Macroeconomics Qualifying Exam-302 Module
Claremont Graduate University
January 2013
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 (1-3) (75 points). Each question is worth
25 points).
1. Consider a standard Solow model without population growth described by the
following equations:
Y = (1 − τ ) K α ( AL)1−α , 0 < α < 1
.
.
A
K = sY , = g
A
.
τ is a government tax on output, and all tax revenue is spent abroad and does
not contribute to either output or capital stock in the economy.
a) Define capital per effective worker as k =
K
, and derive an expression for its
AL
.
evolution overtime: k .
b) Derive the steady state for capital per effective worker kss and output per
Y
effective worker yss, where y =
.
AL
c) What would be the effect of an increase in the tax rate on actual investment in
the economy and the steady state of output per effective worker ?
d) Now assume that the tax on output also hurts individual’s incentives to invent
new technologies. Specifically assume that the growth rate of technology, g,
1
is given by g = b(1 − τ ) α where b>0. What is the new steady state level of
output per effective worker? What is the effect of an increase in the tax on yss
now?
e) Explain in words the result you got in d).
2. Assume a closed economy where firms produce output using only labor, i.e.,
Y= F(L) under the assumptions of diminishing and positive marginal product
of labor. Households live forever and derive utility from consumption and
holding real money balances, and disutility from working. The representative
household’s utility function is given by
𝑈=
∞
!
!!! 𝛽
𝑈 𝐶! + Γ
!!
!!
− 𝑉(𝐿! ) ,
0<β<1, with 𝑈 ′ (.) >0, 𝑈 ′′ . < 0,
Γ′ . > 0, Γ′′ . < 0, 𝑉 ′ > 0, 𝑉 ′′ > 0. U and Γ have relative-risk-aversion forms,
𝑈 𝐶! =
!!!!!
!!!
,
θ > 0, and
Γ
!!
!!
=
!
( ! )!!!
!!
!!!
, v > 0.
There are two assets: Money which pays no interest and Bonds which pay an
interest rate of 𝑖! . Households have a labor income WtLt per period, its
consumption expenditures are PtCt., W and P represent nominal wages and the
price level respectively. At is the household’s wealth at the start of period t.
a) Write down an equation describing the evolution of wealth. (3 points)
b) Set up the maximization problem of the household. (3 points)
c) Using First Order Condition find, graph, and interpret the IS and LM curves.
(10 points)
d) Show and explain the effect of an increase in nominal Money supply.(4
points)
e) Sketch the derivation of Aggregate Demand.
3 . Consider the classical model with perfect information, where a representative
1
producer (consumer) of good i supplies labor (in logs) according to li =
( pi − p ) ,
1− γ
where γ  1, pi and p are the log of Pi and P respectively.
a) What does the labor supplied by each individual implies for the
labor supply?
b) Assume that demand for good i is represented by the following loglinear demand function qi = y − η ( pi − p) . Find the equilibrium
output for each producer.
c) 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?
d) Assume Aggregate Demand is represented in logs by y = m – p.
What is the effect of money in this model. Explain.
e) Assume that the monetary rule is given by 𝑚! = 𝑚!!! + 𝑐 + 𝑢! ,
where c is the trend and ut is a white noise. Show that
unexpected changes in m can generate a tradeoff inflation-output.
Part II: Answer one question (25 points).
.
4. Assume an economy with government that produces with the following
technology, Yt = AK tα Gt1−α . A is a constant, and G represents government spending
which is assumed to be desirable. To finance G the government collect income tax
from individuals which are taxed at a rate τ. Tax revenue is proportional to income.
Capital accumulates according to K (t ) = sY (t ) − δK (t ) . Assume exogenous population
L
growth, which is given by
=n .
L
Yd
G
and y d ≡
, where Yd is
L
L
disposable income do the necessary transformations to write
down the capital accumulation equation in per-capita terms.
Assume that government spending is equal to tax collection in
any period and write down the government budget constraint in
per-capita terms.
Using what you did in b) find and expression for economic growth
and briefly explain your result.
Show that y, c, g, and Y grow at a constant rate.
What is effect of taxes on economic growth? Provide a brief
explanation.
Find the tax rate that maximizes economic growth.
a) Using the following definitions, g ≡
b)
c)
d)
e)
f)
5. Assume the simple model of efficiency wages,
Y = F (e( w), L) , F ' (.) > 0 , F '' (.)  0
e = e(w) , e ' (.) > 0
L=L
a) Assuming profit-maximizing firms derive the optimality condition for the
typical firm.
b) Explain the condition you derived in a)
c) What will be the effect of a recession on the efficiency wage and
unemployment? Explain your result.
d) What will be the effect on unemployment and efficiency wages of an
increase in the labor force?
e) What would be the effect of economic growth on the efficiency wage and
unemployment? Explain your result.