SAMPLE FINAL EXAMINATION
Economics 122a. Fall 2012
Mr. Nordhaus and staff
December 14, 2012: 2:00 pm – 5:30 pm
This is a 3½ hour test. There are three parts. Points are proportional to minutes. Please
write each part in a separate blue book. Put your name, college, TA, and class on each blue
book. All questions are required.
Your examination will be judged on the soundness of your macroeconomic analysis
and the quality of your writing. Long and rambling answers will be penalized. Illegible
answers will also be penalized. This is a closed-book exam. No electronic equipment of any
kind is allowed.
Part I. Warm-up Exercises (60 minutes total)
A. Definitions (15 minutes)
Define each concept in no more than two sentences:
1. Real GDP
2. Real interest rate for business
3. Baumol-Tobin model
B. Taxes in macroeconomics. (15 minutes)
Describe the predictions about the impact of tax changes in the following examples. Use a
graph where appropriate.
1. A cut in personal tax rates in a closed economy IS-MP analysis (on real output
and real interest rates)
2. An investment tax credit in the neoclassical investment model (on the desired
capital stock)
C. Macro ABCs. (15 minutes)
For each pair, define both concepts and explain how they are related.
1. Current account: financial account of the balance of payments
2. Taylor rule: MP curve
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D. Macroeconomic Problems in Boolaland (15 minutes)
Consider the global economy, which you can treat as a closed economy. Assume that world
monetary policy is set by the Fed, and that we are in normal times. Because of the fear of the
fiscal cliff, the Eurozone collapse, and war in the Mideast, consumers increase their desired
precautionary saving. What is the effect of this savings shift on world output, investment, and
interest rates in the Keynesian short run?
II. Problems and Puzzles (60 minutes)
A. To Grow or Not to Grow in Macroland (25 minutes)
Assume that output in a perfectly competitive closed economy called Macroland is produced
by a Cobb-Douglas production function where F(K,L) = KaL(1-a), where Y is output, K is
capital, and L is labor. Also assume that the depreciation rate of capital is 10 percent per year,
the savings rate is 20 percent, there is no labor force growth, and the income shares of the
factors of production are equal in national income.
1. Suppose the initial capital per worker level (k1) is 16. Calculate output per worker (y1),
consumption per worker (c1), investment per worker (i1) in period 1 and capital per
worker in period 2 (k2). Also explain whether this economy accumulating capital per
worker or not.
2. Now, solve for capital per worker (kss) output per worker (yss), consumption per
worker (css), investment per worker (iss) and the change in capital stock per worker
(∆k) in the long run or steady state. Show the relationship between (k1), (k2), and (kss)
using the standard Solow diagram.
3. What is the growth rate of capital per worker (k), output per worker (y), aggregate
capital (K) and aggregate output (Y) in the long run? Explain your reasoning.
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B. Macroeconomic wisdom (10 minutes).
The following are statements by two eminent macroeconomists. Explain each statement using
the appropriate macroeconomic model or analysis. State whether you agree with the
statement. Defend your view with either historical evidence or macroeconomic theory. One
bluebook page per statement is sufficient. Choose one of two.
1. “Under present circumstances, a 4 percent unemployment rate means about 5
percent inflation for the long run, while a 2 percent inflation rate would require an
unemployment rate of 5½ percent.” (Arthur Okun, “Mirage of Steady Inflation,”
1971)
2. “The substitution of a budget deficit for current taxes (or any other rearrangement
of the timing of taxes) has no impact on the aggregate demand for goods.” (Robert
Barro, Journal of Economic Perspectives, Spring 1989)
C. A Consuming Question. (25 minutes) Answer all parts.
You are a fully rational Yale student, planning consumption for your two periods of life
(periods 1 and 2). You sit down at the start of period 1 to optimize your consumption for both
periods (C1 and C2). Assume that the utility function of consumption each period is U(Ct).
You can borrow and lend at interest rate r and you have a personal discount rate of ρ. You
know you will earn Y1 in period 1 and Y2 in period 2. All prices are 1.
1) Write the lifetime budget constraint and solve it for C1.
2) Next, write down the optimization problem you are trying to solve. Use the lifetime
budget constraint to change this to an optimization problem in one variable, C1. Derive a
first-order condition between U’(C1) and U’(C2).
3) Now, assume that you have the following parameter values:
r = 0.10
ρ =0
Y1 = 100
Y2 = 0
U(C) = ln(C)
[Recall that the derivative of ln(x) w.r.t. x is U’(x) = 1/x]
Find your optimal consumption bundle for period 1 and period 2. Draw a graph showing
the budget set, the indifference curve, and the optimum point. Make sure to label your
graph.
4) Assume that you are liquidity constrained (you cannot borrow against future income).
Resolve (3) for the optimal consumption. Next assume that your income stream is Y1 = 40
and Y2 = 66. Resolve for your optimal consumption for these numbers.
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III. Some final questions about current issues.
A. The Fed at Work (25 minutes) Limit to one bluebook page.
In its statement after the Federal Open Market Committee (FOMC) meeting in October
2012, the FOMC issued the following statement (in part):
To support a stronger economic recovery,… the Committee agreed today to increase
policy accommodation by purchasing additional agency mortgage-backed securities at
a pace of $40 billion per month. The Committee also will continue through the end of
the year its program to extend the average maturity of its holdings of securities....These
actions, which together will increase the Committee’s holdings of longer-term
securities by about $85 billion each month through the end of the year….
The Committee also decided today to keep the target range for the federal funds rate
at 0 to 1/4 percent and currently anticipates that exceptionally low levels for the
federal funds rate are likely to be warranted at least through mid-2015.
(http://www.federalreserve.gov/newsevents/press/monetary/20101103a.htm)
Explain:
(a) What actions the Fed took;
(b) what are the expected impacts of these actions on the financial markets and
the real economy;
(c) how these steps differ from “normal” Fed actions;
(d) and why these “unconventional” steps were necessary at that time.
Use the relevant tools from the course.
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B. An inflationary question (25 minutes)
Priceland is a country with the following short-run Phillips curve, where t is in
years:
 t   te   (ut  6%),
 1
a. Define the natural rate of unemployment. Calculate the natural rate of
unemployment for Priceland. Explain your answer.
b. Draw the short-run Phillips curve in a graph with unemployment on the
horizontal axis and inflation on the vertical axis.
c. In period 0, the unemployment rate is 6%, and actual and expected inflation are
8% per year. Suppose the Central Bank of Priceland decided it wants to reduce
the expected rate of inflation by 1 percentage point in 1 year. Qualitatively, what
would it do to monetary policy? What would it need to do to the
unemployment rate? Be specific. Graph a path of the unemployment rate that
would achieve the objective.
d. Assume output in Priceland is $10,000 billion. What is the cost of such the policy
in terms of the difference between actual and potential output?
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