Macroeconomics Qualifying Exam-302 Module
Claremont Graduate University
May, 2011
Lamar
There are 100 points on this part of the Qualifying Exam. All questions are equally
weighted. Show all your work.
Part I: Answer all three questions (each question is worth 25 points).
1. Consider the standard Solow model with a Cobb-Douglas production function,
. Population is growing at the exogenous rate n. suppose the government
decides to subsidize investment at the rate , that is, for each unit invested in the
economy the government adds units. Do not worry about the financing of the subsidy.
a) Write down the capital accumulation equation.
b) Using the appropriate transformation obtain the capital accumulation equation in
per-capita terms.
c) Draw the diagram of this model and compare to the standard Solow model
without technological progress. What is the main difference?
d) Find k, y, and c in the steady state.
e) How would the government set so to induce the economy to converge to the
golden-rule level of capital?
f) What is the impact of a decrease in on the transitional dynamics of K(t)? Draw
the time path for K(t) from the old balanced growth path
to the new one
on a graph with time in the horizontal axis.
2. Assume a closed economy with the following two-period utility function
[
]
[
]
and Cobb-Douglas technology,
, where technology follows an
AR1 process. Capital depreciation rate is equal to 1 every period.
a) Write out the household’s lifetime budget constraint.
b) Set up the utility maximization problem for the representative household and find
the First Order Conditions for the household maximization problem.
c) Combine the appropriate FOCs to explain the household’s labor-leisure choice.
d) Show what a positive technology shock does to the labor-leisure decision of
households. Prove your answer and provide the intuition for the result.
e) Derive and interpret the Euler equation for this economy. How the same positive
technology shock affect the consumption path? Explain.
f) Show the persistency effects of the positive technological shock on output.
3. Suppose the effort is a function of the prevailing wage w, the unemployment rate u,
and the average wage paid wa:
{
(
)
}
Where 0<β<1 and b > 0. There are perfectly-competitive firms with profits defined as .
The production function is given by
a) Find the first-order conditions for the firm’s maximization problem.
b) Find the equilibrium real wage w* and unemployment rate in terms of the
parameters.
c) Explain the intuition for how this model implies there is equilibrium with
unemployment. That is, why is the equilibrium real wage different from the
market-clearing real wage wm?
d) Are the rigidities in the efficiency-wage model real or nominal? Explain briefly and
provide an example to prove your point.
Part II: Answer one of the following two questions ( 25 points).
4. Consider the following flexible price Rational Expectations macroeconomic model:
Aggregate Supply :
Yt  Y   ( Pt  Pt e )
Aggregate Demand:
Yt  M t  Pt  vt
where vt is a velocity term. Velocity is random, but it is assumed to be correlated with its
own past values, that is,
[ ]
Agents know that money supply behaves according to: M t  vt 1  et ;
here et is normally distributed N(0,δ)
a) Find the rational expectations solution to Pt. Identify in the solution the systematic
component of monetary policy and the entirely random components.
b) Solve for Yt and interpret the solution.
c) Is monetary policy neutral? Can monetary policy influence output?
5. Assume an economy described by the following IS-MP model,
IS:
Y  C (Y  T )  I (r )  G
MP: r  r ( , Y ) , where r  0 ,
a) Derive graphically the Aggregate Demand curve. State your assumptions.
b) Show analytically that the Aggregate Demand curve slopes downward.
c) How would a change in the monetary-policy rule to become more
expansionary affect r and Y?
d) If the Aggregate Demand curve is downward sloping, then an increase in
π should lower the equilibrium Y. Is this true in this model?
e) Suppose now the monetary authority has the following monetary rule,
MP: r  r ( ) , where r  0 . What is the slope of the Aggregate Demand
curve? Explain.