Claremont Graduate University
Macroeconomics Qualifying Exam - 302 Module
May, 2010
Lamar
There are 100 points on this part of the Qualifying Exam. Show all your work.
Part I: Do all questions (1-3) (75 points). All questions are equally weighted.
1. Consider a Solow model without technological progress. Output is produced with CobbDouglas technology,
. Population grows exogenously at the rate n.
Capital accumulates according to ̇
where δ is the depreciation rate.
The resource constraint in the economy is given by
, where C(t) is
consumption, I(t) is private investment, and G(t) is government expenditures.
Aggregate consumption is given by a constant fraction θ of income, that is,
, and government expenditures are given also by a constant fraction of income γ of
income, that is,
.
a) Express all the variables in per capita terms and rewrite the resource constraint in per
capita terms. Use the definitions of C(t) and G(t) given above to simplify.
b) Derive the Solow fundamental equation.
c) Find the steady state of capital per capita, and income per capita of the model as a
function of the parameters of the model.
d) How an increase in γ, from γ0 to γ1 on the steady states. Show and explain your result
graphically.
e) Suppose the economy is initially at a steady state with
What happens to the
growth of income per capita after the rise in γ. Explain your answer.
f) Now assume a fraction µ of G(t) is added to the capital stock as public investment.
What is the effect of a rise in µ on steady-state income per capita. Explain your
answer.
2. Consider the standard IS-MP model and do the following:
a) Show and explain why the IS curve is steeper when the sensitivity of investment to
the interest rate falls.
b) Use the IS-MP model to examine how the relative effectiveness of fiscal policy
changes as investment becomes less sensitive to the interest rate. Explain the intuition
of this.
c) Now derive the slope of the Aggregate Demand curve from the IS-MP model.
d) How the slope of Aggregate Demand depends on the sensitivity of investment to the
interest rate. Does it matter for the effectiveness of fiscal policy?
3. Consider an economy that last two periods (1 and 2). The economy has a representative
household with the following preferences,
, where β is a discount
factor. Households are endowed with income (Y1,Y2) and can borrow/save an amount s
during period 1. The representative household faces consumption taxes τ2 on period 2,
and does not pay taxes in period 1. The representative household has the following
budget constraint:
The government has expenditures (G1, G2) in the two periods financed by levying
consumption taxes
in the second period and by rising debt b in the first period. At the
end of time 2 the government budget constraint must be balanced.
a) Solve the household problem and derive first order condition for consumption in both
periods, and derive the Euler equation.
b) State the meaning of Ricardian Equivalence in this economy.
c) Does Ricardian Equivalence hold in this economy? Prove your answer.
Part II: Answer one of the following two questions (25 points)
4. Assume an economy where output is produced with the following technology:
Y  AK  BK  L1 ,   1 ,
where Y is output, and K is capital, L is labor. Population grows at an exogenous rate n. A
constant fraction of output s is saved and invested to increase the capital stock. The evolution of
capital is given by,
K (t )  sY (t )  K (t ) , where  is the depreciation rate.
a) Is the production function neoclassical?
b) Derive the Solow fundamental equation of this model.
c) Using the transitional dynamics of the model show that the model exhibits
endogenous growth. What condition is required?
d) What element in this technology is fundamental to generate endogenous growth?
e) Does the model show convergence?
5. Consider the classical model with perfect information, where a representative producer
1
( pi  p) , where
(consumer) of good i supplies labor (in logs) according to li 
1 
  1 , pi and p are the log of Pi and P respectively.
i. What does the labor supplied by each individual implies for the labor
supply?
ii. Assume that demand for good i is represented by the following log-linear
demand function qi  y   ( pi  p) . Find the equilibrium output for each
producer.
iii. Now assume that information about prices is not perfect. Explain how
labor supplied by each individual changes and what it implies for the labor
supply?
iv. Assume Aggregate Demand is represented in logs by y = m – p. What is
the effect of money in this model. Explain.
v. Assume that the monetary rule is given by
,
where c is the trend and ut is a white noise. Show that unexpected
changes in m can generate a tradeoff inflation-output.