Customization Material for Econ 304 – Spring 2012
1
Getting Started: The Cruise Ship Analogy
Use the space below to draw a cruise ship that represents the US economy.
Key Terms from cruise ship example:
1. Fiscal policy (FP)
2. Monetary policy (MP)
3. Recognition lag
4. Implementation lag
5. Effectiveness lag
6. NAIRU
7. Full employment
8. Open market operations
9. Potential growth rate of economy
10. Stagflation
11. The FOMC
12. Exogenous shocks
13. Overheating
14. Speed limit of the economy
2
The Cruise Ship
Goals (the port)
1. Stable Prices
2. Full Employment (NAIRU)
3. Economic Growth (PGE)
NAIRU (Non Accelerating Inflation Rate of Unemployment) – the lowest the
unemployment rate can go without inflation accelerating. We really don’t know exactly
what this number is and it probably changes through time. Most economists would agree
that NAIRU is somewhere around 5%, although this number is more uncertain given the
Great Recession of 1997 – 1999.
PGE (The Potential Growth rate of the Economy) – The fastest real GDP can grow
without inflation accelerating. This growth rate is often referred to as the speed limit of
the economy or the sweet spot of economic growth. Similar to NAIRU, PGE is a concept
and we are not really sure what number to use and thus, we often talk about NAIRU and
PGE in ranges. I would think that most economists put PGE between 2.5 and 3.5%. Any
growth above that would be inflationary with the implication of overheating.1
Policy Lags
1. Recognition lag: The recognition lag is the time it takes policy makers to identify
the current level of economic activity as well as where the economy is headed. We
would think it would be easy to know current economic conditions given the constant
stream of economic data available, but this is not necessarily the case since much of
this data is reflecting previous economic activity. For a case in point of the
recognition lag consider the following: At an FOMC meeting in October of 1990,
Chairman Alan Greenspan did not recognize the economy was in the midst of an
“official recession,” a recession that is commonly referred to as the gulf war
recession.2
Lags are so important for policy makers and we assume that the recognition lag is the
same for Fiscal policy makers (FP) as it is for Monetary policy makers (MP). That is,
we assume that the economists that work on the council of economic advisors to the
President and the economists that work for the Federal Reserve are equal in their
abilities to recognize where the economy is and where it is headed.
Overheating is a common ‘economic’ term and is associated with aggregate demand outstripping
aggregate supply.
2
The National Bureau of Economic Research (NBER) is the official recession dating body and they
typically identify recessions well after they are over. For example, the trough (end of) the 2001 recession
occurred in November 2001 but wasn’t announced by the NBER until July 17, 2003! Chairman Bernanke
used to be a member of this committee. For all the official recession dates, as well as more information
about the process, go to http://www.nber.org/cycles/cyclesmain.html.
1
3
2. Implementation lag: The implementation lag represents the time lag between
recognizing a need for discretionary policy and the time it takes to implement the
policy (i.e., how long it takes the fiscal authorities to turn the wheel. For Fiscal
policy, this lag can be quite long since our elected officials have to write up the policy
and then talk about the details. As we all know, the political process, say, for a
recommended tax cut can become very tedious and take many months of discussion
in the House of Representatives and/or US Senate.
For Monetary policy the implementation lag is very short, as the FOMC directs the
federal funds desk to change the target for the federal funds rate by conducting open
market operations. According to a high ranking Federal Reserve official, open
market operations take about 15 seconds to perform!
3. Effectiveness Lag: The effectiveness lag refers to the time it takes for the
implemented policy to influence real economic activity. In term of the cruise ship
example, it represents the time it takes for the cruise ship to turn once the wheel is
turned (i.e., once the policy is implemented). For Fiscal policy, the effectiveness lag
is thought to be relatively short. For example, once a tax cut becomes effective,
households immediately have more disposable income and chance are good, they will
spend it and thus, economic activity will rise quite quickly.
For Monetary policy, the effectiveness lag is long and variable, with the typical range
of time being anywhere from 6 months to 2 years.3 Some economists believe that the
effectiveness lag for monetary policy can be even longer than two years.4 This lag in
monetary policy means that the Federal Reserve must be forward looking and thus,
the “Fed” spends a lot of its resources in building and analyzing economic forecasting
models.
3
This range is associated with the following reference: Milton Friedman and Anna Jacobson Schwartz, A
Monetary History of the United States, 1867-1960. Princeton: Princeton University Press (for the National
Bureau of Economic Research), 1963. xxiv + 860 pp.
4
When I spoke with Frederic Mishkin during his visit to Penn State, he suggested that the lag between
changes in Federal Reserve policy and its impact on inflation is “at least two years.” This fact must be kept
in mind since there is a group of economists adamant about inflation targeting, and thus, to successfully
target inflation, you must be able to forecast inflation 2 plus years into the future, a difficult task indeed!
4
Example Problems from lesson 2
1. Consider an economy that produces only two goods: fresh apricots and dried apricots.
In this economy, the technology of producing dried apricots is to place fresh apricots on special
racks and allow them to dry in the sun. Fannie’s Farms is the only company that grows fresh
apricots, while Darryl’s Dried Victuals is the only producer of dried apricots. Fannie’s sells some
of its apricots directly to consumers for consumption. The relevant revenue and cost information
for each of the two firms in the economy is given below:
Darryl’s
Revenue from selling dried apricots:
Cost of buying fresh apricots from Fannie’s:
Interest on funds borrowed to buy drying racks:
Wages paid to employees
Taxes
$2,300,000
1,200,000
250,000
600,000
100,000
Fannie’s
Revenue from selling fresh apricots:
Rent on land (including apricot trees)
Wages to employees
Taxes
$2,000,000
300,000
1,200,000
200,000
Calculate nominal GDP using (a) the expenditure approach (b) the production (value added)
approach, and (c) the income approach and show that all three give the same answer.
2. Suppose that you buy a one-year government bond on January 1, 2004 for $1,000.
You receive principal plus interest totaling $1,070 on January 1, 2005. The CPI was 150 on
January 1 2005. Imagine that you expected that the CPI would be 156 on January 1, 2005.
However, it turned out that the CPI was 159 on January 1, 2005.
a) Find the nominal interest rate, the inflation rate, and the real interest rate (the actual,
ex-post real interest rate).
b) What was your expected real rate of interest (ex-ante real rate)? Why did your
expected real rate of interest differ from the actual real rate of interest? Explain.
3. Consider Country T whose economy produces only three items, Tomatos, Tofu, and
Tacos. The base year is arbitrarily chosen as 2004
Good
Tomatoes
Tofu
Tacos
2004
Quantity
1000
2000
600
Price
$1.00
$3.00
$5.00
2005
Quantity
1200
1800
500
Price
$1.50
$4.00
$6.00
5
a. Find nominal GDP in the current year (2005) and in the base year. What is the
percentage increase since the base year?
b. Find real GDP in the current year (2005) and in the base year. By what percentage
does real GDP increase from the base year to the current year (2005)?
c. Find the GDP deflator for the current year (2005) and the base year. By what
percentage does the price level change from the base year to the current year (2005)?
d. Would you say that the percentage increase in nominal GDP in this economy since the
base year is due more to increases in prices or increases in the physical volume of output?
6
Answers to Example Problems for Chapter 2
1. (a) Production approach: The value added of Fannie’s is $2 million, since Fannie’s
does not purchase any intermediate inputs. The value added of Darryl’s is the total value of its
production, $2.3 million minus the $1.2 million value of the intermediate inputs purchased from
Fannie’s = $1.1 million. So the total of the values added is $2 million + $1.1 million = $3.1
million. (*)
Expenditure Approach: The expenditure approach adds up the value of the goods that are
produced for final consumption. All of Darryl’s dried apricots are sold to consumers, so their
value is $2.3 million. $1.2 million of Fannie’s fresh apricots are sold to Darryl, so only $2 – 1.2 =
$.8 million of Fannie’s production is for final consumption. So the total expenditure on final
goods and services is $.8 million on the fresh apricots sold by Fannie’s to consumers plus $2.3
million on the dried apricots sold equals $3.1 million. (*)
.
Income Approach: There is only one tricky part here, and that is to realize that there are several
types of income generated in this economy. That is we have to consider, wage or labor income,
profits, land-owner income, interest income and taxes.

Total labor income for the economy is $0.6 million + $1.2 million = $1.8 million.

Total interest income is $0.25 million

Darryl’s profits are given by the value of its sales minus its expenses -- $2.3 million –
$1.2 million - $0..25 million - $0.6 million – .1 million = $0.15 million.

Fannie’s profits are equal to $2 million - $0.3 million - $1.2 million – $0.2 million.=
0.3 million.

So, total profits for the economy are $0.45 million.

Land owner income: $0.3 million.

Taxes = .1 million + .2 million = .3 million.
Thus total income generated from current production is
Labor income
Interest Income
Profits
Land income
Taxes
Total
$1.8 million
$0.25 million
$0.45 million
$0.3 million
$0.3 million
$3.1 million (*)
Finally note that the three approaches give the same number for the Nominal GDP that is
we have $3.1 million in all three cases. This fact is why we use GDP and Income
interchangeably throughout the course (in a close economy setting).
7
2.a) Find the nominal interest rate, the inflation rate, and the ex post real interest rate (the actual,
ex-post real interest rate).
The information we have is the following:
Value of the bond as of Jan-2004: 1,000
Value of the bond as of Jan-2005: 1,070
CPI as of Jan-2000: 150
CPI as of Jan-2001: 159
Expected CPI as of Jan-2001: 156
Nominal interest rate (i)
i = (1,070 – 1,000)/1,000 = 0.07 or 7%
Inflation Rate ()
= (159 –150)/150 = 0.06 or 6%
Ex post Real interest rate
Ex post Real interest rate = i –  = 7% – 6% = 1%
2 b) In order to calculate the ex ante real interest rate, we need to compute the expected rate of
inflation (e)
e=(156 – 150)/150 = 0.04 or 4%
Therefore, John was expecting a 4% rate of inflation (πe = 4%) but the actual or ex-post rate of
inflation turned out to be 6% (see part a)
Now we can calculate the expected real interest rate (same as ex-ante):
r = i – e= 7% – 4% = 3%
So the last calculation tells us that John was expecting to have a 3% real return on the government
bond, but we know that he got just 1%. This is so because the ex-post inflation and the expected
inflation do not coincide. Note importantly that economists believe that human behavior is
primarily driven by expectations – so in this case, John’s behavior was based on the ex ante rate
and thus, he probably would have saved more than he would have if he had perfect foresight.
3.a. Find nominal GDP in the current year (2005) and in the base year. What is the percentage
increase since the base year?
Nominal GDP Base Year = (1000)(1) + (2000)(3) + (600)(5) = 10,000.
Nominal GDP Current Year = (1200)(1.5) + (1800)(4) + (500)(6) = 12,000.
8
Percent increase since base year is (12,000 – 10,000)/10,000 = 20 %
b. Find real GDP in the current year (2005) and in the base year. By what percentage
does real GDP increase from the base year to the current year (2004)?
Real GDP Base Year = (1000)(1) + (2000)(3) + (600)(5) = 10,000 (Always the same as nominal
GDP in the base year, so you really don’t have to do this calculation.)
Real GDP Current Year = (1200)(1) + (1800)(3) + (500)(5) = 9100.
Percent change since base year is (9100 – 10,000)/10,000 = –9 %
So in this case we have a percentage decline in Real GDP.
c. Find the GDP deflator for the current year (2005) and the base year. By what
percentage does the price level change from the base year to the current year (2005)?
GDP deflator for the base year = 100.
GDP deflator for the current year = (100)(12,000)/9100 = 131.9
Percent change = (100)(131.9 – 100)/100 = 31.9%
d. Would you say that the percentage increase in nominal GDP in this economy since the
base year is due more to increases in prices or increases in the physical volume of output?
Prices went up 31.9 percent, and real GDP went down by 9 percent. Clearly the increase in
nominal GDP is associated only with changes in prices.
9
Chapter 3: Productivity, Output, and Employment
II. The Aggregate Supply (AS) side of the economy
When you think of AS, you should be thinking of production and all the costs associated
with producing goods and services! There is a lot to discuss when thinking about any
particular production process. First, we need to consider the production function (PF).
Think of the production function as a ‘black box,’ one that takes inputs (land, labor,
capital, technology) and turns it into output, output that is typically used to increase the
welfare of society. In fact, it is often stated that increases in the growth rate of
productivity are the key to increasing living standards since increases in the growth
rate of productivity allows the economy to produce more with the same inputs
(alternatively: produce the same output with less inputs). As we will see via an example,
an increase in productivity growth allows firms to pay higher real wages (workers are
better off) as well as increase profits (firms are better off).
Exercise: In the space below, draw a production function and discuss the
assumptions underlying any production function, what the shape implies, and the
factors that cause the production function to shift.
10
Deriving labor demand the production function: A similar example can be found in
chapter 3 of the textbook (the Clip Joint example).
We start with the extremely important assumption that the firm’s objective is to
maximize profits. In what follows, we are going to obtain a firm’s profit maximizing
condition regarding the profit maximizing level of labor input (N is the notation for
labor). For now, we take prices (P) and the nominal wage (W) as given (and
therefore the real wage (W/P) is also given) and examine the behavior of the firm in
terms of their profit maximizing objective.
We begin by defining the marginal product of labor (MPN) and the importance of
the marginal revenue product of labor (MRPN).
The marginal product of labor (MPN) is simply the change in output given a change
in labor input. Formally, the MPN = ∆Y/∆N
The marginal revenue product of labor (MRPN) is the ADDITIONAL revenue that
is generated by each ADDITIONAL worker. Note the caps on additional,
emphasizing the fact that we are employing marginal analysis and we often do in
economics. To convert the additional output that each additional worker produces
into $ terms, we simply multiply the MPN times the price of the product:
MRPN = MPN X P
The intuition underlying the MRPN is very clear – think of the MRPN being the
most you would be willing to pay each worker – for example, consider worker
number 1 (see below). The MPN is 10 and since the price of output is $10, then
worker 1 has an MRPN of $100. Given that the nominal wage is given at $80, we
would make $20 in profit off of worker 1. If we paid them $100, we would be
breaking even – we would not be willing to pay the worker more than $100 because
then we would be losing money on worker 1 which is not consistent with profit
maximization. In fact, we can make the following conclusions:
If W < MRPN hire more workers
If W >MRPN hire less workers
IF W = MRPN, we are at profit maximization, that is, we keep hire workers until W
= MRPN – THIS IS THE PROFIT MAXING CONDITION IS THAT THE FIRMS
HIRE WORKERS UNTIL THE REAL WAGE =MPN (THIS IS THE FORM WE
WILL USE THE REST OF THE SEMESTER)
W = MRPN
W = MPN x P
W/P = MPN
11
Fill in the table below and figure out how many workers I should hire to maximize
profits. The current (given) nominal wage (W) = $80 and the given price of the output
(P) = $10.
TABLE 1
N
Y
MPN
0
0
-
1
10
2
25
3
36
4
45
5
52
6
55
MRPN
-
Marginal Profit
-
Total Profit
0
12
In the space that follows, draw:
1) The production function
2) A labor market diagram including labor demand and labor supply (a bar chart that
clearly depicts the MRPN, the labor costs, and the marginal profit/loss.)
LABEL THIS INITIAL EQUILIBRIUM AS POINT A
13
Exercise #1: Higher Wages and its influence on the firm’s labor input decision.
Let’s return to our original conditions (TABLE 1) except that wages (W) have risen to
$100 (rather than the original $80).
QUESTION: What could cause such an increase in nominal wages?
Fill in the table below and figure out how many workers I should hire to maximize
profits.
TABLE 2
N
Y
0
0
1
10
2
25
3
36
4
45
5
52
6
55
MPN
-
MRPN
-
Marginal Profit
-
Total Profit
0
Exercise: Show the influence of the higher wages on:
1) Your production function diagram
2) Your labor market diagram
AND LABEL THIS NEW EQUILIBRIUM AS POINT B
Conclusion: All else constant, an increase in wages will result in lower employment
and lower profits. In terms of economy wide statistics, the unemployment rate will
likely rise, the stock markets will likely fall (lower profits): There will also be
upward pressure on prices as firms may try to maintain profits by raising prices (in
effect, passing this increased cost of labor onto the consumer).
Note also that this exact analysis holds regarding increases in the costs of other
inputs, including material costs (e.g., cotton for making T-shirts) as well as health
benefits, etc. It is conventional to focus on changes in labor costs (wages) since labor
costs account for roughly 70% of the costs of the ‘typical’ good or service, but there
14
are many other costs of production that are relevant. See how many other inputs
costs we can name that applies to this ‘plastering’ example.
Exercise #2: A Change in productivity
Let’s return to our original conditions (W = $80 and P = $10) and focus on how a
technological innovation changes the firm’s behavior. In particular, suppose a
technological innovation increases the productivity of each worker by two, i.e., each
worker’s MPN rises by two (again, assume no change in wages or output prices). Fill in
the table below. What is my profit maximizing level of labor input now?
TABLE 3
L
0
Q
MPL
MRP
-
-
Marginal Profit
-
Total Profit
0
1
2
3
4
5
6
15
Exercise: In the space below, redraw the original diagrams (with equilibrium point
A) and then show the influence of the higher productivity on:
1) Your production function diagram
2) Your labor market diagram
PLEASE LABEL THE NEW EQUILIBRIUM AS POINT C
16
Conclusion: All else constant, an increase in productivity growth will result in
higher profits and likely result in more employment, as firms have an incentive to
hire more workers since the gain in productivity makes each and every worker
more valuable and thus, provides an incentive for firms to hire more.5
Finally, suppose workers want a “piece of the action” and demand an increase in wages
to $90 (after all, they are the ones that are being more productive). Assume that you give
it to them. Compare profits now with the original profits. The very common statement
that you hear often when discussing the new economy and the surge in productivity
growth is as follows: increases in the growth rate of productivity allow firms to raise
profits, and pay workers higher wages, without raising prices. This is what the new
economy is all about – the ability of the economy to grow faster without inflation
(i.e., a change in the speed limit).
Supply Shocks

Refers primarily to changes or “shock” to a country’s production function usually
due to changes in capital (K), both human and physical. Changes in technology
or total factor productivity (denoted A) are also often the cause of a productivity
(supply) shock. In addition, shocks to Land Resources (gifts from nature) will also
shift the production function, the most common example is of course the oil
shocks of the 1970s (this example is covered in the text).

Shocks to labor supply are also referred to supply shocks since changes in labor
supply, under certain conditions, will shift the aggregate supply curve. Note
importantly that changes in labor supply DO NOT shift the production function
but changes in capital and technology do.

Positive productivity shocks raise the amount of output that can be produced for a
given amount of labor. Adverse productivity shocks have the opposite effect.

Examples: changes in weather (drought or unusually cold winter), inventions or
innovations in management techniques that improve efficiency (such as
minicomputers and statistical analysis), changes in government regulations,
5
Whether or not firms hire more labor depends critically on (aggregate) demand conditions. For example,
during the ‘new economy’ years (1996-2000), demand was very strong and thus, labor growth was
significant as the unemployment rate got below 4% on two occasions. Conversely, as the economy slowed
during the beginning years of the new millennium, growth in the labor force slowed as well even though
the growth rate of productivity ‘held its own.’ In fact, the recovery following the 2001 recession is referred
to as the job-loss recovery, consistent with high productivity growth rates combined with slack aggregate
demand. During this period, the Fed continued to lower their target for the federal funds rates to 40 + year
lows (at the time) all the way to 1%).
17
changes in the supply of the factors of production (except for labor) that affect
the amount that can be produced for a given amount of labor.

The MPN Curve (Labor Demand Curve)
In this class we focus on real labot demand which is exactly the same as the MPN
function: Nd = MPN.
 Amount of labor, N, is on horizontal axis
 MPN and real wage are on the vertical axis
 Downward-sloping MPN curve relates marginal product of labor, MPN, to the
amount of labor employed by the firm, N.
 MPN slopes down due to diminishing marginal productivity of labor.
Explain the intuition and a couple examples of the law of diminishing marginal returns tp
labor (you should be familiar with the law of diminishing returns from your principles
class).
Exercise – deriving the real labor demand curve from our plastering example. With the
real wage (ω = W/P) and MPN on the vertical axis and labor (N) on the horizontal axis,
identify point A from the original conditions (use the space below).
Now let nominal wages rise to $100 as before (all else constant). Locate this new point as
point B. Connect the dots and you have just derived the real labor demand curve. Why
exactly are firms changing their desired labor input, given the change in W?
Finally, let’s go back to the original conditions and now account for the technological
innovation (all else constant). Locate this point as point C. What has happened to the
labor demand curve and why? Be sure to include all the shift variable in parentheses next
to your (real) labor demand curve.
18
Generic example – see graphic below.
Horizontal line represents real wage firms pay, which firms take as given.
Explain the assumption of a given real wage via the Orlando example – the idea that
small firms can hire all the workers they want at a given real wage.





Refer to diagram below.
Pt. A shows the profit-maximizing condition, that is the amount of labor that
yields the highest profit for any real wage.
N* represents profit-maximizing level of labor input
At levels less than N*, marginal product of labor exceeds the real wage, so firms
could still increase profits by hiring more workers. At levels of labor input beyond
N*, the real wage exceeds the marginal product of labor implying that firms could
increase profits by hiring less workers.
Therefore, profit-maximizing condition is when MPN=w (where w = W/P)
19
MPN Curve shocks
 Beneficial supply shock shifts the MPN curve upward and to the right and
raises the quantity of labor demanded at any given real wage, and vice versa.
Labor Supply
Workers like me and you determine Labor Supply – and the real wage is the price of
leisure. Let us state that again, the real wage is the price of leisure. So as the real wage
rises, the price of leisure rises (it costs me more to watch my hour long favorite TV show)
so I will consume less leisure and work more. This notion generates a positively sloping
labor supply curve.
Income and Substitution Effects Along the Labor Supply Curve
When discussing labor supply, it is important to understand the income and substitution
effects in labor supply. The income effect is simply the fact that a higher real wage will
increase your purchasing power (income) and if leisure is a ‘normal’ good, you will
purchase (consume) more of it. This income effect, all else constant, suggests that a
higher real wage results in us working less (since we are ‘buying’ more leisure) resulting
in a negatively sloped labor supply curve! But of course, all else is not constant, the
substitution effect is also at work. The substitution effect, as mentioned in the paragraph
introducing labor supply, is the idea that the real wage is the price of leisure and when the
real wage rises, we substitute away from leisure towards work. The substitution effect,
all else constant, results in a positively sloped labor supply curve. Given that the income
and substitution effects work in opposite directions, the magnitude of each will determine
(the sign of) the slope of the labor supply curve. Since we always draw the labor supply
curve as being positively sloped, we assume that the substitution effect dominates the
income effect.
Shifts in Labor Supply
Anything that changes your desire to work, at the same real wage (i.e., all else constant)
will shift the labor supply curve. Suppose you win the lottery, what will happen to your
desire to work at the same real wage? If the winnings are large enough, I would
definitely work less, at the same real wage. Similar effects occur with the ups and downs
of the stock market. During the mid to late 1990s, the stock market was soaring and thus,
people were becoming wealthier than they ever imagined. Hopefully, you can intuit that
the labor supply was shifting to the left (all else constant) during this time. Naturally,
when the stock market falls appreciably, we have the opposite effect on labor supply.
Other factors that shift labor supply are below. Note, it is important to always distinguish
between movements along vs. shifts in labor supply. Remember that shifts are changes in
labor at the same wage (something other than a change in the wage is changing your
behavior) where movements along are changes in behavior (recall income and
substitution effects) due to changes in the real wage (all else constant).
20
Factors that Shift Labor Supply





Changes in wealth
Changes in Expected Income
Changes in Demographics
Changes in Immigration Laws
Changes in Labor Force Participation
Labor Market Equilibrium

Occurs when Nd (MPN)=Ns (labor supply)
21
Example Problems for Chapter 3
1. The production technology of a firm is given in the table below.
Number of workers
0
1
2
3
4
5
6
7
Units of output
0
100
175
225
265
295
320
340
a. Define and find the marginal product of labor (MPN) for each level of employment.
b. Assume that the price of a unit of output is $5. Calculate the number of workers that
will be hired if the nominal wage rate = $190. Calculate the number of workers the firm will hire
if the nominal wage is $140. Calculate the number of workers that the firm will hire if the
nominal wage is $100.
c. Explain and graph the demand for labor curve of the firm.
d. Assume that the nominal wage = $190 and the price of a unit of output = $9. Calculate
the number of workers that the firm will hire and the number of units of output that will be
produced. Compare the answer with that in part (b). Give an intuitive economic explanation for
the different answers.
e. Assume that the price of a unit of output = $5 and the nominal wage rate = $190.
Assume that a new technology increases the number of units of output that each worker can
produce by 60%. Calculate the number of workers that the firm will hire and the number of units
of output that will be produced. Compare the answer with that in part (b). Give an intuitive
economic explanation of the different answers.
2: Assume that the marginal product of labor is given by
MPN = A(200 – 2N)
Assume that the price of output = $2
a. Assume that A =2. Compute the number of workers hired when the nominal wage is
$32, $48 and $64. Graph the labor demand function.
b. Repeat part (a) for A = 4
22
3. The production function for an economy is given by
Y = A·K½ N½
For this production function the marginal product of labor is given by
MPN = (A/2)·(K/N)½
Suppose that the value of capital stock (K) for this economy is K = 100.
(a) Assuming that A = 4, graph the production function for output as a function of labor for
this economy over the range N = 0 to N = 100. (Hint: This can be done easily in Excel).
(b) Graph the marginal product of labor for this economy over the range N = 0 to N = 100.
(Hint: Again, this can be done easily in Excel.)
(c) What would happen to the graphs in part (a) and part (b) if A increased from 4 to 5 due to
an improvement in the economy’s technology. Given an intuitive economic explanation.
4. Suppose that the marginal product of labor for an economy is given by
MPN = 600 – 3N
and labor supply is given by
NS = 20 + 13w + 2T,
where T is a lump-sum tax levied on households.
a. Why would an increase in lump-sum taxes increase the amount of labor supplied?
(Hint: Use income and substitution effects in your answer.)
b. If T = 50, what are the equilibrium values of the real wage and employment?
c. If T remains at 50, but that the government passes minimum wage legislation that
requires firms to pay their workers a real wage of at least 9, what are the new values of the real
wage and employment?
5. Explain how each of the following would effect the real wage, the level of
employment, and the level of real output of the economy.
a. A relaxation of immigration laws leads to a large increase in the number of immigrants
entering the country.
b. Oil reserves are used up, causing the amount of energy available for production to
decline.
c. Applications of technology to education improve the abilities of high school seniors.
d. A terrorist attack destroys a large part of a country’s capital stock.
23
6. How would each of the following affect an individual’s supply of labor?
a. Stock prices unexpectedly double in value.
b. The individual returns to school and learns new skills that increase his/her
productivity.
c. The government increases the percentage of the individual’s income that he/she must
pay in taxes. This is a temporary increase that will be used to pay the cost of hurricane
reconstruction.
7. How would the following event affect the current level of output, employment and the real
wage rate? Illustrate your answer with appropriate graphs and explain carefully.
A practical technology that uses nuclear fusion to produce electricity from sea water is
discovered. The effect of this innovation is expected to make energy cheap and abundant
in the future.
24
Answers to Example Problems for Chapter 3
1.a. Definition: The marginal product of labor is the additional output that is produced
due to the addition of one additional unit of labor
or
Definition: The marginal product of labor is the additional output that is produced due to the
addition of a small additional unit of labor, per unit of labor. (MPN = ΔY/ΔN where Y is the
quantity of output and N is the quantity of labor.)
b. When P = 5 and W = $190, the real wage w = W/P = $190/$5 = 38. When the real
wage is 38, the firm will hire 4 workers, because the MPN of the 4th worker = 40 and the MPN of
the 5th worker = 30.
When P = 5 and W = $140, the real wage w = W/P = $140/$5 = 28. When the real wage is 28, the
firm will hire 5 workers, because the MPN of the 5th worker = 30 and the MPN of the 6th worker
= 25.
When P = 5 and W = $100, the real wage w = W/P = $100/$5 = 20. When the real wage is 20, the
firm will hire 7 workers, because the MPN of the 6th worker = 25 and the MPN of the 7th worker
= 20. In this case the firm would be indifferent between hiring 6 workers and 7 workers (its profit
would be the same in either case) but we always assume that the firm hires the greater number of
workers.
c. The labor demand curve is the graph of the relationship between the real wage and the
number of workers that the firm wants to hire. We get this relationship by applying the same
reasoning that we applied in part (b)
25
w
100
The Firm’s
Demand
for Labor
75
50
40
30
25
20
1
2
3
4
5
6
7
N
d. When P = 9 and W = $190, the real wage w = W/P = $190/$9 = 21.11. When the real
wage is 21.11, the firm will hire 6 workers, because the MPN of the 6th worker = 25 and the MPN
of the 7th worker = 20
The higher price of output means that the marginal revenue produce of each worker increases,
which leads to the firm’s desire to hire more workers at the given nominal wage rate.
e.
Number of workers
0
1
2
3
4
5
6
7
Units of output
0
160
280
360
424
472
512
544
MPN
160
120
80
64
48
40
32
When P = 5 and W = $190, the real wage w = W/P = $190/$5 = 38. When the real wage is 38, the
firm will hire 6 workers, because the MPN of the 6th worker = 40 and the MPN of the 7th worker
= 32.
Additional productivity of workers means that the MPN of each additional worker is greater.
Therefore, for a given price of output and nominal wage, and therefore for a given real wage, a
firm is willing to hire more workers.
26
2: a. Assume that A =2. Compute the number of workers hired when the nominal wage is
$32, $48 and $64. Graph the labor demand function. (5 points)
Substituting A = 2, we get MPN = 2(200 – 2N).
When the nominal wage is $32, real wage is w = $32/$2 = 16. Since the firm will maximize profit
by hiring workers up to the point that w = MPN, we can set w = to MPN and solve for N:
16 = 2(200 – 2N) = 400 – 4N so that N = (400 – 16)/4 = 96.
Similarly, when the nominal wage = $48, the real wage w = $48/$2 = 24, so
24 = 2(200 – 2N) = 400 – 4N and N = (400 – 24)/4 = 94.
Finally, when the nominal wage = $64, the real wage w = $64/$2 = 32, so
32 = 2(200 – 2N) = 400 – 4N and N = (400 – 32)/4 = 92.
b. Substituting A = 4, we get MPN = 4(200 – 2N).
When the nominal wage is $32, real wage is w = $32/$2 = 16. Since the firm will maximize profit
by hiring workers up to the point that w = MPN, we can set w = to MPN and solve for N:
16 = 4(200 – 2N) = 800 – 8N so that N = (800 – 16)/8 = 98.
Similarly, when the nominal wage = $48, the real wage w = $48/$2 = 24, so
24 = 4(200 – 2N) = 800 – 8N and N = (800 – 24)/8 = 97.
Finally, when the nominal wage = $64, the real wage w = $64/$2 = 32, so
32 = 4(200 – 2N) = 800 – 8N and N = (800 – 32)/8 = 96.
3. a. This problem can also be handled easily without Excel. Since the production
function is
Y = A·K½ N½
A = 4 and K = 100, we can substitute to get
Y = 4·100½ N½ = 40 N½
We can then substitute a few values of N (N = 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 all work
well, since they are perfect squares, although you don’t need this many values to produce a good
graph.) and find the corresponding values of Y.
27
Production Function
450
400
350
300
Y
250
200
Y
150
100
50
0
0
20
40
60
80
100
120
N
(b) This problem can also be handled easily without Excel. Since the marginal product of
labor is given by
MPN = (A/2)·(K/N)½
A = 4 and K = 100, we can substitute to get
MPN = (4/2)·(100/N)½ = 2·10/N½ = 20/N½
We can then substitute a few values of N (N = 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 all work
well, since they are perfect squares, although you don’t need this many values to produce a good
graph.) and find the corresponding values of MPN.
Marginal Product of Labor
45
40
35
30
MPN
25
20
MPN
15
10
5
0
0
20
40
60
80
100
120
N
28
(c) If A were to increase from 4 to 5, the graph of the production function and the graph of
the marginal product of labor would both shift upward.
4. (a) The Lump sum tax on workers creates a pure income effect; it does not effect the
real wage. In other words, the relative price of current leisure in terms of foregone consumption is
not affected by the size of the tax. Therefore, the effect of an increase in the lump-sum tax will be
to cause an increase in the amount of labor supplied.
(b) We know that the labor demand curve will be determined by the profit maximizing
behavior of firms, which is characterized by the condition w = MPN. So the labor demand curve
can be written as
w = 600 – 3ND,
which can usefully be rewritten as
ND = (600 –w)/3.
We know that equilibrium in the labor market occurs when the wage rate has adjusted so that ND
= NS, so we set ND equal to NS to determine the equilibrium real wage:
(600 –w)/3 = 20 + 13w +(2)(50) = 13w + 120
or
600 – w = 39w + 360,
which can be solved for w = 6.
The equilibrium level of employment can then be solved for by plugging w = 6 into either the
labor supply curve or the labor demand curve. (Plugging into both is a good way to check that
you got the correct answer for the equilibrium real wage.
NS = (13)(6) + 120 = 198
ND = (600 -6)/3 = 198.
(c) A minimum real wage of 8 is imposed. At a real wage of 9, the quantity of labor
supplied will be
NS = 120+ (13)(9) = 237.
ND = (600 -9)/3 = 197.
Since there is excess supply at the real wage of 9, we know that the real wage will not be greater
than 9. The level of employment will be determined by the amount of labor that firms want to
hire, in other words by the labor demand curve, so the level of employment will be 197.
29
5. a. If a large number of new immigrants enter the country, this would increase labor
supply which would lower the real wage and increase the full-employment level of employment.
Since more employment means more output, output would increase. See graphs
below:
Y
w
N0
S
N1S
Y1
Y0
ŵ0
ŵ1
ND
Ň0
Ň1
Ň0
N
Ň1
N
b. If the supply of energy available for production declines, the price of energy will
increase, causing firms to use less energy. This will reduce total factor productivity, which will
shift the production function downward and reduce the marginal product of labor at each level of
labor input. This, of course, means that the demand for labor curve, which is the same as the
marginal product of labor curve, will shift to the left. This will reduce the real wage and reduce
the full-employment level of employment. So the level of real output will decrease for two
reasons: (1) labor and capital will be less productive, and (2) the level of employment will fall.
Y
w
NS
Y0
ŵ0
Y1
ŵ1
N0
D
N1D
Ň1
Ň0
N
Ň1
Ň0
N
30
c. Presumably, the greater educational performance of high school students will be
reflected in greater productivity when they become workers. However, this effect will not show
up in increased current activity, but in an increase in labor productivity in the future. So there will
be no effect on current output.
d. If some capital stock is destroyed, labor productivity will be reduced, so the production
function that expresses output as a function of labor will shift down and the marginal product of
labor will decrease at every level of employment. Thus, the labor demand curve will shift to the
left, the real wage will decline, and the full-employment level of employment will decline. So
output will decline for two reasons (1) the level productivity of labor will decline, and (2) the
level of employment will decline. The graphs are the same as the ones for part (b).
6. (a) This represents an increase in the individual’s real wealth, so the individual’s
supply of labor will decrease. (His/her labor supply curve will shift to the left.)
(b) The increase in productivity means that the real wage that the individual can earn will
increase, so the quantity of labor that she will supply will increase as long as the substitution
effect is greater than the income effect. (This is a movement along the individual’s labor supply
curve, not a shift in the individual’s labor supply curve.)
(c) The temporary increase in the individual’s income tax reduces the individual’s after
tax real wage. Since this is only a temporary decrease, we would expect that the substitution
effect would be greater than the income effect, so that the individual would reduce the current
quantity of labor supplied. (Again, this is a movement along the individual’s labor supply curve,
not a shift in the individual’s labor supply curve.)
31
7. How would the following event affect the current level of output, employment
and the real wage rate? Illustrate your answer with appropriate graphs and explain
carefully.
A practical technology that uses nuclear fusion to produce electricity from sea water is
discovered. The effect of this innovation is expected to make energy cheap and abundant in
the future.
ND
w
NS1
NS0
w1
w0
0
Y
N1
N
0
N0
Y0
Y1
N1
N0
The news that energy will be cheap and
plentiful in the future will not effect current
production. However, it will change current
expectations about future income. Namely,
people will believe that because they will be
more productive in the future, they will earn
more. As a result, they will reduce their work
effort today. Graphically, this will be
represented by a leftward shift in the labor
supply curve. From the graph of the labor
market, we can see that the real wage will
increase and the quantity of labor employed will
fall. The reduction in employment will cause a
decline in the level of output, as shown in the
lower graph.
N
0
32
Chapter 4: Consumption, Saving, Investment
Consumption-Smoothing
 Refers to the desire to have a relatively even pattern of consumption over time,
avoiding periods of very high or very low consumption.
 Goal is to maximize lifetime utility.
In space below draw a diagram with age on the horizontal axis and real income /
consumption on the vertical axis.
Substitution Effect on Saving
 Reflects tendency to reduce current consumption and increase future consumption
as the price of current consumption, 1+r, increases.
 When real interest rates rise, current consumption becomes more expensive
(relative to future consumption).
 In response, consumers substitute away from current consumption toward future
consumption.
 This reduction in current consumption implies that savings increases.
 Thus, substitution effect implies that current saving increases in response to
an increase in the real interest rate.
Income Effect on Saving
 Reflects the change in current consumption that results when a higher real interest
rate makes a consumer richer or poorer.
 Income effect depends whether the consumer is a saver/lender or a borrower.
 For a saver, income effect of an increase in real interest rate is to increase current
consumption and reduce current saving. (Opposite effect as the substitution
effect)
 For a borrower, increase in real interest rate makes his/her interest payments more
expensive, which is effectively a loss of wealth. Therefore, he/she will decrease
33
current consumption and future consumption, which means that saving increases.
(Same effect as the substitution effect)
Ricardian Equivalence
 The idea that tax cuts do not affect desired consumption and therefore do not
affect desired national saving.
 This theory is based on the assumption that, in the long run, all government
purchases must be paid for by taxes. Therefore, if the government’s current and
planned purchases do not change, a cut in current taxes simply increases the
burden of future taxes, meaning there is no change in consumer behavior (i.e., the
consumer saves the increase in disposable income to pay the expected higher
taxes in the future).
 Many question its relevance in the real world (i.e., Ricardian equivalence is
controversial).
User Cost of Capital
 UCC is the expected real cost of using a unit of capital for a specific period of
time.






Simplest from depends on three components: depreciation (d), real interest rates
(r), and the price of capital Pk.
UC = (r + d)Pk
Tax-Adjusted user cost of capital shows how large the before-tax future marginal
product of capital must be for a firm to willingly add another unit of capital.
Increase in the tax rate, t, raises the tax-adjusted user cost and thus reduces the
desired stock of capital and vica versa.
MPKf = (uc)/(1-t) = [(r + d)Pk]/(1-t)
Effectively, the future marginal product of capital equals the user cost of capital
divided by 1 minus the tax rate. Just divide both sides of the UC equation by 1
minus the tax rate.
Goods Market Equilibrium
 Sd = Id
 Desired Saving, Sd, is the same as Y – Cd – G
 Goods market is in equilibrium when desired national saving equals desired
investment.
 Note importantly that if we rearrange Id = Y – Cd – G, we have Y = Cd +I + G,
which hopefully is familiar from principles. Note also that the left hand side, Y =
aggregate income, is equal to aggregate expenditure, Cd +, I .+ G , a point that we
proved in chapter 2 (i.e., the income approach yields the same GDP as the
expenditure approach).
34


When increases in G cause investment to decline, economists say that
investment has been crowded out.
The crowding out of investment occurs because the government is using real
resources, some of which would otherwise have gone into private investment.
Present Value and the Budget Constraint
 PVLR = present value of lifetime resources
 Defined as the present value of the income that a consumer expects to earn in
current (y) and future periods (yf) , plus initial (a) and expected wealth (af).
 PVLR = y + a + (yf + af)/(1+r)
 PVLC = present value of lifetime consumption equals current consumption (c)
plus the present value of future consumption (cf).
 PVLC = c + (cf/1+r)
 PVLR = PVLC…….this is the condition ensures that you are consuming (using)
all your available resources across the two periods (i.e., you are on your budget
constraint).
35
Example Problems for Chapter 4
1. A consumer has a current before-tax income of $100,000 and a future before-tax
income or $140,000. She has no current wealth. Her current taxes are $30,000 and her
expected future taxes are $49,000. She wants her current consumption to be equal to her
future consumption. The real interest rate is .1 (10%).
(a) How much should her current consumption be? (Hint: Write an expression for
the present value of her (after tax) lifetime resources. Let x be the value of her current and
future consumption. Then the present value of her lifetime consumption is x + x/(1+.1) =
2.1x/1.1. Set this equal to the expression for the present value of lifetime consumption and solve
for x.) (3 points)
(b) Given her current desired consumption, will the consumer be a current borrower or a
current saver. Explain. (3 points)
(c) Suppose that her after tax income increases by $6300. How much will her current
consumption increase? How will this change affect her current saving or borrowing? (3 points)
(d) Suppose that instead of her current after tax income increasing by $6300, her future
after tax income increases by $6300. How much will her current consumption increase? How will
this affect her current saving or borrowing? (3 points)
(e) Suppose that everything is as in the original statement of the problem except that now
the real interest rate is .25 (25%). What will her current consumption and current saving or
borrowing be now? (3 points)
2. Fred’s Frisbees is trying to determine how many Frisbee pressing machines to buy for its new
factory. The real price of a new pressing machine is 7500 Frisbees. The depreciation rate on these
Frisbee presses is equal to 10% per year. In other words, after one year of use the real value of a
Frisbee press is 6750 Frisbees. The expected future marginal product of these fabricating
machines is given by the expression 3350 – 20K, measured in Frisbees. The real interest rate is
8% (.08).
(a) What is the user cost of capital? (Be sure to specify the units in which the user cost is
measured). (4 points)
(b) What is the profit maximizing number of Frisbee presses for Fred’s to purchase for its
new factory? (4 points)
(c) Before purchasing the machines Fred’s finds that it will be subject to a new tax of
32.5 percent on all of its revenue. Now what is the profit maximizing number of machines for
Fred’s to purchase? (Round down to the nearest whole number.) (4 points)
3. A certain economy has the following characteristics
.
Cd = 130 + .6Y – 1000r
Id = 300 – 3000r
36
G = 250
and the full-employment level of output equals 1200.
(a) Derive equation for desired national saving Sd as a function of Y and r.
(b) Find the real interest rate that clears the goods market in two ways. Assume that the
level of output is the full-employment level of output. Illustrate the equilibrium graphically.
(c) Government purchases increase to 290. What is the new the equation describing
desired national saving? Illustrate the change graphically. What is the new equilibrium interest
rate?
4. Analyze the effects of each of the following on national saving, investment, and the real
interest rate. Explain your reasoning and illustrate it with an appropriate diagram.
(a) Consumer confidence falls, so consumers decide to consume less and save more at
every level of the real interest rate.
(b) A new technology breakthrough increases the future marginal product of capital and
expected future income.
5. A consumer has a current income of $80,000, an expected future income of $110,000, and no
current wealth. The real interest rate is .1 (10%).
(a) Calculate the present value of this consumer’s lifetime resources.
(b) Carefully graph this consumer’s budget constraint, labeling all important quantities.
(c) Suppose that this consumer wants to consume equal amounts in the present and in the
future. Will this consumer be a current saver or a current borrower? Explain.
(d) Suppose the real interest rate were to increase. Would this consumer’s current
consumption increase or decrease? Give a justification of your answer that includes a
discussion of income and substitution effects
6. Desired consumption for an economy is given by the equation
Cd = 1000 + .6Y – 4000r.
Government purchases are given by G = 1500.
(a) Write an expression relating desired saving, Sd, to Y and r.
(b) Suppose that the full-employment level of output is 10,000. Graph the relationship
between desired saving, Sd, and the real interest rate r. (Your graph should include
properly labeled axes and an indication of the scale on each axis.)
(c) If desired investment for the economy is given by the equation
Id = 2000 – 6000r,
37
calculate the equilibrium real interest rate for the economy.
(d) Using the equilibrium real interest rate that you calculated in part (c), calculate the
equilibrium level of saving, investment, and consumption in the economy.
Does Y = C + I + G in equilibrium?
(e) Add the relationship between desired investment and the real interest rate to your
graph in part (b), and show the equilibrium values of r, Sd and Id from parts (c) and (d)
7. Use a saving investment diagram (and an explanation) to show what happens to saving,
investment and the real interest rate in the following scenario. (Note: we are just looking at the
goods market here.)
A practical technology that uses nuclear fusion to produce electricity from sea water is
discovered. The effect of this innovation is expected to make energy cheap and abundant in
the future.
38
Answers to Example Problems for Chapter 4
1. A consumer has a current before-tax income of $100,000 and a future before-tax
income or $140,000. She has no current wealth. Her current taxes are $30,000 and her
expected future taxes are $49,000. She wants her current consumption to be equal to her
future consumption. The real interest rate is .1 (10%).
(a) How much should her current consumption be? (Hint: Write an expression for
the present value of her (after tax) lifetime resources. Let x be the value of her current and
future consumption. Then the present value of her lifetime consumption is x + x/(1+.1) =
2.1x/1.1. Set this equal to the expression for the present value of lifetime consumption and solve
for x.)
PVLR = 70,000 + 91,000/1.1 so we can write the consumer’s budget constraint as
2.1x/1.1 = 70,000 + 91,000/1.1
and solve for x. Multiplying through by 1.1 we have
2.1x = 77,000 + 91,000 = 16800,
or
x = 168,000/2.1 = 80,000.
(b) Given her current desired consumption, will the consumer be a current borrower or a
current saver. Explain.
This consumer will be a current borrower, since her desired present consumption of
80,000 is greater than her current after tax income of 70,000. She will have to borrow $10,000.
(c) Suppose that her after-tax income increases by $6300. How much will her current
consumption increase? How will this change affect her current saving or borrowing? (3 points)
If the consumer’s current after-tax income increases by 6300, then her PVLR will increase to
76,300 + 91,000/1.1,
So her desired current consumption can be calculated by solving the equation
2.1x/1.1 = 76,300 + 91,000/1.1
for x. Again, multiply through by 1.1 to get
2.1 x = (1.1)(76,300) + 91,000 =174,930,
39
or
x = 174,930/2.1 = 83,300.
Her current borrowing will decrease to 83,300 – 76,300 = 7000.
(d) Suppose that instead of her current after tax income increasing by $6300, her future
after tax income increases by $6300. How much will her current consumption increase? How will
this affect her current saving or borrowing?
If the consumer’s future after-tax income increases by 6300, then her PVLR will be
70,000 + 97300/1.1,
So her desired current consumption can be calculated by solving the equation
2.1x/1.1 = 70,000 + 97,300/1.1
for x. Again, multiply through by 1.1 to get
2.1 x = (1.1)(70,000) + 97,300 =174,300,
or
x = 174,300/2.1 = 83,000.
Her current borrowing will increase to 83,000 – 70,000 = 13,000.
(e) Suppose that everything is as in the original statement of the problem except that now
the real interest rate is .25 (25%). What will her current consumption and current saving or
borrowing be now? (3 points)
Then the present value of her lifetime consumption is x + x/(1+.25 = 2.25x/1.25.
PVLR = 70,000 + 91,000/1.25 so we can write the consumer’s budget constraint as
2.25x/1.25 = 70,000 + 91,000/1.25
and solve for x. Multiplying through by 1.25 we have
2.25x = 87,500 + 91,000 = 178,500,
or
x = 178,500/2.25 = 79,333.33.
Her current borrowing will be 79,333.33 – 70,0000 = 9333.33.
40
2. Fred’s Frisbees is trying to determine how many Frisbee pressing machines to buy for
its new factory. The real price of a new pressing machine is 7500 Frisbees. The depreciation rate
on these Frisbee presses is equal to 10% per year. In other words, after one year of use the real
value of a Frisbee press is 6750 Frisbees. The expected future marginal product of these
fabricating machines is given by the expression 3350 – 20K, measured in Frisbees. The real
interest rate is 8% (.08).
(a) What is the user cost of capital? (Be sure to specify the units in which the user cost is
measured).
uc = (.08 + .1)(7500) = 1350 units of output.
(b) What is the profit-maximizing number of Frisbee presses for Fred’s to purchase for its
new factory?
The profit-maximizing number of Frisbee presses is determined by setting the future marginal
product of capital equal to the use cost of capital:
1350 =3350 – 20K, so K = (3350 – 1350)/20 = 100.
(c) Before purchasing the machines Fred’s finds that it will be subject to a new tax of
32.5 percent on all of its revenue. Now what is the profit maximizing number of machines for
Fred’s to purchase? (Round down to the nearest whole number.)
The tax adjusted use cost of capital is given by (.08 + .1)(7500)/(1 - .325) = 2000
2000 = 3350 – 20K, so K = (3350 – 2000)/20 = 67.5. We round down to 67 Frisbee presses so
that the last press does not have a marginal product that is less than its tax-adjusted user cost.
A certain economy has the following characteristics
.
Cd = 130 + .6Y – 1000r
Id = 300 – 3000r
G = 250
and the full-employment level of output equals 1200.
(a) Derive equation for desired national saving Sd as a function of Y and r.
Sd = Y – Cd – G = Y – (130 +.6Y – 1000r) – 250 = .4Y – 380 + 1000r.
(b) Find the real interest rate that clears the goods market in two ways. Assume that the
level of output is the full-employment level of output. Illustrate the equilibrium graphically.
First, use Y = Cd + Id + G:
1200 = 130 +( .6)(1200) – 1000r + 300 – 3000r + 250
41
4000r = 130 + 720 + 300 + 250 – 1200 = 200,
so r = 200/4000 = .05.
Second, use Sd = Id:
(.4)(1200) -380 + 1000r = 300 – 3000r,
4000r = 380 – 480 + 300 = 200.
so r = 200/4000 = .05.
(c) Government purchases increase to 290. What is the new the equation describing
desired national saving? Illustrate the change graphically. What is the new equilibrium interest
rate?
Sd = Y – Cd – G = Y – (130 +.6Y – 1000r) – 290 = .4Y – 420 + 1000r = 60 + 1000r.
r
Sd1
Using Sd = Id:
Sd0
(.4)(1200) – 420 + 1000r = 300 – 3000r,
4000r = 420 – 480 + 300 = 240.
so r = 240/4000 = .06.
0
60
S
100
4. Analyze the effects of each of the following on national saving, investment, and the real
interest rate. Explain your reasoning and illustrate it with an appropriate diagram.
(a) Consumer confidence falls, so consumers decide to consume less and save more at
every level of the real interest rate.
r
Id
Sd1
Sd0
r0
If consumers decide to save more at every level of
the real interest rate, the desired saving curve will
shift to the right. This shift causes an increase in the
level of saving and investment and an decrease in the
real interest rate.
r1
0
S 0 = I0
S 1 = I1
S
42
(b) A new technology breakthrough increases the future marginal product of capital and
expected future income.
r
Id1
Id0
Sd1
Sd0
r1
r0
0
60
S
100
The increase in the future marginal product of
capital shifts the desired investment curve to the
right. The increase in expected future income
causes households to increase their current
consumption, thus reducing their desired saving,
which shifts the desired saving schedule to the
left. Both shifts tend to increase the level of the
expected real interest rate. The increase in
desired investment causes an increase in
investment and saving, but the decrease in
desired saving causes a decrease in saving and
investment, so it is not possible to say whether
saving and investment increase, decrease or stay
the same.
5. A consumer has a current income of $80,000, an expected future income of $110,000, and no
current wealth. The real interest rate is .1 (10%).
(a)Calculate the present value of this consumer’s lifetime resources.
80,000 + 110,000/1.1 = 180,000.
(b) Carefully graph this consumer’s budget constraint, labeling all important quantities.
cf
110,000
Slope = – (1.1)
0
80,000
180,000
c
(c) Suppose that this consumer wants to consume equal amounts in the present and in the
future. Will this consumer be a current saver or a current borrower? Explain.
Clearly, this consumer will be a current borrower. It is easy to see that if this consumer were to
consume $80,000 or less during the current period, he/she would be consuming $110,000 or more
in the future, so that his/her consumption could not be equal in the two periods. So the consumer
will want to consume more than $80,000 in the current period, which will make this consumer a
current borrower.
43
(d) Suppose the real interest rate were to increase. Would this consumer’s current
consumption increase or decrease? Give a justification of your answer that includes a
discussion of income and substitution effects.
In this case, the increase in the consumer’s
current consumption will decrease. An increase
in the real interest rate has two effects on
current consumption, a substitution effect and
an income effect. The substitution effect arises
110,000
because an increase in the real interest rate
f*
causes current consumption to become relative
c
Slope = – (1.1)
to future consumption, so the consumer has a
tendency to substitute future consumption for
current consumption, causing current
0
c*
180,000
80,000
consumption to decrease. The income effect
c
depends upon whether the consumer is currently
a saver or a borrower. In this case the consumer
is a current borrower, so the increase in the real interest rate is bad for the consumer. This can be
seen in the diagram above. The consumer’s current consumption of c* is greater than her current
income of $80,000, so she is a current borrower. When the real interest rate increases, she can no
longer afford (c*, cf*) so she must reduce both current and future consumption.
New budget line
c
f
6. Desired consumption for an economy is given by the equation
Cd = 1000 + .6Y – 4000r.
Government purchases are given by G = 1500.
(a) Write an expression relating desired saving, Sd, to Y and r.
Sd = Y – Cd – G = Y – (1000 +.6Y – 4000r) – 1500 = .4Y – 2500 + 4000r.
(b) Suppose that the full-employment level of output is 10,000. Graph the relationship
between desired saving, Sd, and the real interest rate r. (Your graph should include
properly labeled axes and an indication of the scale on each axis.)
r
Id
Sd = .4Y – 2500 + 4000r
= (.4)(10,000) – 2500 + 2000r
= 1500 + 4000r.
Sd
.05
0
1500
1700
2000
S,I
44
(c) If desired investment for the economy is given by the equation
Id = 2000 – 6000r,
calculate the equilibrium real interest rate for the economy.
Set Sd = Id: 1500 + 4000r = 2000 – 6000r. The solve for r: 10,000r = 500 so r = 500/10,000 =
.05.
(d) Using the equilibrium real interest rate that you calculated in part (c), calculate the
equilibrium level of saving, investment, and consumption in the economy. Does Y = C + I + G in
equilibrium?
Sd = 1500 + 4000r = 1500 + (4000)(.05) = 1700.
Id = 2000 – 6000r = 2000 – (6000)(.05) = 1700.
Cd = 1000 + .6Y – 4000r = 1000 + (.6)(10,000) – (4000)(.05) = 6800.
C + I + G = 6800 + 1700 +1500 = 10,000 = Y.
(e) Add the relationship between desired investment and the real interest rate to your
graph in part (b), and show the equilibrium values of r, Sd and Id from parts (c) and (d)
7. Use a saving investment diagram (and an explanation) to show what happens to saving,
investment and the real interest rate in the following scenario. (Note: we are just looking at the
goods market here.)
A practical technology that uses nuclear fusion to produce electricity from sea water is
discovered. The effect of this innovation is expected to make energy cheap and abundant in
the future.
The newly discovered abundance of cheap
r
Id1
energy in the future will cause an increase in the
Id0
Sd1
expected future marginal product of capital. The
increase in the future marginal productivity of
d
S
capital will cause an increase in the level of
0
r1
desired investment at each level of the real
interest rate. Graphically, this will be reflected
r0
in a rightward shift in the desired investment
curve. In addition, there will be an increase in
expected future income, which will cause an
increase in both current and future consumption.
0
S,I
S1 S0
This means that current desired national saving
will decrease at every level of the real interest
rate. (The substitution of current leisure for
future leisure that we found in question #1 will also contribute to a reduction in current desired
national saving, since it leads to a decline in current income.) In the new equilibrium, the real
interest rate will increase, but the effect on the level of saving and investment in the economy is
45
ambiguous. (In the diagram at left, S and I go down, but they could have gone up if the shift in
desired investment had been greater or the shift in desired saving had been smaller.)
46
Chapter 5: Saving and Investment in an Open Economy
Goods Market Equilibrium in Open Economy
 Y = C + I + G + NX
 NX = Y – (C + I + G)
 In goods market equilibrium, the amount of net exports a country sends abroad
equals the country’s total output, less desired spending by domestic residents (C +
I + G).
 Total spending by domestic residents is called absorption.
 Absorption = C + I + G
 When output exceeds absorption (NX > 0), economy has a current account
surplus
 When economy absorbs more than it produces (NX < 0), it is a net importer, and
holds a current account deficit (typical for the US).



Curve above shows a small open economy that lends abroad. The amount of
foreign lending is equal to the amount that the country saves less the amount that
it invests at the given world real interest rate.
In a 2 country world, Net foreign lending + Net foreign borrowing = 0
NXH + NXF = 0
47
Example problems for Chapter 5
Consider two large open economies where (H) denotes the home country and (F)
represents the foreign country that we can treat as the rest of the world (all numbers are in
billion $).
1)SdH = 70 + 10r
2)IdH = 100 - 50r
3)SdF = 50 + 20r
4)IdF = 40 - 40r
a) Find the world real interest rate that “clears” the world financial market. r = 0.16666
b) Draw two diagrams (side by side) depicting the conditions given the desired savings
and desired investment functions for each country. Be sure to completely label your
diagrams.
For Home; Sd = 71.66 ; Id = 91.66 (NX = -20) For Foreign; Sd = 53.33; Id = 33.33 (NX =
20).
c) Now suppose there is a positive temporary supply shock in the home country such that
desired savings is increased by 10 (there is no change in desired investment) for any
given real world interest rate (rw). Find the “new” real world interest rate the ‘clears’ the
world financial market.
r = 0.0833
d) Find the new desired saving(s) and desired investment(s) for both the home (H) and
the foreign (F) countries, respectively. Depict these ‘new’ conditions on your diagram
above (make sure you label everything).
For Home; Sd = 80.83 ; Id = 95.83; For Foreign; Sd = 51.66; Id = 36.66
e) Given the temporary supply shock in c), now suppose that the government of the home
country has discovered that the scientists of the foreign country have developed a new
technology such that desired investment in the foreign country (IdF) has increased by
unknown amount, call it x. Even though the home government does not observe x
directly, they do observe that the real world interest rate (rw) that clears the world
financial market is the same as it was originally (as in part a). Find x! x = 10
f) Finally, depict these new conditions in two new diagrams, similar to the one above.
Again, be sure to label your diagram completely.
48
Below are numerous problems from previous exams – excellent practice!
Exam 1 – Econ 304 – Chuderewicz – Spring – 2006 –
Name _______________________ Last 4 __________ Recitation 7 8 9 10 11 12
Date____________ Good luck!
The exam is worth 100 points. Answer all questions and please do all your work in pen if
possible.
1) (20 points total) For the new Real World State College season MTV is looking for
Penn State students. Students are asked to produce “drama” as a part of their contract.
The marginal productivity of labor curve is given by MPN = 340-6N.
The supply of Penn State students is given by Ns = 45 + 2 w ; where w is the real
wage per hour.
1a) Compute equilibrium values for the real wage and employment (4 points). Illustrate
this equilibrium on a labor market diagram. Please be sure you label the diagram
completely.
49
A correct and completely labeled diagram is worth 7 points
50
1b) Suppose the state imposes a (real) minimum wage = 5.00 per hour. What is the level
of employment now? Explain. (2 points)
1c) Now the Penn State student union successfully forces MTV to pay each student a
minimum “happy valley living wage” equal to 10.00 per hour. That is, 10.00 per hour
represents the effective ‘new’ minimum wage. What is the level of employment now? (2
points) Is there involuntary unemployment? Why or why not? Explain and show all
work . (2 points) Show this development on your diagram being sure to label the diagram
completely.
1d) Suppose now that a new course offered by the Drama Department increases the
productivity of each student so that the NEW marginal product of labor equals MPN =
400 – 6 N. Find the equilibrium ‘market’ clearing wage and level of employment. (2
points) Show this development on your diagram. How does your answer compare to
your answer in 1c)? Explain. (2 points).
51
2. (25 points total – assume a two period world as we did in class) A sports athlete
named Ben earns $100K in year number one and only $60K in year number two. In
addition, Ben receives a bonus in year one equal to $20K (please do not treat this $20K as
income, it is a one time bonus!) There is no bonus in year two. The real interest rate in
the economy is 10 percent.
a. Derive an expression for Ben’s budget constraint in intercept - slope form (show all
work) (2 points). Be sure to explicitly identify and interpret each intercept and the
slope (i.e., the intuition of each). What is Ben’s present value of life time resources? (2
points)
b. Now draw Ben’s budget constraint being sure to label your diagram completely (i.e.,
label intercepts and slope with real numbers!). Be sure to also label Ben’s no borrowing
– no lending point (again, use real numbers). (2 points)
A correct and completely labeled diagram is worth 7 points
52
c. Suppose that Ben tells you that he wants to smooth consumption completely. What is
Ben’s optimal consumption in each period (please show all work)? (2 points) Is he a
borrower or a lender? Explain using real numbers (2 points). Depict Ben’s optimal
consumption basket in your diagram.
d. Now suppose the real interest rate falls to 5 percent. What is Ben’s optimal
consumption now? (2 points) Does Bens’ saving increase or decrease as a result of the
lower real interest rate? (2 points) Show all work and explain, being sure to address and
explain the income and substitution effects at work here (as we did in class). (2 points)
e. Depict this development (the lower r) on your diagram being sure to label your axes
with real numbers (hint, Ben’s budget constraint has changed).
f) Has Ben’s present value of lifetime resources changed, given the lower r? Why or why
not? Be specific (2 points).
53
3. (15 points total)You are entering the spray painting business and you need to
determine how many spraying machines you need to buy to maximize profits. Please
answer the following questions given the information below. Please be sure to SHOW all
work!
A brand new mixing machine costs 300 units of output and the rate of depreciation is
20% (we assume that you can purchase fractions of machines).
The real interest rate is 10%.
And the expected marginal product of capital is given by MPKf = 400 – 5K.
a) What is the user cost of capital? (Show work) (2 points)
b) How many mixing machines should you buy to maximize profits? (2 points)
c) Draw a graph depicting the state of affairs and label this initial profit maximizing
condition as point A.
A correctly drawn and completely labeled diagram is worth 7 points
54
d) Now suppose the government imposes a tax equal to 20% of gross revenue. What
happens to the profit maximizing number of mixing machines? Show all work and depict
this development as point B on your diagram. (2 points)
e) Given a slow economy, the government decides to give an investment tax credit equal
to 20 percent. Calculate the new profit maximizing level of spraying machines and show
this development on your diagram as point C (2 points).
55
4. (20 points total) A closed economy has full employment level of output of 2,000.
Government purchases, G, are 200, taxes (T) are also 200. Desired consumption and
investment are:
Cd = 400 + 0.5(Y –T) - 600r
Id = 600 - 200r
Where Y is output, r is the real interest rate, and T is taxes.
a. Find an equation relating desired national saving, Sd to r (assume a full employment
level of output). (2 points)
b. Assuming that output equals the full-employment level of output, find the real interest
rate that clears the goods market (show all work). (2 points)
c. Draw a desired saving and desired investment diagram depicting your results (being
sure to completely label your diagram)
A correctly drawn and completely labeled diagram is worth 5 points
56
d. Suppose that the desired consumption function changes and is now:
Cd = 450 + 0.5(Y –T) - 600r
What could cause such a change in desired consumption? (2 points)
e. Given the new desired consumption function (see part d), re-solve for the goods
market clearing real interest rate and market clearing levels of desired investment and
desired savings respectively. Show this development on your diagram and label this new
equilibrium as point B. Please show all work. (4 points)
f) Given the ‘new’ consumption function in part d), the desired investment function also
changes and is now: Id = 700 - 200r. What could cause such a change in investment? (2
points)
g) Re-solve for the goods market clearing level of the real interest rate and the associated
market clearing levels of desired saving and investment respectively. (3 points). Please
show this development on your diagram.
57
5. (20 points total) Consider two large open economies where (H) denotes the home
country and (F) represents the foreign country that we can treat as the rest of the world
(all numbers are in billion $).
1)SdH = 30 + 20r
2)IdH = 40 - 30r
3)SdF = 70 + 10r
4)IdF = 90 - 40r
a) Find the world real interest rate that “clears” the world financial market. (2 points)
b) Find the levels of desired investment and desired savings for both the home country
(H) and the foreign country (F), given your answer in a). (4 points)
58
c) Draw two diagrams (side by side) depicting the conditions given the desired savings
and desired investment functions for each country. Be sure to completely label your
diagrams.
Correctly drawn and completely labeled diagrams are worth 6 points total.
d) Now suppose there is a positive temporary shock in the home country such that desired
investment is increased by 10 (there is no change in desired savings) for any given real
world interest rate (rw). What could cause such a change? (2 points)
e) Find the “new” real world interest rate that ‘clears’ the world financial market (2
points).
59
f) Find the new desired saving(s) and desired investment(s) for both the home (H) and the
foreign (F) countries, respectively. (4 points). Depict these ‘new’ conditions on your
diagram above (make sure you label everything).
60
Exam #1 from spring 2009
Please answer all questions. You must show all work or points will be taken off.
1. Happy days are here again. In this problem we re-visit Dagwood and Homer but this
time, Dagwood cannot wait to open up that envelope and Homer, meanwhile, wishes he
had one to open…..we are in the midst of a giant stock market rally!!!!
Let’s begin with Dagwood’s numbers. Dagwood’s
current income is $130K and expected income next
period is $60K. Dagwood has current wealth equal to
$30K before he opens up the envelope. Note that
Dagwood, just like in the practice problem, prefers to
perfectly smooth consumption across the two periods.
Dagwood faces a real interest rate of 0.01 (1%) since Ben and the Fed
have been pretty easy with the money supply fighting the recession.
a) (5 points) Calculate Dagwood’s optimal consumption bundle showing all work. Then
draw a completely labeled graph (10 points for completely labeled graph) depicting this
initial optimal consumption bundle as point C*A (please use the space below)
61
b) (5 points) The envelope comes in the mail and Dagwood is psyched, he is tired of his
wealth disappearing. He opens up the envelope and finds that his wealth had risen by
50% to $45K (from $30K) and instead of yelling ouch like before, he yells yee-haw!
Recalculate Dagwood’s optimal consumption point and label on your graph as point C*B.
Now Bernanke, finally having something to smile about, decides to get
interest rates back up to ‘normal’ levels, as he is very concerned about
inflation. As such, Ben and the Fed get the real rate up to 0.05 (5%).
c) (5 points) Re-calculate Dagwood’s optimal consumption bundle given the
change in the real rate of interest and label this third optimal point as C*C .
62
d) (5 points) Is Dagwood better or worse off due to the increase in the real rate of
interest? Explain being sure to discuss exactly how the substitution and income effects
play a role here. Be sure to define what the income and substitution effects are and how
they play a role in Dagwood’s decision to alter his previously optimal bundle. Also,
comment on whether these income and substitution effects work in the same or opposite
direction (i.e., is it a tug of war or do they work in the same direction?) in this particular
case.
(NEW GRADER) Homer’s current income is $100K and expected income
is $120K. Just like in the practice problem, he has no current or expected
wealth and is definitely not into smoothing consumption. Homer (just like in
practice problem) prefers to consume twice as much this period relative to
next period. He faces the same initial real rate that Dagwood faces.
f) (5 points) Calculate Homer’s optimal consumption point showing all work. Then
draw a completely labeled graph (10 points) depicting this initial optimal consumption
bundle as point C*A (please use the space below using next page for graph))
63
Now the envelopes come in the mail and Homer gets nothing. He is jealous of his
neighbors but he gets over it quickly, after all, he is Homer!
Now Bernanke, finally having something to smile about, decides to get interest
rates back up to ‘normal’ levels, as he is very concerned about inflation. As
such, Ben and the Fed get the real rate up to 0.05 (5%).
g) (5 points) Re-calculate Homer’s optimal consumption bundle given the
change in the real rate of interest and add as point C*B. on your existing
diagram.
64
h) (5 points) Is Homer better or worse off due to the increase in the real rate of interest?
Explain being sure to discuss exactly how the substitution and income effects play a role
here. That is, how do they play a role in Homer’s decision to alter his previously optimal
bundle? Be sure to comment on whether these income and substitution effects work in the
same or opposite direction (i.e., is it a tug of war or do they work in the same direction?).
65
2. PART 1. This problem is broken into two parts that are totally connected to each other. In this
first part of the question, you apply Chapter 3 (labor mkt., etc) material and in PART 2, you get to
use Chapter 4 (goods market equilibrium) material. Please take all calculations to two decimal
places where appropriate except with real interest rate calculations (PART 2), where you need to
take the calculation to three decimal places, if appropriate. PLEASE SHOW ALL WORK AND
COMPLETELY LABEL ALL DIAGRAMS.
The following equations characterize a country’s closed economy.
Production function: Y = A·K·N – N2/2
Marginal product of labor: MPN = A·K – N.
where the initial values of A = 5 and K = 9.
The initial labor supply curve is given as: NS = 15 + 9w.
Cd = 50 + .50Y – 400r
Id = 400 – 600r
G = 100
a) (5 points) Find the equilibrium levels of the real wage, employment and output.
66
b) (10 points for completely labeled diagrams) In the space below, draw two diagrams
vertically with the labor market on the bottom graph and the production function on the
top graph. Be sure to label everything including these initial equilibrium points as point
A.
We now have numerous changes to our economic conditions (all is not constant). Think
of all these changes happening together, that is, we go from one state of economics
affairs to a different state of economic affairs. Below are the changes.



The labor supply changes and is now: NS = 10 + 9w .
K* goes up from 9 to 10.
The desired investment function changes and is now Id = 500 – 600r
c) (5 points) What could cause such a change in labor supply? Please give two specific
and well supported answers.
67
d) (10 points) Draw a user cost / MPKf diagram and explain why K might rise from 9 to
10. That is, start at initial point A where K* = 9 and then show how, and explain why
(give two well supported reasons), K* might rise to 10. Note, do not use changes in the
real rate of interest as an explanation, use other reasons. Make sure you clearly identify
how your user cost / MPKf diagram is affected given your reasoning.
e) (5 points) Given the change in NS and K*, repeat part a (i.e., find the equilibrium levels
of the real wage, employment and output). Add these results to your existing two
diagrams labeling these new equilibrium points as point B.
68
f) (5 points) Are your results consistent with the New Economy? Why or why not? Be
very specific connecting your results thus far in this problem to the movements in the
relevant economic variables during the New Economy years (hint, wages, both real and
nominal, employment, GDP).
PART 2 (NEW GRADER)
Before we start this problem, put the initial Y as computed in part a) here ____________.
And the new Y (after the change in conditions) here ___________.
g) (10 points) Given the initial conditions, solve for the equilibrium real rate of interest
(that clears the good market) and the associated levels of desired savings and desired
investment. Also, what is the level of desired consumption at this initial equilibrium?
69
10 points for correct and completely labeled diagram) Draw a Sd = Id diagram in the
space below locating this initial equilibrium as point A.
NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1
h) (5 points) What could cause such a change in the desired investment function? Please
provide two specific and well supported answers?
70
i) (5 points) Given these changes (i.e., changes in K*, Y, and Id), calculate the new
equilibrium levels of the real interest rate, desired savings and investment. Please add
this new equilibrium point to your diagram and label as point B.
j) (5 points) Given these new results, calculate the percent change in consumption and
investment and comment on whether these results are consistent with the New Economy
years.
71
3. Open Economy – Two Large country problem
USA Initial Conditions
Cd = 300 + 0.4(Y-T) – 200rw
Id = 150 – 200rw
Y = 1000
T = 200
G =275
China Initial Conditions
CdF = 480 + .4(YF – TF) – 300rw
IdF = 225 – 300rw
YF = 1500
TF = 300
GF = 300
a) (5 points) What is the equilibrium real interest rate that clears the international goods
market? Show all work.
b) (5 points) Compare the level of absorption in each country to the income generated in
each country. Is the US spending beyond its means? Is China the lender? Explain!
72
In the space below, draw two diagrams side by side, with the USA on the left and China
country on right. Locate this initial equilibrium as points A on both diagrams (there are
four point A’s, two on each diagram). Be sure to label diagrams completely labeling the
trade deficit/surplus on each graph, etc.
10 points for correct and completely labeled diagram
Now conditions change in the US. The three changes we need to account for are listed
below:



The consumption function for the US is now: Cd = 360 + 0.4(Y-T) – 200rw
The desired investment function for the US is now: Id = 160 – 200rw
Full employment (=actual) output (Y) for the US is now: Y = 1100
c) (5 points) Give three reasons why the consumption function might change the way it
did.
73
d) (5 points) Re-calculate the new equilibrium real interest rate and the associated new
levels of desired savings and investment for each country and label these new equilibrium
points on your existing diagram as point B.
e) (5 points) What has happened to the US’s trade balance and why?
f) (5 points) What has happened to the desired savings function for the US? Please
explain.
74
Chapter 7 and the first part of Chapter 14 together– The Asset Market,
Money, and Prices








Money: assets that are widely used and accepted as payment (a medium
of exchange)
Money = currency + demand deposits
The cost of holding money is the interest income forgone
%∆P is inflation
Over half the US currency is held abroad – most likely due to its stability
and its good store of value (Belarus example)
Money/Asset demand: quantity of assets that people choose to hold in
their portfolios
Money/Asset supply: quantity of assets that are available
Asset market is in equilibrium when money supplied = money demanded
3 Functions of Money:
1. Medium of Exchange
a. Definition: device for making transactions
b. Allows us to specialize
c. Results in a more efficient use of scarce economic resources
2. Unit of Account
a. Basic unit for measuring economic value
b. This simplifies the comparison among different goods
3. Store of Value
a. Money is a way of holding wealth
b. Any asset can be a store of value and money is typically not
considered as a good store of value (i.e., we assume a zero
nominal return on money and thus, the actual return on money is
negative the rate of inflation). Bonds and Stocks and other nonmonetary assets (e.g., real estate) are usually thought of being a
‘better’ store of value than money.
c. Money’s usefulness as a medium of exchanges is why people
choose to use it as a store of value (vs. stocks, bonds, etc.) even
though the return is less
75
Monetary Aggregates
 M1 includes
a. Currency
b. Checkable deposits
c. Traveller’s cheques
 M2 includes M1 +:
a. Savings Deposits
b. Money market mutual funds and deposit accounts
c. Small denomination time deposits
 M3 includes M2 +:
a. Large denomination time deposits
b. MMMFs held by institutions
c. Deposits of American dollars held abroad
d. Discuss the Chuderewicz research regarding forecasting with
real M3.
Money Supply Notes –(most of this is in Chapter 14 of your textbook)
Define money as below:
1) M = C + D where C = currency (cash) and D = demand deposits (checking accounts)
The Fed has pretty darn good control over what is referred to as the monetary base (MB)
(also referred to as high powered money since changes in MB due to open market
operations result in high powered effects, via the money multiplier, on the money
supply). Define MB as follows with C = currency as before, R equals total reserves, a
combination of required reserves (RR) and excess reserves (ER).
2) MB = C + R
Divide 1) by 2)
3) M/MB = (C + D)/(C + R)
Now a “trick” – divide the numerator and denominator of the RHS (right hand side) of 3)
by D
4) M/MB = (C /D+ D/D)/(C/D + R/D)
Let’s do a few things to 4) – a) get MB on RHS, b) D/D = 1, and c) R = RR + ER
5) M = [(C /D+ 1)/(C/D + RR/D + ER/D)] MB
The term in brackets is referred to as the money multiplier, which is a little
different than what you saw in principles. Equation 5) implies that the money multiplier
is influenced by household behavior via C/D, which is determined by us. C/D is simply
76
the currency to deposit ratio. For example, if you typically carry $100 in cash and you
have $1000 in a demand deposit, then your C/D is 0.1. Think about what happened to
C/D during Y2K.
Equation 5) also implies that bank behavior influences the money multiplier via
ER/D. Even though banks tend to get rid of excess reserves (ER) since they earn zero
interest, sometimes they hold on to them. What do you think banks were doing during
Y2K? Probably holding a lot of ER to meet the liquidity needs of their customers (they
anticipated significant withdrawals)!
The last player that has influence over the money multiplier is the Fed themselves
via RR/D which is simply the reserve requirement ratio (this is what you were supposed
to learn in principles). Note that if we let C/D and ER/D equal zero, the money multiplier
collapses to 1/(RR/D) which is the ‘simple’ money multiplier that you may or may not
have learned about in principles.
Specifics on the money multiplier: If C/D, ER/D, or RR/D go up, then the
multiplier falls. This is important, because if MB remains constant, the money supply
will fall along with the multiplier. We will now use an example that is a simplified
version of what happened during the great depression.
Graphical Analysis, connecting the reserve market to the money market.
Initial Conditions
Let C/D = .2 , RR/D = .1 and ER/D = 0
Money Multiplier = (.2 +1)/ (.2 + .1 + 0) = 4
What does this mean?
A couple things: first, suppose the MB is $ 100 billion ; M = $ 400 billion
Second, a 10 billion dollar open market purchase will result in a $40 billion increase in
the money supply (remember high powered money!) See the two graphs below.
77
MB
MB’
i
i
100
110
Ms
Ms’
400
440
MB
M
78
The Great Depression – an Example
The Fed is blamed by some for causing the great depression or at the very least, failing to
respond appropriately as in they should of conducted more open market purchases! Of
course hindsight is 20/20.
What will a bank run do to C/D ratios?
So C/D rose dramatically as people were trying to get their cash – remember, there was
no FDIC insurance back then.
ER/D also rose for two reasons – one, banks were keeping ER to meet the liquidity needs
of their customers and two, had no one to lend to – banks are reluctant to make loans in
such a dismal environment (i.e., the default risk of the borrower is naturally high in such
a dismal environment).
Ironically, RR/D went up as well. The Fed was young, less than 20 years in existence
and felt that raising the required reserve ratio would make banks more sound as well as
giving the public more confidence so that they would not run on banks – in hindsight,
raising the required reserve ratio was a mistake!
All three components of money multiplier rose during the great depression – impact on
money multiplier?
Recall Money Multiplier equals:
[(C /D+ 1)/(C/D + RR/D + ER/D)]
Initially, let C/D = .2 , RR/D = .1 , and ER/D = 0
With numbers:
[(.2+ 1)/(.2 + .1 + 0)] = 4
Now account for changes in C/D, RR/D, ER/D
Let C/D up to .5, RR/D up to .2, ER/D up to .3
[(.5+ 1)/(.5 + .2 + .3] = 1.5
NEW Multiplier = 1.5
With numbers – before the great depression
M = ( 4 ) MB
If MB = $ 100 billion ; M = $ 400 billion
79
Now great depression hits and the multiplier falls to 1.5
MB still at $100 billion – M = 150 billion
Now the Fed isn’t blind – they buy $ 100 billion in Gov Securities, increasing MB by
$100 billion – Money Supply up to $300 billion (1.5 times $200 billion) – still a 25%
drop from where it was initially.
So the Fed pumped up the Monetary Base via open market purchases – but it was not
enough to offset the dramatic fall in the money multiplier – they should have been
easier!!
The lesson here is that the Fed has incomplete control over the money supply and in order
to have better control, they better try to figure out what determines C/D and ER/D ratios.
In normal times, these are pretty stable so that ‘normally,’ the Fed has pretty good control
over the money supply (M1).
Portfolio Allocation and the demand for assets
Tell Texas Tech story!
We will make the following simplification as the book does – we separate the many
assets in to monetary (money) and non-monetary assets (everything else).
There are three main determinants of asset pricing with each asset having somewhat
unique characteristics.
1) Expected return: The higher the expected return of the asset, all else constant, the
higher the price of the asset. We assume money (C+D) earns a nominal return of zero
and a real return equal to the ‘negative’ of the inflation rate.6 Non-monetary assets have
an expected return of inm. Note, that with QE2, the Fed is purposely lowering the
expected return on bonds so that people buy other non-monetary assets like stocks! We
have discussed this many times before!
Asset price = f (Rete) :
+
{stated as “the asset price is a positive (+) function (f) of it’s expected return (Rete), all
else constant}
2) Liquidity: Liquidity is an attractive quality in any asset and a highly liquid asset has
three qualities:
6
Suppose inflation over a year is 10% and I keep $100 in my pocket. That $100 next year would be able to
purchase 10% less in real goods and services given the 10% rise in the general price level that has occurred
over the year.
80
1) it is easy (low cost) to convert the asset into money where money is defined as
transactions money
2) it can be converted to money quickly
3) the amount that it is converted to is representative of its fundamental value (i.e.,
I can sell my house very quickly and easily for $5, but that doesn’t mean it is
liquid!).
Typically, the more liquid the asset, the lower the return. Take money, typically
considered to be the most liquid asset of all.
Liquidity is especially attractive in a highly uncertain environment. We will ‘say’
more about his in a moment.
Asset price = f (Liq) :
+
{stated as “the asset price is a positive (+) function (f) of it’s liquidity (Liq), all else
constant}
3) Risk: The more risky the asset, the more uncertain as to the assets’ return. Risk arises
for a variety of reasons and we assume that all else equal, investors prefer assets with less
risk (i.e., on average, investors are risk averse). We also note that risk and expected
return are related – typically, the higher the risk, the higher the expected return
(investors require a higher expected return to take on the higher risk).
Asset price = f (Risk) :
{stated as “the asset price is a negative (-) function (f) of it’s Risk, all else constant}
APPLICATION – examining the behavior of these three main characteristics at the
height of the financial crisis – i.e., the fall of 2008. – click Here and zoom in on what
was happening during the fall of 2008.
So during this time, the demand for money rose dramatically, since money is more liquid
(liquidity is highly desirable in a crisis!), ii is less risky, and the expected nominal return
of zero is a lot better than a negative one (money under the mattress is better than losing
it in the stock market).
MONEY DEMAND –
The other half of the money market - money demand
81
There are quite a few determinants of money demand
First –inm , the (opportunity) cost of holding money is the interest foregone by holding
a non-monetary asset that we typically call a bond (inm). The higher the interest rate, the
higher the cost of holding money so the less money you will hold. This idea gives us a
negatively sloped money demand as shown below.
Second – real income (denoted Y) – if your real income goes up you will conduct more
transactions and in order to conduct more transactions, you need to hold more money.
Graphically, an increase in real income (economic growth) shifts the money demand
curve to the right (i.e., you desire to hold more money at any given interest rate)
Third – Prices – if prices go up, you need more money to conduct the same number
(amount) of transactions. In fact, we assume that nominal money demand is proportional
to the price level. For example, if prices rise by 4% then nominal money demand will rise
by 4%. Since we deal with real money supply and real money demand, we can derive a
general form of real money demand as follows (the text does this on pages 253 and 254)
1) Md = P x L(Y, i) L is a function to be determined – but we know a few things from above - Md is
positively related to P and Y and negative related to i (note i = inm).
Noting that i = r+ πe and using the proportionality assumption, we can re-write 1) as
2) Md/P = L(Y, r+πe)
A more specific money demand function is in order – this one is from a numerical
problem from the back of chapter 7
3) Md/P = 500 +.2Y – 1000(r+πe)
Note that 3) is consistent with real money demand being a positive function of real
income (GDP) and negatively related to the nominal interest rate.
THE INTERCEPT IN THE REAL MONEY DEMAND EQUATION – VERY
IMPORTANT!
Beyond the three determinants of money demand, there are others – and given the
recent financial crisis, these other determinant have played a critical role
Fourth determinant of real money demand – the liquidity of non-monetary assets – if
the liquidity of non-monetary assets falls, all else constant, money demand will increase
since money is the most liquid asset on the earth and liquidity is a desirable quality. The
82
result is a rightward shift in the money demand function – even though real income (Y)
and i = r+πe did not change.
Fifth determinant of real money demand – risk on non- monetary assets – if the risk on
non-monetary assets rises, all else constant, then money becomes more attractive since
we assume that people are risk averse, all else constant.
Given the financial crisis, especially during the fall of 2008, we can characterize the
situation with simple graph of the money market.
Now, what should the Fed do?? If they do nothing, then real rates will rise which is
exactly what we DON’T NEED given the financial panic. In addition, the Fed gained
authority to pay interest on reserves (both required and excess) in October, 2008. We
know from our money supply discussions and especially money supply problem #1, that
the real money supply will shift to the left, exacerbating the increase in interest rates due
to the two portfolio shocks to money demand. In summary, the Fed was facing an
increase in money demand and a decrease in money supply during the fall of 2008, both
of which will increase the real rate – to offset this, the Fed needs to conduct massive
amounts of open market purchases. Click Here to see if they did (look at the data during
the fall of 2008)!
How does the story change given the new economy during the mid to late 1990s?
83
Other Determinants of Money Demand –
So far, we have that nominal money demand is a function of positive function of P, Y and
risknm and a negative function of i( = r + πe) and liqnm.
In principles and elsewhere, you probably have the nominal interest rate on the vertical
axis, since the opportunity cost of holding non-interest bearing money is in fact the
nominal interest rate. But since we have been working with real interest rates throughout
the semester and desire to continue to do so, we place r on the vertical axis and hold
inflationary expectations (πe) constant so in effect, inflationary expectations becomes a
shift variable.
Example: if we set πe = 0, then i = r. (i.e., r = i – πe). Now if πe rises to 2% and we
assume that r stays the same, then i must rise by 2% as well – that is, the cost of holding
money has gone up, at the same real interest rate. The influence is that the money
demand function will shift to the left (i.e., money demand is negatively related to πe, all
else constant). See graphic below.
Final Determinants of Money Demand
Wealth – an increase in wealth will cause people to hold more money, since higher
wealth typically means more transactions. We need to remind ourselves that wealth is a
stock variable where income (y) is a flow variable.
Interest rate on money - If banks all of a sudden start paying interest on m, denoted im,
then all else constant, people will hold more money.
84
Efficiency of Payment Systems – years ago, this determinant of money demand was
very relevant. Now, we can pretty much ignore this determinant but through the years,
the increase in the efficiency of payment systems has resulted in people holding less
money, since it is easy to transfer money in savings to money in checking, in fact, many
banks do this automatically if you overdraw.
Identifying the shocks to real money demand is a very big deal when it comes to
monetary policy, If money demand increases because of a nominal shock such as the
risk of non-monetary assets rising, then the Fed should not only accommodate the shock,
they should conduct enough open market purchases so that the real rate falls and thus, we
might be able to offset the negative shock. Conversely, if the shock to money demand is
real, that is, money demand is increasing due to higher output, then the Fed should worry
about overheating and thus ‘allow’ real rates to rise to prevent inflation from accelerating.
All told, it is critical for the Fed to identify the shocks since the appropriate policy
response depends critically on the source of the shock.
85
The quantity theory of money and the equation of exchange
Another way to view supply and demand for money is through the equation of exchange:
MV = PY
Where M is the nominal money balances, V is the velocity of money (the number of
times a dollar bill turns over in a years time), P is the general price level, and Y is real
output (GDP).
Example – island economy with one good, bicycles. In 2010, there were 50 bicycles
produced at a price of $100 per bicycle. So nominal GDP (P times Y) is $5000. We also
have a nominal money supply equal to $1000. What is V? V = 5, which means, each
dollar exchanges hands (turns over) 5 times per year.
MV = PY = $1000 x 5 = $100 x 50
If we take the percent change of the equation of exchange, also known as the quantity
theory of money, we have:
%∆M + %∆V = %∆P + %∆Y
The equation above is extremely useful. Consider the following: Let us assume that V is
constant so that the %∆V = 0. If we go to the right hand side, what is the %∆ in P called?
What is the %∆ in Y called? Do we have any notion as to the optimal values of these
two important macroeconomic variables? Hint, the cruise ship example.
So let us write out the equation with the above information:
%∆M + 0 = 2% + 3%
Which implies that the Fed should allow the nominal money supply to grow at 5%. In
fact, this equation is often associated with Milton Friedman, who was a classical
economist and among many other famous quotes once said that:
“Inflation is always and everywhere a monetary phenomenon”
86
Let us apply this statement to the equation of exchange
Suppose the Fed bumps up money growth from 5% to 8%. Assuming that 1) Velocity is
constant and 2) we are in a classical world so that Y is determined by the production
function meaning that changes in M do not effect output (i.e., the aggregate supply curve
is vertical), then the increase in the growth rate of the money supply will result in an
equal change in the rate of inflation. Using the equation of exchange:
We start ed with:
5% + 0% = 2% + 3%
Then we have:
8% + 0% = 5% + 3%
And therefore “Inflation is always and everywhere a monetary phenomenon”
since the increase in inflation was caused by excessive money growth. In fact, Milton
wanted to kick the monetary policy steering wheel off of the cruise ship and replace
it with a robot that allows the money supply to grow at constant rate, depending on
what is going on with the velocity of money.
More on the velocity of money. To help us understand what make the velocity of money
‘tick,’ we can apply the episode of the fall 2008 when we were at the peak of the
financial crisis. As we know, money became an extremely attractive asset during this
time given the fear on non-monetary assets (except for US Treasuries – often referred to
as the safest asset on the earth). The increase in money holdings during this time,
assuming that prices and inflation along with output and changes in output for the
moment, were not changed means that the velocity of money has fallen! This make sense
since in effect, households are hoarding money so that each dollar is now turning over
less. What are the implications for monetary policy? Let’s start with our original set up
and then let the velocity of money fall by 10%, all else constant.
8% + 0% = 5% + 3%
then
8% + (-10%) ≠ 5% + 3%
87
but we know this cannot be! Something must change so that the equation is satisfied!
Since classical economists believe that prices are perfectly flexible, then we have the
following:
8% + (-10%) = (- 5%) + 3% AHHHH! This is deflation
So what must the Fed do to avoid this CENTRAL BANKING
NIGHTMARE????? You got it, pump up the money supply to
????? 15%
15% + (-10%) = 2% + 3%
In other words, when velocity falls the Fed better react and offset
the fall in velocity by pumping up the money supply to prevent deflation. So have they
been recently. Click Here for impressive evidence! If this link does not work, see the link
on our home page (where to monetary links are).
88
Example Problems for Chapter 7 and 14
1. Assume that the quantity theory of money holds. The velocity of money is 6. The full-
employment level of output is 12,000 and the price level is 2.
(a) Find the real demand for money and the nominal demand for money.
(b) Assume that prices are perfectly flexible and that government sets the money
supply at 6000. What will the price level be? Suppose the money supply increases
to 8000. What will the new price level be?
(c) If the quantity theory of money holds, the growth rate of real GDP is 3% per
year, and the growth rate of the money supply is 10% per year, what will the rate
of inflation be in the economy?
2. Suppose that the real demand for money is given by
Md/P = 100 + .6Y – 4000(r + πe),
Y = 1000, and πe = .05.
a. Draw an accurate graph of the relationship between the quantity of real money
demanded (Md/P on the horizontal axis) and the real interest rate (r on the vertical
axis). Label this line (Y = 1000, πe = .05).
b. Suppose that everything remains as in the original statement of the problem,
except that Y increases to 1500. On the same graph that you used for part (a),
draw an accurate graph of the new relationship between the quantity of real
money demanded and the real interest rate Label this line (Y = 1500, πe = .05).
c.
Suppose that everything remains as in the original statement of the problem, (so
Y is now back to 1000), except that πe increase to 0.1. On the same graph that you
used for parts (a) and (b), draw an accurate graph of the new relationship between
the quantity of real money demanded and the real interest rate Label this line (Y =
1000, πe = 0.1).
d. Suppose that the real interest is determined in the goods market at r = .05, and the
nominal money supply is given by M = 1200. Find the value of the price level in
the economy when (i) Y = 1000 and πe = .05, (ii) Y = 1500 and πe = .05, and (iii)
Y = 1000 and πe = 0.1.
89
Answers to Example Problems for Chapter 7
1. Assume that the quantity theory of money holds. The velocity of money is 6. The full-
employment level of output is 12,000 and the price level is 2.
(a) Find the real demand for money and the nominal demand for money.
According to the quantity theory of money, the relationship MD/P = Y/V, where
MD/P is interpreted as the real demand for money. So, the real demand for money
is given by
12,000/6 = 2000.
The nominal quantity of money demanded just the real demand for money times
the price level, so the nominal demand is given by
(2)(2000) = 4000.
(b) Assume that prices are perfectly flexible and that government sets the money
supply at 6000. What will the price level be? Suppose the money supply increases
to 8000. What will the new price level be?
In equilibrium the quantity of money supplied equals the quantity of money
demanded:
M/P = Y/V.
Substituting the values of M, V and Y we get
6000/P = 12,000/6,
or
P = 6000/2000 = 3.
If the money supply increases to 8000 then we have
8000/P = 12,000/6,
or
P = 8000/2000 = 4.
(c) If the quantity theory of money holds, the growth rate of real GDP is 3% per
year, and the growth rate of the money supply is 10% per year, what will the rate
of inflation be in the economy?
Since M/P = Y/V, we can write
90
ΔM/M – ΔP/P = ΔY/Y – ΔV/V.
Substituting the given growth rates we get
.1 – ΔP/P = .03 – 0,
or
ΔP/P = .1 – .03 = .07.
So the inflation rate will be 7%.
–ΔP/P = (0.6)(525 – 500)/500 = .03,
so
ΔP/P = – .03 (–3%)
ΔV/V = 0 + (.05) – (.02) = .03 (3%).
2. Suppose that the real demand for money is given by
Md/P = 100 + .6Y – 4000(r + πe),
Y = 1000, and πe = .05.
(a) Draw an accurate graph of the relationship between the quantity of real money
demanded (Md/P on the horizontal axis) and the real interest rate (r on the vertical
axis). Label this line (Y = 1000, πe = .05).
When r = .05, Md/P = 100 + (.6)(1000) – 4000(.05 + .05) = 300.
When r = 0, Md/P = 100 + (.6)(1000) – 4000(0 + .05) = 500.
Use these two points to plot the relationship as shown in the graph below.
91
r
Y = 1000
πe = 0.1
Y = 1000
πe = 0.05
Y = 1500
πe = 0.05
.05
100
300
500
600
Md/P
800
(b) Suppose that everything remains as in the original statement of the problem,
except that Y increases to 1500. On the same graph that you used for part (a),
draw an accurate graph of the new relationship between the quantity of real
money demanded and the real interest rate Label this line (Y = 1500, πe = .05).
When r = .05, Md/P = 100 + (.6)(1500) – 4000(.05 + .05) = 600.
When r = 0, Md/P = 100 + (.6)(1500) – 4000(0 + .05) = 800.
Use these two points to plot the relationship as shown in the graph above.
(c) Suppose that everything remains as in the original statement of the problem, (so
Y is now back to 1000), except that πe increase to 0.1. On the same graph that you
used for parts (a) and (b), draw an accurate graph of the new relationship between
the quantity of real money demanded and the real interest rate Label this line (Y =
1000, πe = 0.1).
When r = .05, Md/P = 100 + (.6)(1000) – 4000(.05 + .1) = 100.
When r = 0, Md/P = 100 + (.6)(1000) – 4000(0 + .1) = 300.
Use these two points to plot the relationship as shown in the graph on the previous page.
(d) Suppose that the real interest is determined in the goods market at r = .05, and the
nominal money supply is given by M = 1200. Find the value of the price level in
the economy when (i) Y = 1000 and πe = .05, (ii) Y = 1500 and πe = .05, and (c) Y
= 1000 and πe = 0.1.
From the calculation in part (a), we know that when Y = 1000, r = .05, and πe = .05,
Md/P = 300, so in equilibrium we have
1200/P = 300, or P = 4.
92
From the calculation in part (b), we know that when Y = 1500, r = .05, and πe = .05,
Md/P = 600, so in equilibrium we have
1200/P = 600, or P = 2.
From the calculation in part (c), we know that when Y = 1000, r = .05, and πe = .1,
Md/P = 100, so in equilibrium we have
1200/P = 100, or P = 12.
93
Chapter 9 -- The IS-LM/AD-AS Model: A General Framework for
Macroeconomic Analysis


Asset markets typically clear the fastest!
In the long run, prices and wages clear all markets in the economy
The FE Line – Equilibrium in Labor Market
 FE line is vertical and is at full-employment output
 FE output, Y-bar, = AF(K,N), where K is capital stock, A is total factor
productivity, and F is the production function (recall the material form
chapter 3)
Factors that shift
the FE line
What
Shift of FE
Beneficial supply
shock
↑ FE
↑ in Ns
↑ FE
↑in capital stock
↑FE
↑ FE shifts line right; ↓ FE shifts line
left
Why?
More output can be produced w/ same
amount of N; if MPN rises, Nd
increases and so does output
Equil. employment rises --> raises
output
More output can be produced w/ same
amount of N
The IS Curve – Equilibrium in the Goods Market
 The IS curve represents every point at which Id = Sd
 IS curve derived from Investment-Savings diagram
 Anything that ↓Sd relative to Id will ↑r and shift IS up and right
 An ↑G causes IS curve to shift up and right (b/c r goes up)
Factors that shift the IS curve
What
↑ future Y
↑ Wealth
↑G
Shift of IS Curve
↑ IS
↑IS
↑IS
↑T
↑ MPKf
↑ Effective tax rate on capital
No change or ↓ in IS
↑ IS
↓ IS
Why?
Sd ↓, and r ↑
Sd ↓, and r ↑
Sd ↓, and r ↑
No change w/ Ricardian
equiv.; otherwise, C ↓,
Sd ↑, and r ↓
Id ↑ (which ↑r)
Id ↓ (which ↓r)
94
The LM Curve – Equilibrium in the Asset Market
 LM curve represents Ms/P = Md/P (real money supply = real money
demand)
Factors that shift the LM curve
Shift of LM
What
curve
↑ Ms
↑ LM
↑P
↓ LM
e
↑π
↑ LM
m
↑ i (nominal int. rate of
money)
↓ LM
↑ LM shifts RIGHT (and vice versa)
Why?
Ms/P ↑, which ↓ r
Ms/P ↓, which ↑r
Md ↓ (so ↓r)
Md ↑ (so ↑r)
General Equilibrium of IS-LM Model
 Intersection of FE line, IS curve, and LM curve on IS-LM model
 See diagram on pg. 323
IS-LM vs. AD-AS models
 The two models are essentially equivalent
 IS-LM model relates r to Y, while AD-AS relates P to Y
AD Curve
 Shows relation between quantity of goods demanded (Cd + Id + G) and P
 Anything that shifts the IS curve up and to the right shifts the AD
curve up and to the right
o Increase in expected future output, increase in wealth, increase
in G, reduction in T, an increase in MPKf, and a reduction in
effective tax rate on capital
 Anything that shifts the LM curve to the right shifts the AD curve to the
right
o Increase in nominal Ms; a rise in πe, decrease in nominal interest
on money (im), and any other change that reduces the real
demand for money
AS Curve
 AS curve shows the relationship btwn. P and the aggregate amount of
output that firms supply
 SRAS curve is horizontal
 LRAS curve is vertical (Y = Y-bar, just like FE line)
 Any factor that increases the FE line increase the LRAS curve (and vice
versa)
 SRAS shifts whenever firms change their prices
95
General Equilibrium of AD-AS Model
 Equilibrium occurs at intersection of SRAS, LRAS, and AD curves
To obtain general equilibrium when solving problems:
 Find equilibrium N-bar (from labor market) and solve for Y-bar
 Use Y-bar to get r* (goods market)
 Use Y-bar and r* to obtain P (which will clear the asset market)
 Good example of having to do this process: #4 from chapter 9 (key for
this problem is on website)
Notes on General Equilibrium – the IS/LM/FE model and the AS/AD model in
detail.
To begin, we must recognize that there are three endogenous variables that we need to
find equilibrium values for. We also need to realize that this is a recursive model, with
recursive meaning that “order matters.” Specifically, we need to find Y* (full
employment output) first, by setting labor demand = labor supply (this is our first
equilibrium condition) and solve for the market clearing (same as equilibrium) real
wage (w) and employment (N). Given A (total factor productivity) and K (the desired
capital stock), we can then solve for Y*, our first solution for the first endogenous
variable. This is the scarecrow.
We then use Y* to obtain r*, our second endogenous variable. We do this by going to
our second equilibrium condition (our first was Nd=Ns) and that is goods market
equilibrium (CH 4 material) where desired saving must equal desired investment (i.e.,
Sd = Id). Note that the desired savings function is typically (explicitly) expressed as a
function of Y and r. The desired investment function is typically (explicitly) expressed as
a function of r, so all told, we have two equations and two unknowns. But since we have
already solved for Y*, then we have two equations and one unknown.
Finally, our third endogenous variable, the general price level (P*) that clears the money
market (this is our third equilibrium condition: MS/P = L (Y, r + πe), is obtained by
using Y* and r* to obtain P*. Once we obtain all three endogenous variables, we are said
to be at general equilibrium, which in our context, simple means we are at a point where
all three markets clear, i.e., 1) the labor market clears, 2) the goods market clears, and 3)
the money market clears.
Before we do a problem that depicts the above, let us derive analytically (without
numbers) the FE line, the IS curve, and the LM curve. Note importantly that all points on
the FE curve represent labor market clearing (that is, we are at full employment (FE)), all
points on an IS curve (stands for Investment = Savings) represent goods market clearing,
and all points on an LM curve (stands for L (real money demand) = M (real money
supply)).
Deriving the FE line – the FE line is always going to be vertical since the assumption is
that Y* only changes when there is a change in labor market conditions – i.e., either a
96
change labor demand and / or labor supply (this is a Classical proposition, Keynesians
would argue otherwise – much more on this later). Since we are working in r and Y
space, we argue that changes in r have no direct impact on the labor market or production
function – that is, Y* is independent of changes in r and thus, the FE curve is vertical (see
below).
97
Deriving the IS curve. To derive the IS curve we begin at an initial equilibrium call it
point A (at YA and rA*). We now let Y change (all else constant) and observe what
happens to the equilibrium real interest rate. For example, let’s let Y go up from YA to
YB. Since desired savings go up as a result (a higher Y causes people to consume more
and save more), the equilibrium interest rate that clears the goods market will fall to rB*.
The intuition is that when Y rises, that is the same thing as saying supply has increased
and thus, to obtain a new general equilibrium, demand must rise as well. Part of the
increase in demand is induced by the higher income (consumers will spend more and
save more) but that falls short of the increase in supply since consumption is only going
up by a portion of the change in Y (i.e., the marginal propensity to consume). To
increase demand further and to get to equilibrium, the real interest rate needs to fall
resulting in more consumption via the substitution effect and more investment given that
the user cost of capital falls with the real rate of interest. The real rate will continue to fall
until the change in aggregate demand equals the change Y due to the supply shock.
When we connect points A and B, we have the IS curve. Note importantly that any
change in the equilibrium in the goods market caused by anything other than a
change in Y, will result in a shift of the IS curve. Put differently, any thing that shifts
the savings function, other than a change in Y, will shift the IS curve. Any thing that
shifts the desired investment function will undoubtedly shift the IS curve. So we have
many IS shift variables. Also note that IS curve captures the Fiscal Policy dimension of
the marcoeconomy, i.e., the FP wheel on the cruise ship. As we shall soon see, it is the
LM curve that captures the monetary policy dimension of the macroeconomy.
98
Deriving the LM curve. We derive the LM curve in a very similar fashion as we
derived the IS curve, but here, we focus on how the money market equilibrium changes
when we change Y. Let us begin again, at an initial equilibrium call it point A (at YA and
rA*). We now let Y rise just as before and observe what happens to the equilibrium real
interest rate. Given that real money demand L rises with Y, we see that the real interest
rate must rise to clear the money market. The intuition is that people want more money
to satisfy the higher transactions demand for money. All else constant means that the Fed
is not ‘accommodating’ this higher demand for money and thus, people must sell nonmonetary assets to obtain the money – prices of bonds fall, yield on bonds rises. This
will continue to occur until the money market clears at a higher real interest rate. As was
the case with the IS curve, anything that changes (alters) money market equilibrium other
than changes in Y, will result in a shift in the LM curve. For example, anything that
changes the position of the real money supply curve will result in a shift in the LM curve
(Fed policy, changes in P, money multiplier shocks). Likewise, anything that shifts the
real money demand curve (L), except for changes in Y, will also shift the LM curve.
99
Deriving aggregate demand. Aggregate demand is a very powerful concept as any
point on the aggregate demand curve is consistent with goods and money market
equilibrium, at varying price levels and output. We start at point A in the IS – LM
framework (at YA and rA*) and let the general price level fall. The fall in the price level,
all else constant, results in a higher real money supply and at the same real rate of
interest, the money market is no longer in equilibrium since real money supply exceeds
real money demand. Households get rid of their excess money by buying bonds bidding
their price up, their yield down. The lower real rate of interest will stimulation
Consumption (via the substitution effect) and Investment, via the lower user cost of
capital. The higher C and I results in higher Y since Y = C + I + G. This is the aggregate
demand curve. The questions is: What are the shift variables of aggregate demand?
Anything that shifts the IS curve or anything that shifts the LM curve, except of course
changes in P will also shift the AD curve.
100
Key for numerical problem #4 from the book (chapter 9):
4.
(a)
First, look at labor market equilibrium.
Labor supply is NS  55 
10(1 – t)w. Labor demand (ND) comes from the equation w  5A – (0.005A  ND).
Substituting the latter equation into the former, and equating labor supply and labor
demand gives N  100. Using this in either the labor supply or labor demand equation
then gives w  9. Using N in the production function gives Y  950.(b)
Next, look at goods market equilibrium and the IS curve.
(b) Sd  Y – Cd – G  Y – [300  0.8(Y – T) – 200r] – G  Y – [300  (0.4Y – 16) – 200r] –
G  – 284  0.6Y  200r – G.
Setting Sd  Id gives – 284  0.6Y  200r – G  258.5 – 250r. Solving this for r in terms
of Y gives r  (542.5  G)/450 – 0.004/3Y.
When G  50, this is r  1.317 – 0.004/3 Y (IS Expression).
With full-employment output of 950, using this in the IS curve and solving for r
gives r  0.05. Plugging these results into the consumption and investment
equations gives C  654 and I  246.
(c) Next, look at asset market equilibrium and the LM curve.
Setting money demand equal to money supply gives 9150/P  0.5Y – 250(r  0.02),
which can be solved for r  [0.5Y – (5  9150/P)]/250. With Y  950 and r 
0.05, solving for
P gives P  20.
(d)
With G  72.5, the IS curve becomes
r  (542.5  G)/450 – 0.004/3Y
r  (542.5  72.5)/450 – 0.004/3Y
r  1.367 – 0.004/3 Y. (note that the IS curve has shifted up and to the right as G rises)
With Y  950, the IS curve gives r  .10, the LM curve gives P  20.56, the consumption
equation gives C  644, and the investment equation gives I  233.5. The real
wage, employment, and output are unaffected by the change.
Note: Investment has fallen – Higher G has “crowded out” private domestic investment
The higher G has also increased the price level (inflation), with no change in output.
101
Example Problems for Chapter 9
1. Desired consumption, government spending, and desired investment for an
economy is given by
Cd = 600 + .5Y – 2000r
G = 200
Id = 600 – 2000r.
b. Find the equilibrium value of the real interest rate if Y = 2000.
c. Find the equilibrium value of the real interest rate if Y = 2600.
d. Graph the equilibrium relationship between the real interest rate r and output
Y. Put Y on the horizontal axis and r on the vertical axis. (Hint: Plot your
answers to parts (a) and (b) and connect the two points with a straight line.
2. Suppose that the real demand for money is given by
Md/P = 2000 + .2Y – 5000i,
and that M = 7500, P = 2 and πe = .01.
a. What real interest rate r is consistent with equilibrium in the asset market when Y
= 10,000? What real interest rate r is consistent with equilibrium in the asset
market when Y = 11,000? Use these answers to graph the LM curve.
b. Repeat part (a) for M = 7700. What is the relationship between this LM curve and
the one that you found in part (a)?
c. Let M = 7500. Repeat part (a) for πe = .02. What is the relationship between this
LM curve and the one that you found in part (a)?
3. The Production function for an economy is given by
Y = 2(10N - .005N2).
The marginal product of labor for this production function is given by
MPN = 20 - .02N
The labor supply curve is given by
NS = 250 + 25w.
a. What are the equilibrium levels of the real wage, employment and output?
102
b. Suppose that for this economy we have desired consumption, desired investment,
government spending and taxes given by
Cd = 500 + .8(Y – T) – 2000r
G = 1500
T = 1000
Id = 450 – 3000r.
Find the general equilibrium values of the the real interest rate, consumption and
investment.
c. Suppose that the demand for money in this economy is given by
Md/P = 275 + .2Y – 2500i,
the nominal money supply is 600, and πe = .02. Find the price level for this economy.
d. Suppose that government spending G in this economy increases from 1500 to
1700. Find the new general equilibrium values of the real wage, employment, output,
the real interest rate, consumption, investment and the price level.
4. Find the effects of each of the following on the general equilibrium values of the
real wage, employment, output, the real interest rate, consumption, investment, and
the price level. Illustrate your answers with appropriate graphs.
a. Desired investment increases.
b. Labor supply increases
c. The demand for money for money decreases.
5. Analyze the short-run (the price level is fixed) and the long-run (general equilibrium)
effects of each of the following on the level of output, the real interest rate, and the price
level. Illustrate your analysis graphically in two ways: (1) in an IS-LM-FE framework,
and (2) in an aggregate demand-aggregate supple framework.
(a) The expected rate of inflation declines.
103
(b) Consumers increase their desired level of consumption at each level of income
and the real interest rate.
(c) A temporary negative supply shock (productivity decreases).
104
Answers to Example Problems for Chapter 9
1. Desired consumption, government spending, and desired investment for an economy is
given by
Cd = 600 + .5Y – 2000r
G = 200
Id = 600 – 2000r.
a. Find the equilibrium value of the real interest rate if Y = 2000.
Sd = Y – Cd – G = Y – (600 + .5Y – 2000r) – 200 = .5Y – 800 + 2000r.
When Y = 2000, this becomes Sd = (.5)(2000) – 800 + 2000r = 200 + 2000r.
Setting Sd = Id we get
200 + 2000r = 600 – 2000r
or
4000r = 400
or
r = 0.1
b. Find the equilibrium value of the real interest rate if Y = 2600.
When Y = 2600, this becomes Sd = (.5)(2600) – 800 + 2000r = 500 + 2000r.
Setting Sd = Id we get
500 + 2000r = 600 – 2000r
or
4000r = 100
or
r = 0.025
c. Graph the equilibrium relationship between the real interest rate r and output Y.
Put Y on the horizontal axis and r on the vertical axis. (Hint: Plot your answers to
parts (a) and (b) and connect the two points with a straight line.
105
r
(You now know this as the IS curve.)
.1
.025
2000
2600
Y
2. Suppose that the real demand for money is given by
Md/P = 2000 + .2Y – 5000i,
and that M = 7500, P = 2 and πe = .01.
a. What real interest rate r is consistent with equilibrium in the asset market when Y
= 10,000? What real interest rate r is consistent with equilibrium in the asset
market when Y = 11,000? Use these answers to graph the LM curve.
Equilibrium in the asset market requires M/P = Md/P: Letting Y = 10,000 we get
7500/2 = 2000 + (.2)(10,000) – (5000)(r + .01),
which can be solved for r = .04.
Letting Y = 11,000 we get
7500/2 = 2000 + (.2)(11,000) – (5000)(r + .01),
which can be solved for r = .08.
LM
r
.08
.04
10,000
11,000
Y
106
b. Repeat part (a) for M = 7700. What is the relationship between this LM curve and
the one that you found in part (a)?
Letting Y = 10,000 we get
7700/2 = 2000 + (.2)(10,000) – (5000)(r + .01),
which can be solved for r = .02.
Letting Y = 11,000 we get
7700/2 = 2000 + (.2)(11,000) – (5000)(r + .01),
which can be solved for r = .06.
r
LM
.06
.02
10,000
11,000
Y
The LM curve is shifted down (or to the right) compared to the LM curve in part (a)
c. Let M = 7500. Repeat part (a) for πe = .02. What is the relationship between this
LM curve and the one that you found in part (a)?
Letting Y = 10,000 we get
7500/2 = 2000 + (.2)(10,000) – (5000)(r + .02),
which can be solved for r = .03.
Letting Y = 11,000 we get
7500/2 = 2000 + (.2)(11,000) – (5000)(r + .02),
which can be solved for r = .07.
107
r
LM
.07
.03
10,000
11,000
Y
The LM curve is shifted down (or to the right) compared to the LM curve in part (a)
3. The Production function for an economy is given by
Y = 2(10N – .005N2).
The marginal product of labor for this production function is given by
MPN = 20 – .02N
The labor supply curve is given by
NS = 250 + 25w.
a. What are the equilibrium levels of the real wage, employment and output?
As you recall, the firm maximizes profit when it chooses the amount of labor that it
wants to hire so that the real wage is equal to the marginal product of labor, so we can
use this relationship to get the demand for labor:
w = 20 – .02ND,
so ND = (20 –w)/.02
Equilibrium in the labor market requires ND = NS, so in equilibrium
(20 –w)/.02 = 250 + 25w,
Which can be solved for w = 10.
The equilibrium level of employment can be found by substituting w = 10 into the
labor demand or labor supply function:
ND = (20 –w)/.02 = = (20 –10)/.02 = 500.
108
Output is given by Y = 2(10N – .005N2) = 2(10·500 – .005·5002) = 7500.
b. Suppose that for this economy we have desired consumption, desired investment,
government spending and taxes given by
Cd = 500 + .8(Y – T) – 2000r
G = 1500
T = 1000
Id = 450 – 3000r.
Find the general equilibrium values of the real interest rate, consumption and
investment.
Substituting Y = 7500 from part (a), we can write desired saving as
Sd = Y – Cd – G = 7500 – (500 + .8(7500 – 1000) – 2000r) – 1500 = 300 + 2000r.
Setting desired saving equal to desired investment we get
300 + 2000r = 450 – 3000r
which can be solved for r = .03
Consumption is given by 500 + .8(7500 – 1000) – (2000)(.03) = 5640.
Investment is given by 450 – (3000)(.03) = 360
c. Suppose that the demand for money in this economy is given by
Md/P = 275 + .2Y – 2500i,
the nominal money supply is 600, and πe = .02. Find the price level for this economy.
Using r = .03 from part (b), we get i = .03 + .02 = .05. Using this value of i and the
value of Y from part (a), we can write money real money demand as
Md/P = 275 + (.2)(7500) – (2500)(.05) = 1650.
Setting real money supply equal to real money demand gives
600/P = 1650,
which can be solved for P = .3636.
109
d. Suppose that government spending G in this economy increases from 1500 to
1700. Find the new general equilibrium values of the real wage, employment, output,
the real interest rate, consumption, investment and the price level.
The level of government spending has no effect on the labor market, so the
equilibrium values of the real wage, employment and real output will be the same as
in pat (a) (w = 10, N = 500 and Y = 7500)
The increase in government spending will effect desired national saving, so there will
be an effect in the goods market. Desired national saving is now given by
Sd = Y – Cd – G = 7500 – (500 + .8(7500 – 1000) – 2000r) – 1700 = 100 + 2000r.
Setting desired saving equal to desired investment we get
100 + 2000r = 450 – 3000r
which can be solved for r = .07
Consumption is given by 500 + .8(7500 – 1000) – (2000)(.07) = 5560.
Investment is given by 450 – (3000)(.07) = 240
Now r = .07 so i = .07 + .02 = .09. Using this value of i and Y = 7500, we can write
money real money demand as
Md/P = 275 + (.2)(7500) – (2500)(.09) = 1550.
Setting real money supply equal to real money demand gives
600/P = 1550,
which can be solved for P = .387.
4. Find the effects of each of the following on the general equilibrium values of
the real wage, employment, output, the real interest rate, consumption, investment,
and the price level. Illustrate your answers with appropriate graphs.
a. Desired investment increases.
110
The change in desired investment will have no effect on the labor market, so the real
wage, employment and output will be unaffected. In terms of the IS-LM-FE model, there
will be no shift in the FE line.
An increase in desired investment shifts the desired investment curve to the right. This
means that for any fixed value of Y, the equilibrium interest rate that clears the goods
market will be higher. As a result, IS curve will shift up (to the right).
The upward shift in the IS curve will throw the economy out of general equilibrium.
Eventually, the economy will return to general equilibrium by way of an upward shift in
the LM curve caused by an increase in the price level in the economy.
In the new general equilibrium, the real interest rate will be higher than its original level.
Because consumption depends negatively on the real interest rate, the level of
consumption spending will be lower. Since Y = C + I + G, and there is no change in G or
Y, while C decreases, it must be the case that investment increases.
As described above, the process of adjusting to the new equilibrium involves an increase
in the price level, so the new price level will be higher. The graph is below.
FE
r
r1
r0
LM1
LM0
E1
E0
IS1
IS0
Yf
Y
b. Labor supply increases
An increase in labor supply will cause a reduction in the real wage and an increase in
the level of employment. An increase in employment will lead to an increase in real
output. This is reflected in the rightward shift in the FE line in the diagram below.
The lower real wage will lead to a lower unit cost of production for firms, so they will
begin to reduce prices in order to maximize profit. As a result of the falling price
111
level, the LM curve will shift downward until a new general equilibrium is reached at
E1. The real interest rate will decrease as shown in the diagram. Investment will
increase because of the lower real interest rate. Consumption will increase due to the
lower real interest rate and the increase in real income.
r
FE0
FE1
LM0
r0
E0
LM1
r1
E1
IS0
Yf0
Yf1
Y
c. The demand for money for money decreases.
There is no effect on labor supply or labor demand, so there will be no change in the real
wage, the level of employment or the full-employment level of output.
The decrease in the demand for money will shift the LM curve down and to the right. At
this point the economy is no longer in equilibrium. To return the economy to general
equilibrium, the LM curve will upward to its original position, due to an increase in the
price level. After the return to general equilibrium, real output and the real interest rate
will be at their original levels. This is shown in the general equilibrium diagram on the
next page.
Since there is no change in output or the real interest rate, there will be no change in
consumption or investment.
112
r
FE0
LM0
r0
E0
LM1
E1
IS0
Yf0
Y
5. Analyze the short-run (the price level is fixed) and the long-run (general
equilibrium) effects of each of the following on the level of output, the real interest rate,
and the price level. Illustrate your analysis graphically in two ways: (1) in an IS-LM-FE
framework, and (2) in an aggregate demand-aggregate supple framework.
(a) The expected rate of inflation dedclines.
A decrease in the expected rate of inflation will cause an increase in the demand for
money. An increase in the demand for money will cause an upward (rightward) shift in
the LM curve. In the short rune the economy will move from E0 to ES in the IS-LM
diagram. So output will fall and the real interest rate will increase. The leftward shift of
the LM curve is represented by a leftward shift in the aggregate demand curve in the ADAS diagram, which shows the short-run decrease in output when the price level does not
change. In the long run, the LM curve will shift downward to return the economy to
general equilibrium. The shift in the LM curve is due to a reduction in the price level.
Thus the real interest rate and the level of real output will return to their original levels;
there is no long-run effect on the real interest rate or the level of output. However, the
long-run effect of the decrease in the expected rate of inflation is a reduction in the price
level. This is seen more directly in the AD-AS diagram.
113
FE
LM1
r
LRAS
P
LM0
SRAS0
E0
ES
rS
P0
ES
E0
r0
SRAS1
P1
AD0
E1
IS
AD1
YS
Y0
YS
Y
Y0
Y
(b) Consumers increase their desired level of consumption at each level of income and
the real interest rate.
An increase in consumption at each level of consumption and the real interest rate causes
a decrease in desired national saving at each level of the real interest rate, which causes
an increase in the equilibrium real interest rate at each level of national income which
corresponds to an upward (rightward) shift in the IS curve. The short-run effect is an
increase in the real interest rate and an increase in the level of real output. This rightward
shift in the IS curve corresponds to a rightward shift in the aggregate demand curve.
In the long run, the the LM curve will shift up to return the economy to general
equilibrium. This upward shift will be brought about by an upward shift in the price level.
In the long run there will be an increase in the real interest rate and the price level, but no
change in the level of real output.
FE
r
LM1
P
LRAS
E1
r1
LM0
r0
E1
ES
rS
SRAS1
P1
ES
E0
IS1
P0
AD1
E0
IS0
Y0
YS
SRAS0
AD0
Y
Y0
YS
Y
(c) A temporary negative supply shock (productivity decreases).
114
A temporary negative supply shock will shift the FE curve to the left because both the
level of employment will fall and the level of output at each level of employment will
fall. However, in the short run there willl be no change in output, the price level or the
real rate of interest. How is this consistent with the leftward shift in the FE curve? The
answer is, in the short-run, firms will continue to meet the aggregate quantity demanded,
that is determined by the intersection of the IS and LM curves. The long run adjustment
to a new lower rate of real output occurs as firms realize that they are not maximizing
profit at Y0, and so begin to raise their prices. In the long run the price level will increase,
the level of output will fall, and the real interest rate will increase.
r
FE1
FE0
LM1
P
LM0
E1
LRAS1
LRAS0
E1
SRAS1
P1
r1
E0 = ES
r0
E0 = ES
P0
AD1
IS
Y1
Y0
SRAS0
AD0
Y
Y1
Y0
Y
115
Exam 2 – Econ 304 – Chuderewicz – Fall 2010
Name ______________________________ Last 4 (PSU ID) __________
Section?
Hosler.
Sparks
(circle one)
PLEASE PUT THE FIRST TWO LETTERS OF YOUR LAST NAME ON TOP RIGHT
HAND CORNER OF THIS COVER SHEET – THANKS AND GOOD LUCK!!!
116
Exam 2 – Econ 304 –Fall 2010 – we will do this in its entirety in class
1. THIS IS THE GENERAL EQUILIBRIUM PROBLEM THAT I PROMISED. YOU FIRST SOLVE
FOR THE INITIAL EQUILIBRIUM AS POINT A. WE CONSIDER TWO DIFFERENT AND
SEPARATE SHOCKS (I CALL THEM SCENARIOS). THE FIRST SHOCK IS TO THE LM CURVE,
THE SECOND SHOCK IS AN ‘IS’ SHOCK. AGAIN, WE CONSIDER THESE SHOCKS
SEPARATELY SO THAT AFTER YOU COMPLETE SCENARIO 1 (THE LM SHOCK), WE GO
BACK TO THE ORIGINAL CONDITIONS AND CONSIDER THE SECOND SCENARIO WHICH IS
THE ‘IS’ SHOCK.
Consider the following model of the economy
Production function: Y = A·K·N – N2/2
Marginal product of labor: MPN = 2A·K – N.
where the initial values of A = 5 and K = 6.
The initial labor supply curve is given as: N S = 20 + 3w.
Cd = 85 + .50(Y-T) – 500r
Id = 50 – 500r
G = 50
T= 100
Md/P = 85 + 0.5Y- 1000r
Nominal Money supply M = 400
We assume that expected inflation is zero (πe- = 0) so that money demand depends directly on the real
interest rate (since i = r).
1 a) (6 points) Solve for the labor market clearing real wage (w*), the profit maximizing level of labor
input (N*), and the full employment level of output (Y*). Please show work.
117
In the space below, draw two diagrams vertically with the labor market on the bottom graph and the
production function on the top graph. Be sure to label everything including this initial equilibrium point as
point A. (10 points for completely labeled and correct diagrams)
b) (4 points) Derive an expression for the IS curve (r in terms of Y). Please show all work
c) (3 points) Find the real interest rate that clears the goods market. Please show all work
d) (3 points) Find the price level needed to clear the money market. Please show all work
118
e) (3 points) Find the expression for the LM curve (r in terms of Y). Please show all work
Now draw three separate diagrams: (30 points total) a FE - IS – LM diagram, a desired savings
equals desired investment (Sd = Id ), and a money market diagram locating this initial equilibrium
point as point A. BE SURE to LABEL all diagrams completely (10 points for each correctly drawn
and labeled diagram…each diagram will have three different equilibriums points A, B, and C)
119
SCENARIO #1 – AN LM SHOCK!
Now suppose that the real demand for money has changed and is now:
Md/P = 105 + 0.5Y- 1000r
S1 a) (6 points) What would cause such a development?? Explain using the relevant characteristics of
asset demand.
S1 b) (4 points) What is the new, short run (fixed price level) expression for the LM curve? Please show
all work.
S1 c) (4 points) What is the short run, Keynesian (fixed price) level of equilibrium output and real interest
rate? Please show all work.
Please label these new short run conditions on your FE, IS, LM diagrams as point B. Be sure to label
diagram completely with the inclusion of all the relevant shift variables like we did numerous times
in class.
120
S1 d) 3 points) If the Fed did nothing, explain how exactly the economy will return to full employment.
S1 e) (4 points) Assuming that the Fed did nothing, find the new price level associated with the long run
general equilibrium.
Please label this long run equilibrium on your FE, IS, LM diagrams as point C. Be sure to label
diagram completely with the inclusion of all the relevant shift variables like we did numerous times
in class.
S1 f) (5 points) Is this result desirable? That is, with perfect information, would the Fed allow this long
run adjustment to take place? Why or why not? Explain in as much detail as possible using a real world
event (hint, it’s a central banking nightmare!).
S1 g) (5 points) Suppose otherwise and that the Fed wanted to keep prices constant at their original level
at points A and B. What would the Fed have to do exactly, as in open market operations? Assume that the
money multiplier is 1. Be specific and show work.
121
Finally, draw an aggregate demand and aggregate supply curve locating points A, B, and C. Please
label everything completely. Be sure to add the SRAS curves and the LRAS curve to your two AD
curves. A completely drawn and labeled diagram is worth 10 points.
SCENARIO #2 – AN IS SHOCK! (A new Grader)
Let’s return to our original conditions: Please write down the expressions for your ORIGINAL IS curve
and LM curves in the space below (so the grader can follow your starting points).
IS: r = ___________________________
LM: r = __________________________
Now draw another set of diagrams, i.e., three separate diagrams, identical to the first part of this
problem (i.e., we are starting at the same equilibrium point = point A): a FE - IS – LM diagram, a
desired savings equals desired investment (Sd = Id ), and a money market diagram locating this initial
equilibrium point as point A. Be sure to LABEL all diagrams completely (10 points for each
correctly drawn and labeled diagram)…each diagram will have three different equilibriums points
A, B, and C. (30 points total)
122
In this scenario #2, we let those wonderful elected officials of ours increase G to 80 (from 50)
S2 a) (4 points) (4 points) Derive a ‘new’ expression for the IS curve (r in terms of Y). Please show all
work
S2 b)(4 points) Now solve for the short-run equilibrium output (Keynesian) and the corresponding real rate
of interest. Please show all work. Please label this short run (fixed price) equilibrium as point B.
S2 c) )(4 points) In the short run, what is the “Keynesian” Government spending multiplier? Please show
all work
S2 d) (4 points) Solve for the real rate of interest in this long run equilibrium.
S2 e) (4 points)We now consider the long run when prices adjust. Find the new price level associated with
the long run equilibrium. Please show all work
123
S2 f) (4 points) Derive a new expression for the LM curve. Please show all work.
S2 g) (4 points) In the long run, how much investment has been crowded out? Please show all work.
Label this long run equilibrium as point C in all three of your diagrams.
124
2. (35 points total)
Suppose the real money demand function is:
Md/P  1500  0.2 Y – 10,000 (r  e).
Assume M  4000, P  2.0, e  0.01, and Y  5000. Note: we are holding P and Y constant in this
problem.
a) (4 points) What is the market clearing real interest rate?
Show your results on a real money supply, real money demand diagram and label this initial equilibrium
point as point A. Be sure to label your graph completely!
Correctly drawn and completely labeled diagram is worth 10 points total.
b) (6 points) Suppose Bernanke and the Fed were successful in their campaign to raise inflationary
expectations to 4% (.04). Why would they want to do this and how would they do this??
125
c) (4 points) Solve for the real interest rate that clears the money market given the change in inflationary
expectations. Please show work and Label this new point as point B
d) (10 points) Explain how this strategy of raising inflationary expectations is supposed to stimulate
output. Recall that output is equal to C + I + G! Be very specific as this question is worth 10 points.
e) (6 points) Now its your turn to be critical of this Fed strategy – that is, provide arguments as to why this
strategy won’t work and may actually result in lower output rather than raise output. Again, be as
specific as possible.
126
3. (30 points total) We discussed the money supply process in some detail along with the concept of
quantitative easing. In particular, we argued that the Fed, with the most astute student of the Great
Depression (GD) at the helm (Ben Bernanke), appears to have learned their lesson from the Great
Depression(GD). Please answer the following questions.
a) (10 points) What lesson did the Fed learn from the GD exactly? That is, if you wanted to blame the Fed
for the GD, where would we start. In the space below, write an essay criticizing the Fed for their behavior
during the GD making sure to address the behavior of the money multiplier (and its components), the
monetary base, and the nominal money supply during the GD.
b) (5 points) If we could go back in time and you could be the Fed Chair during the GD, what would you
do different?? Make sure you refer to percent changes in your answer. As a hint, what would you make
sure of when it comes to the percent change in the monetary base?
127
c) (10 points) Let’s fast forward to the recent financial crisis and quantitative easing. The graph below
depicts the money multiplier during the ‘great recession.’ Explain exactly why the money multiplier has
plummeted and what the appropriate response is, given that the Fed learned their lesson from the Great
Depression. How can we tell if the Fed truly learned their lesson from the GD and how can we be sure that
their behavior is consistent with quantitative easing? Be as specific as possible.
128
Chapter 10- Classical Business Cycle Analysis
Real Business Cycle Theory:
 Argues that “real shocks” to the economy are the primary cause of business cycles
 These are shocks to the “Real side” of the economy, such as shocks that affect the
production function, size of the labor force, real quantity of government
purchases, and the spending and savings decisions of consumers
 In the IS-LM model, real shocks directly affect the IS curve or the FE line
 The primary form of these real shocks is productivity shocks, which are shocks
involving the production of new products or methods.
Effect of an Adverse Productivity Shock
 Lowers the general equilibrium of the real wage, employment, and output.
Real interest rates rises, consumption and investment are depressed, and
price level is raised.
 This information supports the economists’ claim that these shocks are
recessionary and lead to a decline it output. Firms utilize labor less
intensively during recessions
RBC Theory Predictions:
 Recurrent fluctuation in aggregate demand
 Procyclical employment and real wage
 Procyclical average labor production
 Countercyclical movement of price level – This is the flaw in the RBC
Theory!
Unemployment in the Classical Model:
 Major weakness of the classical model is that it does not explain why involuntary
unemployment occurs!!
 In this model, there is no cyclical unemployment.
 Workers and jobs have different requirements so there is a matching problem.
According to the model, it takes time to match workers and jobs, and this is why
there is unemployment.
 In recessions, there is a larger degree of mismatch due to productivity shocks and
other macroeconomic disturbances, and this is why unemployment is higher
during recessions
 Most of the evidence indicates that increased mismatches cannot account for all
of the increase in unemployment that happens during recessions, but that the
dynamic relocation of workers is an important aspect of unemployment.
Money in the Classical Model:
 Besides real shocks, there are nominal shocks to the money supply and
demand.
129


Because classical economists believe that the price adjustment process is
rapid, they view money as neutral for any time horizon, short run or long run.
Money is pro-cyclical because of reverse causation
Reverse causation: the tendency of expected future changes in the output to
cause changes to the current money supply in the same direction (the storm
window and winter coming analogy).
The Misperceptions Theory
 According to the theory, the aggregate quantity of output supplied rises above the
full unemployment level, when the aggregate price level is higher than expected.
 If a supplier expects prices to go up 5% and the price of the product increases by
5%, then the supplier believes that all prices have risen by 5%, and output remains
the same.
 For a change in nominal prices to affect the quantity produced, the increase in the
nominal price must differ from the expected increase in the general price level.
Unanticipated Changes in Money Demand:
The reason money is not neutral in this model is that producers are fooled. Each producer
perceives the higher nominal price of her output as an increase in its relative price, rather
than an increase in the general price level. Although output increases in the short run,
producers are not better off. They end up producing more than they would have had they
known the true relative prices.
130
The economy does not stay long at the equilibrium at point F. Over time, people will
obtain information about prices and adjust their expectations. Thus, according to the
Misperceptions Theory, money is not neutral in the short run, but is neutral in the long
run (this is consistent with the empirical facts).
Anticipated Changes in the Money Supply:
In this model, the producers know about the increase in the money supply, and are not
fooled into increasing production when the prices rise. The anticipated increase has not
affected output, but does raise prices proportionally. Therefore, anticipated changes in the
money supply are neutral in the short run as well as in the long run.
Rational Expectations:
 According to the extended classical model based on the misperceptions theory,
only surprise changes in the money supply can affect output. If the public has
rational expectations about macroeconomic variables, including the money
supply, the Fed cannot systematically surprise the public, because the public will
understand and anticipate the Fed’s behavior. Thus classical economists argue
that the Fed cannot systematically use changes in the money supply to affect
output (policy implications: hands off!).
131

Example Problems for Chapter 10
1. Suppose that an economy is described by the following equations.
Cd = 1000 + .6(Y – T) – 100r
Id = 690 – 100r
L = .2Y – 200(r + πe)
Ỹ = 5000 (full-employment level of output)
πe = .05
G = 800.
M = 3920
a. Use the general equilibrium model to find the equilibrium values of real output,
the real interest rate, the price level, consumption, and investment.
b. Suppose that the money supply increases to 4410. Recalculate the values that you
found in part (a). Is money neutral? Explain.
c.
Suppose that the money supply returns to 3920, but that the level of government
spending G increases to 825. Recalculate the values that you found in part (a).
(Assume that the increase in G has no effect on labor supply.) Is fiscal policy
neutral? Explain.
2. Suppose that the expected future product of capital increases.
a. Use the general equilibrium model to determine the effect of the increase in the
expected future marginal product of capital on the current values of the real wage,
employment, real output, the real interest rate consumption, investment and the
price level. (You can assume that the increase in the future marginal product of
capital does not the expected future real wage or expected future income.)
b. Use the AD-AS with AS based on the misperceptions theory to analyze the effect
of the increase in the expected future marginal product of capital on current
output and the current price level. Explain why the result is different from the
result in part (a).
3. In parts (a), (b) and (c) below, you will use the general equilibrium model, analyze the
effect of a permanent increase in government spending that is fully financed by a
permanent increase in lump-sum taxes.
132
a. First, graphically analyze and explain the effects of the changes on the labor
market. How would the effect differ if the change in government spending and
taxes were temporary instead of permanent?
b. Second, graphically analyze and explain the effects of the permanent changes on
desired national saving and the IS curve. (Hint: Since the increase in taxes is
permanent, it makes sense to assume that households will decrease their
consumption spending by the full amount of the tax.) (6 points)
c. Use your answers in parts (a) and (b) and the general equilibrium model to
analyze the effects of the permanent increase in government expenditures and
taxes on current output, the real interest rate, and the price level. How would your
answers change if households did not reduce their consumption spending by the
full amount of the tax?
133
Answers to Example Problems for Chapter 10
1. Suppose that an economy is described by the following equations.
Cd = 1000 + .6(Y – T) – 100r
Id = 690 – 100r
L = .2Y – 200(r + πe)
Ỹ = 5000 (full-employment level of output)
πe = .05
G = 800.
M = 3920
In this economy, the government’s budget is always balanced so G = T.
a. Use the general equilibrium model to find the equilibrium values of real output,
the real interest rate, the price level, consumption, and investment.
Output: In the classical model, output is always at
the full-employment level so Y = 5000.
Real Interest Rate: Sd = Y – Cd – G, so
Sd = 5000 – (1000 + .6(5000 – 800) – 100r) – 800
= 680 + 100r.
Setting Sd = Id and solving for r gives
680 + 100r = 690 – 100r
or r =.05
Price Level: Set M/P = L and solve for P.
3920/P = (.2)(5000) - (200)(.05 + .05)
or
P = 3920/980 = 4.
134
Consumption: Plug values of Y, r and T into the consumption equation and do the
arithmetic.
C = 1000 + (.6)(5000 -800) - (100)(.05) = 3515.
Investment: Plug value of r into the investment equation and do the arithmetic.
I = 690 - (100)(.05) = 685.
You can also do a final check of your answers C + I + G = 3515 + 685 + 800 = 5000 = Y.
b. Suppose that the money supply increases to 4410. Recalculate the values that you
found in part (a). Is money neutral? Explain.
There is no effect on Y, Cd, or G, so there is no effect on desired saving. There is also
no effect on Id. Since there is no effect on either Sd or Id, there will be no effect on r.
Since there is no effect on Y or r, there will be no effect on real money demand. Thus,
we can solve for the new price level:
4410/P = (.2)(5000) - (200)(.05 + .05)
or
P = 4410/980 = 4.5.
The real money supply has not changed: M/P = 980. Both the money supply and the
price level have increased by 12.5%. So money is neutral, since the change in the money
supply did not cause a change in any real macroeconomic variable.
c.
Suppose that the money supply returns to 3920, but that the level of government
spending G increases to 825. Recalculate the values that you found in part (a).
(Assume that the increase in G has no effect on labor supply.) Is fiscal policy
neutral? Explain.
Real Interest Rate: Sd = Y – Cd – G, so
Sd = 5000 – (1000 + .6(5000 – 825) – 100r) – 825
= 670 + 100r.
Setting Sd = Id and solving for r gives
670 + 100r = 690 – 100r
or r = .1
135
Price Level: Set M/P = L and solve for P.
3920/P = (.2)(5000) - (200)(.1 + .05)
or
P = 3920/970 = 4.04.
Consumption: Plug values of Y, r and T into the consumption equation and do the
arithmetic.
C = 1000 + (.6)(5000 -825) - (100)(.1) = 3495
Investment: Plug value of r into the investment equation and do the arithmetic.
I = 690 - (100)(.1) = 680.
You can also do a final check of your answers C + I + G = 3495 + 680 + 825 = 5000 = Y.
Government spending is not neutral. The change in G caused changes in the real values r,
C, I and M/P.
2. Suppose that the expected future product of capital increases.
a. Use the general equilibrium model to determine the effect of the increase in the
expected future marginal product of capital on the current values of the real wage,
employment, real output, the real interest rate consumption, investment and the
price level. (You can assume that the increase in the future marginal product of
capital does not the expected future real wage or expected future income.)
Since there is no effect on expected future wages or expected future incomes, there
will be no effect on current labor supply. Since there is no effect on the current marginal
product of labor, there will be no effect on current labor demand. We conclude that there
will be no effect on current employment or the current real wage. Since there is no effect
on the current employment or current
productivity, there will be no effect on the current full-employment level of output. In
terms of the AD-AS approach, there will be no affect on the long-run aggregate supply
curve. In terms of the
IS-LM approach, there will be no effect on the FE line.
The increase in the future marginal product of capital will, however, increase firm's
future desired capital stock, which will increase current investment demand. In terms of
the AD-AS approach, the aggregate demand curve will shift to the right, which will cause
an increase in the price level.
136
LRAS
P
P1
P0
F
E
AD1
AD0
Y0
Y
In terms of the IS-LM approach, the increase in current desired investment will cause
an upward (rightward shift in the IS curve, causing an increase in the real interest rate and
the level of investment spending. As a result of the increase in the real interest rate,
desired consumption spending will fall. Since output does not change, the decrease in
desired consumption will be equal to the increase in desired investment. In order to
restore general equilibrium, the LM curve will have to shift to the left, which will occur
as the price level increases.
In summary, there will be no effect on employment, output or the real wage.
Investment spending, the real interest rate and the price level will increase. Real
consumption spending will fall.
FE
r
LM1
F
r1
r0
LM0
E
IS1
IS0
Y0
Y
b. Use the AD-AS with AS based on the misperceptions theory to analyze the effect
of the increase in the expected future marginal product of capital on current
output and the current price level. Explain why the result is different from the
result in part (a).
137
If the misperceptions theory is an accurate abstraction from reality, then the increase
in the future marginal product of capital will temporarily cause an increase in output,
because in the
misperceptions theory, there is an upward sloping SRAS. In the short run there will be an
increase in the price level, but not as great an increase as occurs in the long run.
LRAS
P
SRAS
F
P1
P e =P0
E
AD1
AD0
Y0
Y
The reason for the difference in the two theories is that in the misperceptions theory,
as the price level begins to increase, firms interpret the increase as an increase in the
relative price of their products, rather than an increase in the average of all prices. They
respond to the perceived increase in the relative price of their own products by increasing
output. However, this increase in output is only temporary, since eventually the
producer's misperceptions will be corrected.
3. In parts (a), (b) and (c) below, you will use the general equilibrium model, analyze the
effect of a permanent increase in government spending that is fully financed by a
permanent increase in lump-sum taxes.
a. First, graphically analyze and explain the effects of the changes on the labor
market. How would the effect differ if the change in government spending and
taxes were temporary instead of permanent?
Recall that a temporary increase in G will cause people to want to work more because
they will feel poorer -- the present value of their after tax income falls if the government
raises taxes immediately or if the government borrows and has to raise taxes to pay back
the borrowing in the future. A permanent increase in government spending will cause a
much larger increase in taxes over a person's lifetime. In other words, the present value of
the taxes that a person will have to pay will be much higher than the present value of the
taxes associated with a temporary increase in G. So
the effect on a person's wealth will be greater, causing an even bigger response in the
form of increased labor supply. Therefore current output should increase more due to a
permanent increase in G than to a temporary increase in G.
138
ND
w
NS1
NS0
w0
w1
0
Y
N0
N
0
N1
Y1
Y0
N0
N1
N
0
b. Second, analyze and explain the effects of the permanent changes on desired
national saving and the IS curve. (Hint: Since the increase in taxes is permanent, it
makes sense to assume that households will decrease their consumption spending
by the full amount of the tax.)
The text suggests that we should assume that the permanent increase in taxes
associated with the increase in G will lead people to reduce their consumption by exactly
the amount that G and their taxes will increase for any given level of income. This seems
reasonable, because it implies an equal reduction in consumption in the present and in the
future, which is consistent with consumption smoothing. Since Sd = Y – Cd – G, for each
given level of Y, there will be no change in desired national saving because the increase
in G will be exactly offset by a decrease in Cd. In other words, for a given level of
income, there will be no change in desired saving, i.e., no shift in the desired saving
curve. since there will also be no change in desired investment, this means that there will
be no shift in the IS curve.
c. Use your answers in parts (a) and (b) and the general equilibrium model to
analyze the effects of the permanent increase in government expenditures and
taxes on current output, the real interest rate, and the price level. How would your
answers change if households did not reduce their consumption spending by the
full amount of the tax?
From part (a) we know that there will be a rightward shift in the FE line, and from part
(b) we know that there will be no shift in the IS curve. When the FE curve shifts the
economy will no longer be in general equilibrium, which means that the price level will
139
have to adjust. The price level will decrease in order to shift the LM curve to the right
until all three of the markets are in equilibrium, as shown in the diagram below.
r
FE0
FE1
LM0
E
LM1
r0
F
r1
IS
Y0
Y1
Y
If consumers reduce consumption by less than the increase in G at every level of output,
then the IS curve will shift up and to the right. In this case, the real interest rate could go
down or up, depending on how large the shift in the IS curve is relative to the shift in the
FE line. You should be able to draw pictures to illustrate both possibilities (i.e, an
increase in r and a decrease in r. Furthermore, the price level could actually increase in
this case if the shift in the IS curve is large
enough relative to the shift in the FE curve to require an upward shift in the LM curve.
Again, you should be able to draw the picture that illustrates an increase in the price
level.
140
Chapter 11: Keynesian Model
Real Wage Rigidity:
 Keynesians believe that real wages do not adjust quickly, and the real wage
moves too little to keep the quantity of labor demanded equal to the quantity of
labor supplied.
 There are three reasons why real wages remain rigid in the face on excess labor
1) Legal and institutional factors such as minimum wage laws and union
contracts
2) Reduce turnover costs by paying a higher wage than they have to
3) Workers who are paid well have greater incentive to work hard and effectively
(the carrot) and less incentive to shirk (the stick)- Efficiency Wage Model
Efficiency Wage Model:
 The idea that workers productivity (effort) depends on the real wage received, and
therefore firms will pay wages above the market clearing level.
 There is a carrot and a stick aspect to this theory, carrot- the idea that workers
who feel well treated will work harder and more efficiently. Stick- the idea that a
worker receiving a higher wage will place a greater value on keeping their job,
and will work hard to avoid being fired (shirking is costly).
 In this model, firms will choose the wage that gets the most effort from workers
per dollar in real wages spent (efficiency wage)
 Because the employer chooses the real wage that maximizes effort received per
dollar paid, as long as the effort curve doesn’t change, employers will not change
the real wage. This implies that the real wage is permanently rigid, and equals the
efficiency wage (in reality, the real wage is relatively stable).
Employment and Unemployment in the Efficiency Wage Model
141
When the efficiency wage, w* is paid, the firms demand for labor is represented by
point A. However, the amount of labor workers are willing to supply at w* is at point
B. The horizontal line between point A and B is the amount of involuntary
unemployment when w* is paid.
The unemployed cannot bid down the real wage in this model, because the firms will
not hire them, because employers know that workers working at a lower wage will
not put out as much effort per dollar as the worker receiving the real wage.
Efficiency Wages and the FE line: In the efficiency wage model, labor supply does
not affect employment, so changes in the labor supply do not affect the FE line.
However, a change in productivity will shift the FE line.
Price Stickiness:
 Keynesians refer to the tendency of prices to adjust slow to the economy
(price rigidity) as price stickiness
 They account for monetary nonneutrality with this theory, if prices do not
adjust quickly, the price level cannot adjust immediately to offset changes in
the money supply
 It is not free to change prices; the cost of changing prices is referred to as
menu costs. If the loss in profits is less than the cost of changing prices, the
firm will not change its prices. The implications are that in the short run, the
firm will meet the increase in demand without changing prices (the vending
machine analogy).
Monetary Policy
 In the IS-LM model, due to price stickiness, the economy doesn’t have to be in
equilibrium in the short run. The economy always lies at the intersection of the IS
and LM curves. Prices remain the same and output can be different (greater or
less than) than full employment output. However, the rigidity of the price level is
not permanent, and in the long run firms will re-adjust their prices.
 With the AD-AS model, the main difference is the speed of the price adjustment
(prices remain fixed for awhile, and then adjust)
Fiscal Policy
 Keynesians believe that increased government purchases and lower taxes can be
used to raise output and employment.
 Keynesians consider these to be expansionary changes, as they shift the IS curve
up and to the right. See pages 412-413 in the book for the complete explanation.
Keynesian Business Cycles
 Keynesians attribute most business cycles to aggregate demand shocks – shocks
that shift either the IS or LM curve, thereby affecting the aggregate demand for
output.
 The Keynesian theory can account for the procyclical behavior of employment,
money, inflation and investment.
142


To explain the pro-cyclical behavior of average labor productivity, Keynesians
include an additional assumption the firms hoard labor by employing more
workers than necessary during recessions.
There are three ways in which policymakers can respond to a recession:
1) No change in macroeconomic policy: with no intervention, the economy will
eventually correct itself. However, during the potentially lengthy adjustment
process, output and employment remain below full employment levels.
2) An increase in the money supply: this would shift the LM curve down and to
the right. This policy will cause the economy to move more quickly to general
equilibrium.
3) An increase in government purchases and/or lower taxes/tax rate: This will
shift the IS curve up and to the right.
Keynesian anti-recessionary policies lead to a higher price level than what would occur
with the absence of policy changes!
143
Example Problems for Chapter 11
1. Suppose that an economy is given by the equations below.
Cd = 900 + .5(Y – T) – 300r
Id = 400 – 700r
L = .2Y – 800(r + πe)
Ỹ = 3000 (full-employment level of output)
G = T = 500.
M = 2600
πe = .05
a. Derive the equations for the IS and LM curves.
b. Find the full-employment levels of output, the real interest rate, the price level,
consumption and investment.
c. Suppose that desired investment increases to
Id = 550 – 700r
If the economy was at full employment before the increase in desired investment,
find the new values of output, the real interest rate, the price level, consumption and
investment in the short run and in the long run. Illustrate your answer with an
appropriate graph.
2.
Use the Keynesian model to analyze the effects of each of the following
events on output, the real interest rate, employment and the price level in the short run
and in the long run.
a. Desired investment increases.
b. Desired saving increases.
c. The future marginal product of capital decreases.
d. Consumers increase their level of consumption expenditures at each level of Y and
r..
144
Answers to Example Problems for Chapter 11
a.
Suppose that an economy is given by the equations below.
Cd = 900 + .5(Y – T) – 300r
Id = 400 – 700r
L = .2Y – 800(r + πe)
Ỹ = 3000 (full-employment level of output)
G = T = 500.
M = 2600
πe = .05
a. Derive the equations for the IS and LM curves.
IS Curve: First compute desired saving:
Using Sd = Y – Cd - G and the expressions for Cd and the value of 100 for G and T we get
Sd = Y – (900 + .5(Y – T) – 300r) – 500 = .5Y + 300r –1150.
To get the IS curve we set Sd = Id
.5Y + 300r –1150 = 400 – 700r,
and solve for r.
r = –.0005Y + 1.55.
LM Curve: Set real money supply equal to real money demand and solve for r.
2600/P = .2Y – 800(r + .05),
or
r = .00025Y – 3.25/P – .05 .
b. Find the full-employment levels of output, the real interest rate, the price level,
consumption and investment.
145
The full-employment level of output is Y = 3000. To get the full-employment level of the
price level, find the aggregate demand curve by solving for the intersection of the IS and
the LM curves:
–.0005Y + 1.55 = .00025Y – 3.25/P – .05,
which can be solved for Y:
Y = 2133⅓ + 4333⅓/P.
Setting aggregate supply equal to aggregate demand gives
3000 = 2133⅓ + 4333⅓/P.
or
P=5
.
Substitute the long-run equilibrium value of Y into the IS curve (or the LM curve) to get
the real interest rate:
r = –(.0005)(3000) + 1.55.= .05.
Substitute the long-run equilibrium values of r and Y into the consumption and
investment functions to get the C and I.
Cd = 900 + .5(3000 – 500) – (300)(.05) = 2135
Id = 400 – (700)(.05) = 365.
c. Suppose that desired investment increases to
Id = 550 – 700r
If the economy was at full employment before the increase in desired investment,
find the new values of output, the real interest rate, the price level, consumption and
investment in the short run and in the long run. Illustrate your answer with an
appropriate graph.
Short Run: In the short run, P does not change, so P = 5. The change in investment
demand shifts the IS curve to the right. Get the new IS curve algebraically by solving
.5Y + 300r –1150 = 550 – 700r,
146
for r:
r = –.0005Y +1.7.
In the short run the price level does not adjust and the level of aggregate demand
determines the level of output. The level of aggregate demand is again determined by the
intersection of the IS and LM curves:
–.0005Y +1.7 = . 00025Y – 3.25/5 – .05
or
Y = 3200.
We can again get r from the IS curve:
r = –(.0005)(3200) + 1.7 = 0.1
Get C and I as in part (b):
Cd = 900 + .5(3200 – 500) – (300)(.1) = 2220.
Id = 550 – (700)(.1) = 480.
Long Run: In the long run, the price level will adjust, so we proceed as in parts (a) and
(b).
Aggregate demand is determined by the intersection of the IS and LM curves:
–.0005Y + 1.7 = .00025Y – 3.25/P – .05,
or
Y = 2333⅓ + 4333⅓/P.
Since the long-run level of output will be 3000, we can set supply (3000) equal to
demand and solve for the price level:
3000 = 2333⅓ + 4333⅓/P.
or
P = 6.5.
147
Using the IS curve to get r, we have
r = – (.0005)(3000) + 1.7 = .2.
Use the C and I equations to get
Cd = 900 + .5(3000 – 500) – (300)(.2) = 2090.
Id = 550 – (700)(.2) = 410.
These short-run and long-run responses are shown in the graph below.
FE
r
.2
LM0
E1
.1
.05
LM1
ES
E0
IS1
IS0
3000
b.
3200
Y
Use the Keynesian model to analyze the effects of each of the following
events on output, the real interest rate, employment and the price level in the short run
and in the long run.
a. Desired investment increases.
The IS curve shifts to the right.
Short Run: The rightward shift in the IS curve results in an increase in aggregate demand,
represented by the intersection of the new IS curve with the LM curve. Since this is the
short run, the price level does not adjust, and firms adjust output in response to the
increase in aggregate demand, so that output increases and the price level does not
change. The new intersection of the IS and LM curves is at a higher real interest rate, so
148
the real interest rate increases. The level of employment is determined by the level of
effective demand, which increases as output increases, so employment goes up.
Long Run: The price level adjusts upward to restore the economy to general equilibrium.
Graphically, the LM curve will shift upward, which means that there will be a further
increase in the real interest rate. Since the level of output returns to the full-employment
level of output, the level of employment returns to the full-employment level of
employment. So in the long run, there is no effect on output or employment, but the real
interest rate and the price level increase.
FE
r
r1
LM1
LM0
E1
rS
r0
ES
E0
IS1
IS0
Yf
YS
Y
b. Desired Saving increases.
The IS curve will shift down (to the left).
Short Run: The leftward shift in the IS curve results in an decrease in aggregate demand,
represented by the intersection of the new IS curve with the LM curve. Since this is the
short run, the price level does not adjust, and firms adjust their output to the decrease in
aggregate demand so that output decreases and the price level does not change. The new
intersection of the IS and LM curves is at a lower real interest rate, so the real interest rate
decreases. The level of employment is determined by the level of effective demand,
which decreases as output decreases, so employment goes down.
Long Run: The price level adjusts downward to restore the economy to general
equilibrium. Graphically, the LM curve will shift downward, which means that there will
be a further decrease in the real interest rate. Since the level of output returns to the full-
149
employment level of output, the level of employment returns to the full-employment
level of employment. So in the long run, there is no effect on output or employment, but
the real interest rate and the price level decrease.
r
E0
LM0
FE
LM1
r0
rS
ES
r1
E1
IS0
IS1
YS
Yf
Y
c. The future marginal product of capital decreases.
The reduction in the expected future profitability of investments will cause the desired
investment curve to shift to the left. This means that, at every level of income, the real
interest rate will now be lower, so the IS curve will shift down (to the left). From here on
the analysis is the same as in part (b).
Short Run: The leftward shift in the IS curve results in an decrease in aggregate demand,
represented by the intersection of the new IS curve with the LM curve. Since this is the
short run, the price level does not adjust, and firms adjust their output to the decrease in
aggregate demand so that output decreases and the price level does not change. The new
intersection of the IS and LM curves is at a lower real interest rate, so the real interest rate
decreases. The level of employment is determined by the level of effective demand,
which decreases as output decreases, so employment goes down.
Long Run: The price level adjusts downward to restore the economy to general
equilibrium. Graphically, the LM curve will shift downward, which means that there will
be a further decrease in the real interest rate. Since the level of output returns to the fullemployment level of output, the level of employment returns to the full-employment
level of employment. So in the long run, there is no effect on output or employment, but
the real interest rate and the price level decrease.
150
r
E0
LM0
FE
LM1
r0
rS
ES
r1
E1
IS0
IS1
YS
Yf
Y
d. Consumers increase their level of consumption at every level of Y and r.
Increasing consumption today will lead to a leftward shift in today’s desired saving
curve, so that the real interest rate will be higher at every level of real income. This
means that the IS curve shifts upward (to the right). From here on the analysis is the same
as in part (a)..
Short Run: The rightward shift in the IS curve results in an increase in aggregate demand,
represented by the intersection of the new IS curve with the LM curve. Since this is the
short run, the price level does not adjust, and firms respond to the increase in aggregate
demand so that output increases and the price level does not change. The new intersection
of the IS and LM curves is at a higher real interest rate, so the real interest rate increases.
The level of employment is determined by the level of effective demand, which increases
as output increases, so employment goes up.
Long Run: The price level adjusts upward to restore the economy to general equilibrium.
Graphically, the LM curve will shift upward, which means that there will be a further
increase in the real interest rate. Since the level of output returns to the full-employment
level of output, the level of employment returns to the full-employment level of
employment. So in the long run, there is no effect on output or employment, but the real
interest rate and the price level increase.
151
FE
r
r1
LM1
LM0
E1
rS
r0
ES
E0
IS1
IS0
Yf
Ys
Y
152
Chapter 6: Long-Run Economic Growth
Sources of Economic Growth
 ∆Y/Y = ∆A/A + (aK * ∆K/K) + (aN * ∆N/N)
 aK is the elasticity of output with respect to capital, and represents the percentage
increase in output resulting from a 1% increase in capital.
 aN is the elasticity of output with respect to labor, and represents the percentage
increase in output resulting from a 1% increase in the amount of labor used.
 Both elasticities are numbers between 0 and 1 that are determined from historical
data.
 Typically, aK = 0.3, aN = 0.7
 Growth Accounting Equation, shown in the first bullet, is the production function
written in growth rate form.
The Solow Model
 Solow model examines economy as it evolves over time, and uses per worker
units.
 yt = Yt/Nt = output per worker in year t
 ct = Ct/Nt = consumption per worker in year t
 kt = Kt/Nt = capital stock per worker in year t
 Capital stock per worker, kt, is also called the capital-labor ratio
 Production function in per worker terms: yt = f(kt)
Steady States
 Steady State is a situation in which the economy’s output per worker,
consumption per worker, and capital stock per worker are constant over time.
153




It = (n + d)Kt, in a steady state
Ct = Yt – (n + d)Kt, in a steady state
ct = f(k) – (n + d)k, in a steady state
Above equation shows that an increase in the steady-state capital-labor ration,
k, has two opposing effects on steady-state consumption per worker, c. First,
an increase in k raises the amount of output each worker can produce, f(k).
Second, increase in k increases the amount of output per worker that much be
devoted to investment, (n + d)k. More goods devoted to investment leaves
fewer goods to consume.



Steady-State consumption per worker, cG, is at the widest point between
the two curves.
Level of Capital-Labor ratio that maximizes consumption per worker in
the steady state, kG, is known as Golden Rule capital-labor ratio
For high values of k (values greater than Golden Rule capital-labor ratio,
kG), increases in the steady-state capital-labor ratio actually result in
lower steady-state consumption per worker because so much investment
is needed to maintain the high level of capital per worker.
Reaching the Steady State
 St = sYt
 St is national saving in year t, and s (a number between 0 and 1) is the saving rate,
which we assume to be constant.
 In every year, national saving, St, equals investment, It, therefore: sYt = (n + d)Kt
 By substituting in the equations we have already derived, the steady state equation
becomes: sf(k) = (n + d)k
 Above equation indicates that saving per worker, sf(k), equals steady-state
investment per worker. Because the capital-labor ratio, k, is constant in steady
state, subscripts t are dropped.
154
Example Problems for Chapter 6
1. According to the economic growth theory that we have studied, how would each of the
following events affect per capita consumption in the long-run (i.e., after return to the steady
state).. Illustrate graphically and explain. In all of the parts, we can assume that the rate of
saving is less than the golden rule level of saving, so that a reduction in steady-state
output per worker leads to a reduction in steady-state consumption per worker.
a. A terrorist attack destroys a portion of the nation’s capital stock.
b. An increase in the birth rate leads to a permanent increase in the nation’s rate of
population growth.
c. Discovery of a new energy technology leads to a permanent increase in productivity.
d. A change in consumer attitudes leads to a permanent reduction in the national saving rate.
e. The fraction of the population in the labor force decreases permanently.
155
Answers to Example Problems for Chapter 6
1. According to the economic growth theory that we have studied, how would each of the
following events affect per capita consumption in the long-run (i.e., after return to the steady
state).. Illustrate graphically and explain. In all of the parts, we can assume that the rate of
saving is less than the golden rule level of saving, so that a reduction in steady-state
output per worker leads to a reduction in steady-state consumption per worker.
a. A terrorist attack destroys a portion of the nation’s capital stock.
Assume that the economy begins (pre-attack) in the steady state. The destruction of a
portion of the nation’s capital will reduce the capital-labor ratio to a level that is below
the steady-state level. (We are assuming here that the population and labor force were not
reduced significantly by the war.). We know that when the capital-labor ratio is below its
steady-state level, the rate of saving (and therefore investment) will be greater than the
rate required to replace worn out capital and equip new workers, so the capital labor ratio
will be growing. This growth in the capital labor ratio will continue until the economy
returns to the steady state. Since there was no change in f, s, n, or d, the steady state will
be the same as it was before the war.
Per capita
investment
(n+d)k
sf(k)
k0
k*
k
b. An increase in the birth rate leads to a permanent increase in the nation’s rate of
population growth.
An increase in the rate of population growth translates into an equal increase in the rate of
growth of the labor force (from n0 to n1). The steady-state capital-labor ratio falls from
k*0 to k*1, which reduces output per worker (and therefore consumption per worker).
156
Per capita
investment
(n1+d)k
(n0+d)k
sf(k)
k*1
k*0
k
c. Discovery of a new energy technology leads to a permanent increase in productivity.
A permanent increase in productivity shifts f shifts up from f0 to f1. The steady state level
of capital increases from k*0 to k*1. As a result, output per worker (and therefore
consumption per worker) increase for two reasons: (1) increased capital per worker, and
(2) increased productivity of capital and labor.
157
Per capita
investment
(n+d)k
sf1(k)
sf0(k)
k*0
k*1
k
158
d. A change in consumer attitudes leads to a permanent reduction in the national saving
rate..
A temporary decrease in the saving rate s would have no effect on the steady state. If the
increase in the saving rate is permanent, as in the statement of the problem, it would shift
the per capita saving (= per capita investment) curve dodewards, and would then increase
the steady state level of capital per worker, output per worker, and consumption per
worker.
Per capita
investment
(n+d)k
s0f (k)
s1f (k)
k*1
k*0
k
e. The fraction of the population in the labor force decreases permanently.
A decrease in the fraction of the population that is in the labor force would have no effect
on the steady state. There would be a one time drop in the rate of growth of the labor
force, but its growth rate would then return to the original rate of growth. Therefore, there
would be no change in the steady state level of capital per worker, output per worker, or
consumption per worker. (Notice, however, that consumption per person would decrease,
because the ratio of people to workers would increase.)
159
160