University of California, Davis
Date: June 30, 2008
Department of Economics
Time: 3 hours
Macroeconomics
Reading Time: 20 minutes
PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE
Directions: Answer all questions.
SHORT QUESTIONS
1. Consider two closed economies that have the same real interest rate.
If con
sumption growth is higher and less volatile in Economy A relative to Economy
B, what implications does this have for preferences in the two economies?
ANSWER: A starting point for this question is the KeynesRamsey condition
describing the optimal consumption path in the CassKoopmans model (no
uncertainty; assume no population growth)
r
=
°
+
±²
c
where
°
is agent°s subjective discount factor (
³
°
1
1+
°
)
,
±
is the elasticity of
agents° marginal utility, and
²
c
is the average growth rate of consumption.
Assume that
°
is the same in both economies. Given that interest rates are the
same in both economies, it must be the case that
±
is smaller in Economy A:
given the higher growth in Economy A, this should imply that interest rates
are higher since present consumption is scarce relative to future consumption.
But the smaller elasticity of
MU
in Economy A will counteract this e/ect  i.e.
future growth does not lower
MU
as much in Economy A. If uncertainty is added
to this economy (BrockMirman model), then the optimal consumption path
will be characterized (obtained by either assuming a log normal distribution for
consumption growth (see Ljungvist and Sargent handout) or by taking a second
order Taylor series expansion of the Euler equation associated with bonds (see
Romer, p. 369):
r
=
°
+
±²
c
±
±
(
±
+ 1)
2
´
c
where
´
c
is the standard deviation of consumption growth.
Lower volatility
will, ceteris paribus, cause interest rates to be higher (the certainty equivalence
of future consumption increases). Again, a lower value of
±
(risk aversion) is
needed to keep interest rates the same in both economies.
2. One of the stylized facts of growth is a growing wage rate and a (relatively)
constant labor supply. What restrictions does this place on agents°preferences?
1
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ANSWER: Agents°optimization implies:
U
l
(
c;
1
±
h
)
U
c
(
c;
1
±
h
)
=
w
In a balanced growth path, consumption and the real wage grow at the rate
of technological progress.
If preferences are separable, then a constant labor
(
h
)
implies the numerator will be constant and that
U
(
c
) = ln
c:
If preferences
are not separable, then the elasticity of the
MU
of leisure with respect to
consumption must balance the elasticity of the
MU
of consumption with respect
to consumption.
3. In the Solow model, what happens when there is a permanent increase in the
savings rate?
Describe both the transition and steadystate e/ects.
What
economic forces are at work?
ANSWER: There is a permanent increase in the level in growth of output per
worker and a transitory increase in its growth rate. But because of diminishing
marginal products, there is no permanent increase in growth.
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 Winter '06
 PONTUSRENDAHL
 Economics, Macroeconomics, Interest Rates, certainty equivalence

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