: direct price regulation limits market power
- Generally: prevent firms from obtaining excessive market power  mergers & acquisitions
 prevent firms that already have market power from using it to restrict competition
- Antitrust laws: rules & regulations prohibiting actions that restrain competition
o It is not illegal to be a monopolist or to have market power
Restricting What Firms Can Do:
- Section 1 of the Sherman Act (1890): prohibits contracts, combinations, or conspiracies in
restraint of trade
o Implicit collusion  parallel conduct (= one firm consistently follows actions of another)
can be construed as violating the law
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Section 2: it’s illegal to monopolize or to attempt to monopolize a market & prohibits
conspiracies that result in monopolization
o Predatory pricing = pricing to drive current competitors out of business & to discourage
new entrants in a market so that a firm can enjoy higher future profits
- Clayton Act (1914) prohibits mergers & acquisitions if they “substantially lessen
competition” or “tend to create a monopoly”
- Federal Trade Commission Act  deceptive advertising & labelling, agreements with
retailers to exclude competing brands, …
Enforcement of the Antitrust Laws:
1. Through the Antitrust Division of the Department of Justice. As an arm of the executive
branch, its enforcement policies closely reflect the view of the administration in power.
Responding to an external complaint or an internal study, the department can institute a
criminal proceeding, bring a civil suit, or both. The result of a criminal action can be fines for
the corporation & fines or jail sentences for individuals. Losing a civil action forces a
corporation to cease its anticompetitive practices & often to pay damages.
2. Through the administrative procedures of the Federal Trade Commission. Action can result
from an external complaint or from the FTC’s own initiative. Should the FTC decide that
action is required, it can either request a voluntary understanding to comply with the law or
seek a formal commission order requiring compliance.
3. Through private proceedings. Individuals or companies can sue for treble (three-fold)
damages inflicted on their businesses or property. The prospect of treble damages can be a
strong deterrent to would-be violators. Individuals or companies can also ask the courts for
injunctions to force wrongdoers to cease anticompetitive actions.
Antitrust in Europe:
- Separate & distinct antitrust authorities within individual member states are responsible for
those issues whose effects are felt largely or entirely within particular countries
- Article 101 of the Treaty of the European Community is similar to Section 1 of Sherman Act
- Article 102: abuses of market power by dominant forms  Section 2
- Europe only imposes civil penalties, whereas the U.S. can impose prison sentences & fines
Chapter 11 – Pricing with Market Power
-
Managers of a monopoly must worry about the characteristics of demand  estimate of the
elasticity of demand to determine price
Objective: capturing consumer surplus & converting it into additional profit
11.1 Capturing Consumer Surplus
-
maximize profit  P* & Q* at the intersection of marginal cost & marginal revenue curves
To capture consumer surplus  charge different prices to different customers, according to
where they are along the demand curve  price discrimination
11.2 Price Discrimination
First-Degree Price Discrimination:
- = Firms charge customers at reservation price (=maximum price a customer is willing to pay)
- Incremental profit for P* is needed  P*Q* = MR – MC  for Q*, MR = MC
- Sum of each incremental unit produced  variable profit (= area between MR & MC curves)
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- Consumer surplus = area between AR curve & P*
Perfect Price Discrimination – almost never possible:
- MR is no longer relevant to output decision
- Incremental revenue earned = price paid  given by demand curve
- Price discrimination doesn’t affect the cost structure  MC curve
- The additional profit from producing & selling an incremental unit is
the difference between demand & marginal cost
- Demand > marginal cost  profit by expanding production until demand = MC
- Variable profit  area between demand & MC curves
- All consumer surplus is captured by the firm
Imperfect Price Discrimination – often used by professionals:
- Charging a few different prices based on estimates of customers’ reservation prices
- Client’s willingness to pay can be assessed & fees set accordingly
- Lowest price charged  MC intersects demand curve
- People who aren’t willing to pay P* or greater, are better off  some consumer surplus
- If price discrimination brings enough new customers into the market, consumer welfare can
increase to the point that both producer & consumers are better off
Second-Degree Price Discrimination:
- In some markets  reservation price declines with the number of units purchased
- Discriminate by charging different prices for different quantities  second-degree
- E.g. quantity discounts, blocking pricing (=different prices for different “blocks”)
- Scale economies cause AC & MC to decline  block pricing encouraged  expands output,
greater scale economies, increases consumer welfare, greater profit
Third-Degree Price Discrimination:
- = divides consumers into 2+ groups with separate demand curves & charges different prices
- E.g. regular vs special airline fares, premium vs nonpremium brands, canned vs frozen, …
Creating Consumer Groups:
1. Total output should be divided between the groups, so MR are equal  profit max
2. Total output must be such that MR = MC
- Algebraically: 𝜋 = 𝑃1 𝑄1 + 𝑃2 𝑄2 − 𝐶(𝑄𝑇 )
∆𝜋
-
Incremental profit to the 1. Group = 0  ∆𝑄 =
-
∆(𝑃1 𝑄1 )
∆𝑄1
1
= 𝑀𝑅1 ;
∆𝐶
∆𝑄1
= MC

∆(𝑃1 𝑄1 )
∆𝐶
− ∆𝑄
∆𝑄1
1
=0
𝑀𝑅1 = 𝑀𝐶; 𝑀𝑅2 = 𝑀𝐶
- Prices & output must be set so that 𝑀𝑅1 = 𝑀𝑅2 = 𝑀𝐶
Determining Relative Prices:
- MR can be written in terms of the elasticity of demand: 𝑀𝑅 = 𝑃(1 + 1/𝐸𝑑 )
1
1
2
1
-
Equating 𝑀𝑅1 = 𝑀𝑅2  𝑃1 /𝑃2 = (1 + 𝐸 )/(1 + 𝐸 )
-
Higher price will be charged for customers with lower demand elasticity
To find quantities 1 & 2  horizontal line at intersection of MC & 𝑀𝑅𝑇 (at 𝑄𝑇 )
If demand is small for the 2. Group & MC is rising steeply, the increased cost of producing &
selling to the group may outweigh the increase in revenue  better off at a single price P*
11.3 Intertemporal Price Discrimination & Peak-Load Pricing
-
Intertemporal price discrimination: separating consumers with different demand functions
into different groups by charging different prices at different points in time
- Peak-load pricing: charging higher prices during peak periods when capacity constraints
cause MC to be high
Intertemporal Price Discrimination:
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Divides into high-demand & low-demand groups  higher price at first but falls later
E.g.: higher price for new, technologically advanced equipment for a small group who value
the product highly & after, price is lowered for a larger group (more elastic demands) who
are willing to forgo the product if the price is too high
Peak-Load Pricing:
- Objective: increase economic efficiency by charging prices that are close to MC
- MC = MR for each period  prices for peak & nonpeak period
- Increases profit & is more efficient: sum of producer & consumer surplus is greater because
prices are closer to MC
- For monopolist: prices are set at point where demand curves intersect with MC curve
-
11.4 The Two-Part Tariff
- = charges consumers both an entry & a usage fee
- E.g. amusement park, tennis & golf clubs, telephone service, …
- Problem: how to set entry vs usage fee
Single Consumer:
- Set usage fee P = MC & entry fee T = total consumer surplus for each consumer
- Pays T* to use the product & P* = MC per unit consumed  all consumer surplus captured
Two Consumers:
- Set usage fee above MC & entry fee = remaining consumer surplus (smaller demand)
- P* > MC  profit = 2T*+(P* – MC)( 𝑄1 + 𝑄2 )
- To determine the exact values of P* & T*, knowledge of the demand curves is needed
Many Consumers:
- There is no simple formula to calculate two-part tariff
- Trade-off:
o Lower entry fee  more entrants  more profit
o As entry fee falls  entrants larger  profit falls
- Profit max  starting with a price for sales P, finding optimum entry fee T, then estimating
resulting profit  P is then changed, entry fee calculated, along with the new profit level
- If consumers’ demands are fairly similar  charge P closer to MC & make T large
- Different demands  set P > MC & lower T  two-part tariff less effective  single price
Two-part tariff with a twist:
- Entry fee T entitles the customer to a certain number of free units  lets firms set higher
entry fee without losing as many small customers  captures their surplus without driving
them out of the market, while also capturing more of surplus of large customers
11.5 Bundling
- = selling 2 or more products as a package
- Bundling: when customers have heterogeneous demands & the firm can’t price discriminate
Relative Valuations:
- Relative valuations of the products are reversed  demands are negatively correlated
- Sold as a bundle for a total price of 𝑃𝐵 = 𝑟1 +𝑟2
- Consumers have reservation prices that add up to more than 𝑃𝐵  will buy
- Consumers  reservation prices less than 𝑃𝐵  won’t buy  lost to the firm
- Demands perfectly positively correlated  no gain in bundling
- Demands perfectly negatively correlated  bundling  all consumer surplus extracted
Mixed Bundling:
- = selling 2 or more both as a package & individually
- Pure bundling = selling products only as a package
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When demands are only somewhat negatively correlated &/or MP costs are significant
Even if demands are perfectly negatively correlated, mixed bundling is the most profitable
 for each good, marginal production cost exceeds the reservation price of one consumer
- If marginal costs = 0  mixed bundling is not the preferred strategy  could be more
profitable than pure bundling if demands aren’t perfectly negatively correlated
Bundling in Practice:
- By conducting market surveys, firms may be able to estimate the distribution of reservation
prices, & then use this info to design a pricing strategy
- They might first choose a price for the bundle, then try individual prices  separate
consumers into 4 regions (buys: nothing, both, good 1, good 2)  calculate resulting profits
- Then raise or lower 𝑃𝐵 , 𝑃1 , 𝑃2  see if it leads to higher profits  until rough estimate
Tying:
- = requirement that products be bought or sold in some combination
- Pure bundling, copying machine – paper
- Benefits: allows a firm to meter demand & practice price discrimination more effectively;
extends market power; protects consumer good-will connected with a brand name
11.6 Advertising
Firm with market power  suppose it sets only 1 price & knows its quantity demanded
depends on both its price & advertising expenditures  Q (P, A)
- Advertising causes the demand curve to shift out & to the right
- AR & MR curves are AR’ & MR’; AC rises to AC’ MC remains the same
- It must choose its price & advertising expenditure A to maximize profit, which is now:
𝜋 = 𝑃𝑄(𝑃, 𝐴) − 𝐶(𝑄) − 𝐴
- More advertising  more sales & more revenue
- It should increase advertising until MR from an additional dollar of advertising = full MC
- Full MC = sum of the dollar spent directly on advertising & MP cost from increased sales 
∆𝑄
∆𝑄
𝑀𝑅𝐴𝑑𝑠 = 𝑃
= 1 + 𝑀𝐶
= 𝑓𝑢𝑙𝑙 𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑎𝑑𝑣𝑒𝑟𝑡𝑖𝑠𝑖𝑛𝑔
∆𝐴
∆𝐴
A Rule of Thumb for Advertising:
- Rule of thumb for pricing: (𝑃 − 𝑀𝐶)/𝑃 = −1/𝐸𝐷
-
-
-
∆𝑄
𝐴
Rewrite equation in 11.6: (𝑃 − 𝑀𝐶) ∆𝐴 = 1  multiply both sides by 𝑃𝑄 (advertising-to-sales
ratio = ratio of advertising expenditures to sales):
𝑃 − 𝑀𝐶 𝐴 ∆𝑄
𝐴
[
]=
𝑃
𝑄 ∆𝐴
𝑃𝑄
Advertising elasticity of demand (term in the brackets) = percentage change in quantity
demanded resulting from a 1% increase in advertising expenditure  𝐸𝐴
So  𝐴/𝑃𝑄 = −(𝐸𝐴 /𝐸𝑃 )  rule of thumb for advertising  profit max
Advertising-to-sales ratio = –ratio of advertising & price of elasticities of demand
Firms should advertise a lot if demand is very sensitive to advertising (𝐸𝐴 is large) or if
demand is not very price elastic (𝐸𝑃 is small)
A small elasticity of demand implies a large markup of price over marginal cost
Chapter 12 – Monopolistic Competition and Oligopoly
-
Monopolistic competition is similar to a perfectly competitive market:
o There are many firms, & entry by new firms are not restricted
o Difference: the product is differentiated  each firm sells a brand or version of the
product that differs in quality, appearance, or reputation, and each firm is the sole
producer of its own brand
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Amount of monopoly power depends on its success in differentiating its product from those
of other firms (e.g. toothpaste, laundry detergent, packaged coffee)
Oligopoly: a few firms compete with one another, & entry by new firms is impeded
o Product might be differentiated, or it might not be
Monopoly power & profitability in oligopolistic industries depend in part on how the firms
interact
Cartel: some or all firms explicitly collude  they coordinate prices & output levels to
maximize joint profits  different from monopoly:
o Cartels must consider how pricing decisions will affect noncartel production levels
o Members of a cartel are not part of one big company: they may be tempted to “cheat”
their partners by undercutting prices & grabbing bigger shares of the market
o  many cartels tend to be unstable & short-lived
12.1 Monopolistic Competition
The Making of Monopolistic Competition:
- Two key characteristics:
1. Firms compete by selling differentiated products that are highly substitutable for one
another but not perfect substitutes  cross-price elasticities of demand: large (not infinite)
2. There is free entry & exit
o Entry is relatively easy, so if profits are high in a neighbourhood because there are only
a few stores, new stores will enter
Equilibrium in the Short Run & the Long Run:
- Monopolistic competition firms face downward-sloping demand curves  some monopoly
power  doesn’t mean that they are likely to earn large profits
- Free entry: potential to earn profits attracts new firms with competing brands  drives
economic profits down to zero
- Short-run equilibrium:
o Profit-maximizing quantity is at the intersection of MR & MC curves
o Corresponding price exceeds AC  firm earns profit
- Long-run equilibrium:
o Profit will induce entry by other firms  our firm will lose market share & sales
o Demand curve will shift down (AC & MC may also shift, simplicity: it doesn’t)
o Demand curve will be just tangent to the firm’s AC curve
o Profit maximization implies zero profit because price is equal to AC
o The firm still has monopoly power: demand curve is downward sloping  unique brand
o Firms may have different costs, & some brands will be more distinctive than others 
firms may charge slightly different prices, & some will earn small profits
Monopolistic Competition & Economic Efficiency:
- Two sources of inefficiency in a monopolistic competitive industry:
1. Equilibrium price exceeds MC  value to consumers of additional output
exceeds the cost of producing those units. If output were expanded to
the point where demand curve intersects MC curve, total surplus could
be increased by an amount equal to the yellow-shaded area. Not
surprising, because monopoly power creates a deadweight loss.
2. In the Figure, output is below that which minimizes AC. Entry of new
firms drives profits to zero. Demand curve is downward sloping, so the
zero-profit point is to the left of minimum AC  excess capacity is inefficient because AC
would be lower with fewer firms
- These inefficiencies make consumers worse off
Applied Microeconomics
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Monopolistic competition isn’t a socially undesirable market structure that should be regulated:
1. Usually enough firms compete, with brands that are sufficiently substitutable, so that no
single firm has much monopoly power. Any resulting deadweight loss will therefore be small.
And because firms’ demand curves will be fairly elastic, AC will be close to the minimum.
2. Any inefficiency must be balanced against an important benefit from monopolistic
competition: product diversity. Most consumers value the ability to choose among a wide
variety of competing products & brands that differ in various ways. The gains from product
diversity can be large & may easily outweigh the inefficiency costs resulting from downwardsloping demand curves
12.2 Oligopoly
-
In some oligopolistic markets, some or all firms earn substantial profits over the long run
because barriers to entry make it difficult or impossible for new firms to enter
- Barrier entry:
o Scale economies may make it unprofitable for more than a few firms to coexist
o Patents or access to a technology may exclude potential competitors
o The need to spend money for name recognition & market reputation may discourage
entry by new firms
o Incumbent firms may take strategic actions to deter entry
- Because only a few firms are competing, each firm must carefully consider how its actions
will affect its rivals, & how its rivals are likely to react
Equilibrium in an Oligopoly Market:
- Nash equilibrium: each firm is doing the best it can, given what its competitors are doing
o It is natural to assume that these competitors will do the best they can, given what that
firm is doing
- The chapter focuses on markets in which two firms are competing with each otherduopoly
The Cournot Model:
- Each firm must decide how much to produce, & the two firms make their
decision at the same time  market price depends on the total output of
both firms
- Each firm treats the output level of its competitor as fixed
- Reaction curves: firm 1’s profit-maximizing output is thus a decreasing
schedule of how much it thinks firm 2 will produce  schedule = firm 1’s
reaction curve
- Cournot equilibrium: equilibrium output levels are at the intersection of the
two reaction curves  each firm correctly assumes how much its competitor will produce, &
it maximizes its profits accordingly
o Example of a Nash equilibrium  Cournot-Nash equilibrium
o Say nothing about the dynamics of the adjustment process
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The Linear Demand Curve – an Example:
Total quantity produced: 20
Equilibrium market price: 10
Each firm earn a profit of 100
Suppose the antitrust laws were relaxed &
the two firms could collude:
They would set outputs to maximize
total profit, & presumably they would split
that profit evenly
R = PQ
MR = derivative of R
MR = 0  total profit is maximized,
when Q=15
Collusion curve gives all pairs of
outputs that maximize total profit
Both firms produce less & earn
higher profits than in the Cournot
equilibrium
First Mover Advantage – The Stackelberg Model:
- = one firm sets its output before other firms do
- We assume that both firms have MC = 0, and market demand: P = 30 – Q
- Neither firm has any opportunity to react
- Firm 2 makes its output decision after firm 1  takes its output as fixed
- Firm 2’s profit-maximizing output is given by its Cournot reaction curve (12.2)
- Firm 1: to maximize profit, it chooses output so that MR = MC = 0
- Firm 1’s revenue:
- Firm 1 knows, firm 2’s output level (reaction curve in 12.2)  substitute 12.2 for 𝑄2 in 𝑅1
- Derivate 𝑅1 to get MR and set it = 0  𝑄1 =15, 𝑄2 =7.5
- Firm 1 produces twice as much as firm 2 & makes twice as much profit
- Announcing first creates a fait accompli: no matter what your competitor does, your output
will be large. To maximize profit, your competitor must take your large output level as given
and set a low level of output for itself. If your competitor produced a large level of output, it
would drive price down and you would both lose money. So unless your competitor views
“getting even” as more important than making money, it would be irrational for it to
produce a large amount.
12.3 Price Competition
Price Competition with Homogeneous Products – The Bertrand Model:
- = firms produce a homogenous good, each firm treats the price of its competitors as fixed, &
all firms decide simultaneously what price to charge
- Because good is homogeneous, consumers will purchase only from the lowest-price seller
- Nash equilibrium: both firm set price = MC  both earn zero profit
- In the Cournot model, each firm makes a profit
Price competition with Differentiated Products:
- Choosing prices: both firms set prices at the same time & each takes its competitor’s price as
fixed  Nash equilibrium:
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o
-
Taking firm 2’s price as fixed, firm 1’ profit maximizing price is the derivative of the
profit over firm 1’ price
o Nash equilibrium is at the point where two reaction curves cross  neither firm has an
incentive to change its price
If they collude:
o Both would be better off because each would earn more profits
If firm 1 sets the price first & after observing firm 1’s decision, firm 2 makes its pricing
decision  firm 1 would be at a distinct disadvantage by moving first, because it gives the
firm that moves second an opportunity to undercut slightly & thereby capture a larger
market share
12.4 Competition versus Collusion: The Prisoners’ Dilemma
-
-
Nash equilibrium is a noncooperative equilibrium: resulting profit earned by each firm is
higher than it would be under perfect competition but lower than if the firms collude
Collusion is illegal
Payoff matrix: table showing profit (or payoff) to each firm given its decision & the decision
of its competitor
The prisoners’ dilemma:
o Game theory example in which two prisoners must decide separately whether to
confess to a crime; if a prisoner confesses, he will receive a lighter sentence and his
accomplice will receive a heavier one, but if neither confesses, sentences will be lighter
than if both confess.
Oligopolistic firms must decide whether to compete aggressively, attempting to capture a
larger share of the market at their competitor’s expense, or to “cooperate” & compete more
passively, coexisting with their competitors & settling for their current market share, &
perhaps even implicitly colluding.
12.5 Implications of the Prisoners’ Dilemma for Oligopolistic Pricing
Price Rigidity:
= Characteristic by which firms are reluctant to change prices even if costs or demands change
- It’s the basis of the kinked demand curve model:
o Each firm faces a demand curve kinked at the currently prevailing price
o Prices above: demand curve is very elastic  firm believes that if it raises its price,
other firms will not follow suit, & will therefore lose sales & much of its market share
o Prices lower: other firms will follow suit because they won’t want to lose their shares of
the market  sales will expand only to the extent that a lower market price increases
total market demand
o Demand curve is kinked  MR curve is discontinuous  firm’s costs can change
without resulting in a change in price
o However, it doesn’t say anything about how firms arrived at the price in the first place,
& why they didn’t’ arrive at some different price
Price Signalling & Price Leadership:
- Price signalling: form of implicit collusion in which a firm announces a price increase in the
hope that other firms will follow suit
- Price leadership: Pattern of pricing in which one firm regularly announces price changes that
other firms then match
- Price leadership can also serve as a way to deal with the reluctance to change prices, a
reluctance that arises out of the fear of being undercut or “rocking the boat”
The Dominant Firm Model:
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Firm with a large share of total sales that sets price to maximize profits, taking into account
the supply response of smaller firms
The dominant firm must determine its demand curve (difference between market demand &
supply of fringe firms)
To maximize profit: quantity produced is at the intersection of MR & MC
12.6 Cartels
-
Producers in a cartel explicitly agree to cooperate in setting prices and output levels
If enough producers adhere to the cartel’s agreements, and if market demand is sufficiently
inelastic, the cartel may drive prices well above competitive levels
- Conditions for cartel success:
1. A stable cartel organization must be formed whose members agree on price &
production levels & then adhere to that agreement
2. Potential for monopoly power: Even if a cartel can solve its organizational problems,
there will be little room to raise price if it faces a highly elastic demand curve. Potential
monopoly power may be the most important condition for success; if the potential gains
from cooperation are large, cartel members will have more incentive to solve their
organizational problems
Analysis of Cartel Pricing: OPEC & CIPEC  p. 492 f
Ad prisoner’s dilemma:
- Cross subsidization
- Strategies:
o Always defect
o Tit-for-tat
o Grim