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ECO 301
Intermediate Income Theory
Professor Malamud
November 24, 2003
Classroom Exam #3 Answer all questions.
You will be able to rewrite one question at home after the exam is returned to you (but not, of course, Question 1).
If you rewrite a question at home, you must rewrite the WHOLE question, even parts that you got a perfect
score on in class. Rewrites are graded to a higher standard than answers written in class. The exact same answer
may earn fewer points on the rewrite than on the exam taken in class. Your score on a question that you rewrite is
the average of your classroom score and your rewrite score. Rewrites are due Monday, December 1.
Question 1 Multiple choice (circle the best answer – 3 points each question … 54 points)
1. The best indicator of an improved standard of living is growth in
a. nominal GDP
b. real GDP
c. real GDP per capita
d. real balances per capita
2. “Convergence” has been occurring between the OECD countries because
a. the rich countries give away some of their output to the poor countries
b. the poorer countries have had higher growth rates than the richer countries
c. the richer countries have had higher growth rates than the poorer ones
d. the procedures for measuring growth create an illusion of convergence
3. If a production function has constant returns to scale and both capital inputs and labor inputs
increase by 10%, output will
a. stay constant
b. increase, but by less than 10%
c. increase by just 10%
d. double
4. If a production function has constant returns to scale, successive, equal increases in capital per
worker cause output to
a. decline
b. stay constant
c. increase by a constant amount
d. increase by decreasing amounts
5. In order to indefinitely maintain a high growth rate of output per capita, a country needs
a. technological progress
b. capital accumulation
c. continual increases in capital per worker d. a high saving rate
6. When capital per worker is below the golden rule level, an increase in saving will
a. increase consumption in both the short-run and the long run
b. decrease consumption in the short run and increase it in the long run
c. decrease consumption in both the short run and long run
d. increase capital per worker at the expense of employment
7. A country has capital per worker of 100 units and a depreciation rate of .2. If this year’s
output per worker is 100 units and the saving rate is .1, capital per worker will
a. decrease by 10 units
b. not change
c. increase by 10 units
d. none of these answers is correct
8. If a country’s saving rate is above the golden rule saving rate, a reduction in the rate will
a. reduce the long run rate of growth
b. reduce output per worker in the long run
c. increase the long run rate of growth
d. increase output per worker in the long run
9. Suppose that the economy is initially in the steady state. A reduction in the rate of
depreciation will cause a long run
a. increase in capital per worker
b. increase in output per worker
c. increase in consumption per worker
d. all of these
For the following four questions (10 – 13), assume that the rate of depreciation is 10% per year,
the workforce growth rate is 2% per year, and the growth rate of technology is 3% per year.
10. The annual growth of “effective labor” in this economy is
a. 2%
b. 3%
c. 5%
d. 10%
e. 15%
11. The level of investment needed to maintain a constant capital stock (K) is
a. .02K
b. .03K
c. .05K
d. .10K
3. .15K
12. The steady state growth rate of output (Y) in this economy is
a. 2%
b. 3%
c. 5%
d. 10%
e. 15%
13. The steady state growth rate of consumption per worker (C/N) in this economy is
a. 2%
b. 3%
c. 5%
d. 10%
e. 15%
14. Which of the following will increase the steady state growth rate of output?
a. An increase in the saving rate
b. An increase in the population growth rate
c. A temporary burst of technological change d. All of these
e. None of these
15. An increase in productivity will increase employment whenever
a. output grows at a faster rate than productivity
b. aggregate demand increases
b. productivity grows at a faster rate than output
d. aggregate supply increases
16. Suppose that expectations of productivity growth (Ae)are slow to adjust. Further assume that
productivity (A) has been increasing by 5% per year. Now suppose that productivity increases
by only 2% this year. This slowdown in productivity growth will cause
a. the price setting relation to shift up by more than the wage setting relation
b. the wage setting relation to shift up by more than the price setting relation
c. the natural rate of unemployment to fall
d. the real wage to fall
17. Because of labor hoarding, an increase in output (Y) may signal
a. an increase in employment
b. an increase in productivity
c. all of these
d. none of these
18. Suppose that the modified Phillips Curve for an economy is Δπ = - 1 (u - .06) and that
Okun’s Law for this economy is Δu = - .5 (gy - .03). The sacrifice ratio for this economy is
a. 1
b. .06
c. .5
d. .03
e. none of these
Question 2 (30 points)
Suppose the Federal Reserve believes the modified Phillips Curve for the United States is
Δπ = - 1 (u - .06) and Okun’s Law is Δu = - .5 (gy - .03). The U.S. unemployment rate has been
hovering around 6% of the labor force for the past year and the U.S. CPI inflation rate has been
steady at around 2% per year. In order to “sex up” the economy for the upcoming presidential
election, the Fed wishes to lower the unemployment rate to 5% in 2004. The Fed recognizes that
this will increase inflation in 2004 and plans to do whatever it takes to return annual inflation to
2% in 2005 and beyond.
a. Based on the information given above, at what rate must the U.S. money supply be
growing at present? Show your calculation. (5 points)
gm,2003 =
b. If the Fed succeeds in lowering the unemployment rate to 5% in 2004, what will the 2004
inflation rate be? Show your calculation. (5 points)
π2004 =
c. At what rate must the Fed grow the money supply in 2004 to achieve its target
unemployment rate of 5%? Show your calculation. (5 points)
gm,2004 =
d. Fill in the table below based on the information about the economy provided to you and
on the Fed’s supposed intentions. (15 points)
Year
Inflation rate, π
Δπ
Unempl rate, u
Δu
Output growth, gy
Money growth,gm
2003
2%
2004
0
6%
0
5%
2005
2%
2006
2%
Question 3 (40 points)
Imagine an economy without population growth and without technological progress. Output (Y)
in this economy as a function of capital (K) and labor (N) inputs is given by
Y = F(K,N) = K½ N½
Existing capital stock depreciates at a rate of 10% per year (δ = .1) and people save and invest
10% of their incomes (s = .1).
a) Express output per worker as a function of capital per worker (5 points)
b) Sketch output per worker, saving per worker, and depreciation per worker as
functions of capital per worker. (5 points)
Y/N
K/N
c) Determine the steady state values of capital per worker and output per worker.
Label these numerical values on your sketch. (10 points)
Question 3, continued
d) What is the golden rule saving rate for this economy? (Show your calculation. 10
points)
e) If the golden rule saving rate differs from the current saving rate of 10%, what
will happen to capital per worker, output per worker, and consumption per worker
in the short run and in the long run if people now begin to save at the golden rule
rate? Describe and explain what happens to capital per worker, output per
worker, and consumption per worker over time when the saving rate switches
from 10% to the golden rule rate. Sketch the paths of these variables over time if
you wish. (10 points)
Question 4 (30 points)
Expectations of inflation track actual inflation pretty well but expectations of productivity
growth adjust only slowly. If people expect the high rate of productivity growth experienced
during the late 1990s to continue into the 2000s but the rate of productivity growth actually
slows down, the “natural rate” of unemployment is likely to increase. Explain why. Be sure
to mention what happens to the real wage when productivity growth slows and how this
affects the natural rate of unemployment.