Exam 2
ECON 304.101
June 15th, 2007
Name:
PSU id number:
Read all of the following information before starting the exam:
• The exam is closed book and closed notes
• Show all work, clearly and in order, if you want to get full credit. I reserve the right to take off points
if I cannot see how you arrived at your answer (even if your final answer is correct).
• You may use a non-programmable calculator.
• Cellphones are not allowed in the exam.
• Circle or otherwise indicate your final answers.
• Clearly label all graphs (axis, numbers, names of the curves, etc.)
• Please keep your written answers brief; be clear and to the point. I will take points off for rambling
and for incorrect or irrelevant statements.
• This test has 7 questions and is worth 100 points (+5 bonus points),
• Good luck!
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1. Suppose there is a permanent fall in total factor productivity (A fall in A in the production function
Y = AF (K, N )).
a. What is the effect of this shock on employment, real wage and current output? Illustrate in a graph.
[5 points]
b. Given that this is a permanent shock what is its effect on national saving, investment and the real
interest rate? Illustrate what happens in a graph. [5 points]
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2. A consumer has current income (y1 ) of $150 and future income (y2 ) of $300. The real interest rate is
5%
a. Calculate the present value of income for this consumer [5 points]
b. Write the equation for the consumer’s budget constraint [5 points]
c. Assume that the consumer wants to consume the same amount in every period of his life (in other
words, c1 = c2 ). Calculate the optimal consumption bundle and optimal saving in period 1 for
this consumer. Is this consumer a borrower or a lender? [5 points]
d. Depict the optimal consumption problem for the individual. Include the budget constraint, and the
income and consumption points. [5 points]
e. Suppose that the real interest rate increases. What does the income and substitution effect say
about the individual’s saving? Can you say for sure if saving will increase or decrease? [5 points]
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3. Desired consumption for an economy is given by the equation
C d = 1, 000 + 0.6Y − 4, 000r
Government purchases are given by G = 1, 500
a. Write an equation relating desired saving, S d , to Y and r [5 points]
b. Suppose that the full-employment level of output is 10,000, and desired investment for the economy
is given by:
I d = 2, 000 − 6, 000r
calculate the equilibrium real interest rate that clears the goods market, and the equilibrium level
of consumption, saving and investment [5 points]
c. Suppose that government purchases increase. What happens to the equilibrium levels of the real
interest rate, saving and investment? represent in the situation in a graph (since I am not giving
you the information about how G changes, you cannot calculate the new interest rate, saving and
investment numerically. Just show what happens in the graph.) [5 points]
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4. a. State two reasons for the high level of current consumption in the United States in the last five
years. [5 points]
b. Briefly explain why a high inflation rate can be disruptive to economic growth [5 points]
c. In the Solow model with constant total factor productivity (TFP), what is the rate of growth of
GDP per worker when the economy reaches its steady state? [5 points]
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5. The income elasticity of money demand (ηy ) is 2/3 and the interest elasticity of money demand (ηi ) is
-0.1. Real income is expected to grow by 4.5% over the next year, and the real interest rate is expected
to remain constant over the next year. The rate of inflation has been zero for several years. If the
central bank wants zero inflation over the next year, what growth rate of the nominal money demand
should it choose? (remember the equilibrium condition for the asset market: M = L(Y, r + π e )) [10
points]
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6. An economy is in steady state with no productivity change. Assume that there is a war, and a large
fraction of the economy’s capital stock is destroyed.
a. Explain how is the steady state capital per worker going to be affected. Show what happens in a
graph. [10 points]
b. Show graphically the evolution of the capital stock per worker and the rate of growth of output per
worker when the economy moves from its initial steady state to the new one. [5 points]
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7. Consider a closed economy in which the population grows at a rate of 1% per year. The per-worker
production function is yt = 6kt0.5 . The depreciation rate of capital is 14% per year.
a. Households consume 90% of their income and save the remaining 10%. There is no government.
What are the steady state values of capital per worker, consumption per worker and output per
worker? (remember that the equation for the law of motion of capital per worker is: (1 + n)kt+1 =
(1 − δ)kt + it ) [10 points]
b. Suppose that the introduction of 401(k) plans in this economy raises the saving rate to 25%, and
everything else remains the same as before. What are the steady state values of capital per worker,
consumption per worker and output per worker? [10 points]
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