Macroeconomic Qualifying Exam-302 Module
Claremont Graduate University
May, 2006
Lamar
I. Do question 1. (30 points)
1. Consider the Solow model in continuous time. Assume exogenous laboraugmenting technological progress and exogenous population growth, which are
A&
L&
= g , and
= n respectively. Production takes place through a
given by,
A
L
1−α
Cobb-Douglas production function Y (t ) = K (t ) α [ A(t ) L(t )] , where Y(t) is
output, and K(t) is capital. 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 ) − δK (t ) , where δ is the depreciation rate.
~
a) Transform the Solow model defining a new variable k (t ) , so that the model has a
steady state. Show all the necessary steps to obtain the transformed Solow
equation.
~
~
b) Calculate the steady-state capital k * and steady-state investment c * for the
transformed model. What is the balanced growth rate for aggregate capital K(t)?
c) What is the impact of an increase in g on the transitional dynamics of K(t)? Draw
the time path for K(t) from the old balanced growth path glow to the new one ghigh
on a graph with time in the horizontal axis.
d) Now assume there is no population growth, that is, n = 0. Write the transformed
Solow growth equation in terms of the capital-technology ratio.
~*
e) Derive the golden rule level of capital k GR
~*
f) Interpret graphically k GR on the Solow diagram.
~*
~
g) When k GR and k * are equal?
h) Why would anybody be interested in the golden-rule level of capital?
II. Do either question 2 or question 3. (30 points)
2.
a) Describe the initial version of the Phillips curve and its role in traditional
Keynesian economics.
b) Explain the Friedman-Phelps critique to the initial version of the Phillips curve
and the Expectations-Augmented Phillips curve.
c) Contrast the economic policy implications under the traditional Phillips curve and
the Expectations Augmented Phillips curve.
3. Derive and explain the policy ineffectiveness proposition using a model with
rational expectations, imperfect information, and clearing markets.
III. Do all problems in this section. (40 points)
4. Given the standard closed-economy IS-LM model,
Y=E(Y,i-πe,G,T),
(M/P) = L(i,Y),
EY >0, Ei-πe < 0, EG = 1, ET < 0
Li < 0, LY > 0
a) Graphically analyze the effects of a decrease in expected inflation πe, on Y, i,
and ( i-πe). Please explain your answer.
b) Formalize your answer. Find the signs of the corresponding derivatives.
5. Assume the Fischer model. We have the following expression for income at time t,
φ
1
y t = mt − [
Et −1 mt +
E t − 2 mt ] ,
1+φ
1+φ
Where mt represents money supply at time t, and Et-I is the expectations operator.
a) Interpret the equation for yt.
b) Assume that mt = mt* + vt
Where mt* is the money supply controlled by the monetary authority, and vt a
velocity term.
Assume it takes the monetary authority one period to set the money supply, that
is, mt* is based only on information available at time t-1. Velocity is given by,
vt=K + et, where K is a constant, and et is a random term with mean zero. Can
systematic monetary policy have effects on output? Explain your answer.
c) Does keeping mt* constant (by the monetary authority) eliminates the instability
in this economy?