Claremont Graduate University
Macroeconomics Qualifying Exam
302 Module
September, 2009
Lamar
There are 100 points on this part of the Qualifying Exam. Show all your work.
Section I. Answer all questions (60 points)
1. Consider the Solow model without technological progress. For simplicity, assume
that A is equal to one. There is the possibility that saving rates may be higher at
higher income levels. This version of the Solow model is slightly different from
the standard presentation in the saving rate:
The saving rate is zero if income per worker is less than some critical level, ݂ሺ݇෠ሻ.
The saving rate is s (where s > 0) if income per worker exceeds ݂ሺ݇෠ሻ.
෢ is greater that ሺ݊ ൅ ߜሻ݇෠.
Finally, assume that ‫݂ݏ‬ሺ݇ሻ
a) Describe how, if at all, this change affects the usual Solow diagram for the Solow
model.
b) Describe the behavior of output per worker over time.
c) If the production function is Cobb-Douglas, derive the conditions for the saving
rate where consumption per capita is maximized (sgold).
d) Under what condition the golden rule leads to dynamic inefficiency? Explain
why?
(30 points, each part is equally weighted)
2. Consider the following production function, Y = AK, where A is a constant that
represents the technology level. Also assumes that capital accumulates as it
does in the Solow model.
a) Derive the Solow fundamental equation. Define the appropriate variables. (3
points)
b) Derive an expression for the rate of growth of capital per worker and income per
worker . (4 points)
c) Under what condition the economy will exhibit growth? (What that condition
means?) (4 points)
d) What is the relation between the rate of growth of output per capita and the level
of capital per capita? (3 points)
e) Assume a natural disaster happens (it destroys part of the capital), how this
affects the short and long-run rates of growth? Justify your answer. (3 points)
f) Paul Romer’s 1986 article is an attempt to provide microfoundations to a model
like the one you developed above. This part of the question asks you to provide
in detail how Romer justifies the possibility of a model like this. (10 points)
g) Provide a brief critique to what you did in f). (3 points)
(30 points)
Section II (40 points)
Answer two of the following three questions. Each question is worth 20 points
3. The following comment appeared in the “New York Times” in October 10, 2006.
“Edmund S. Phelps, a Columbia University professor, was awarded the Nobel Memorial
Prize in Economic Science yesterday for his contribution to a sophisticated explanation of
how wages, unemployment and inflation interact with one another. The explanation holds,
in essence, that wages and inflation tend to rise in tandem, one pushing up the other, until
the unemployment rate reaches an ‘equilibrium’ or ‘natural’ level at which prices no
longer rise.”
I want you to analyze the consistency of this comment under:
a) The traditional Phillips Curve.
b) The Expectations-Augmented Phillips Curve.
In both cases you must support your arguments with the appropriate
equations/graphs.
4. Explain why a policy rule may be superior to a discretionary policy. In answering
this question assume that aggregate supply is given by the Lucas Supply Curve
−
y = y + b(π − π e ) b >0, policy makers have a loss function given by
1
1
L = ( y − y*) + a (π − π *) 2 , where * represent optimal levels of output and
2
2
inflation respectively. Assume a policy maker chooses the inflation rate. What is the
role of reputation in this model?
5. What is the “policy ineffectiveness proposition”? Provide a model that reflects this
important macroeconomic result and prove and illustrate the proposition. What
are the key assumptions of this result?
What was the Stanley Fischer answer to this result? Here I do not want you to
develop the full model, only the intuition of Fischer’s answer.