John Hassler

Torsten Persson

March 31, 1995

**EXAM
Macroeconomics I
5 points**

**I Short answers**

Choose 4 out of the following 5. 1 page per question should be enough for your answers. Worth 10 points each.

1. Evaluate the following statement. "A temporarily high government spending, like a war, should be financed by temporarily high taxes."

2. Is the following statement true, false or uncertain? "Humans do not live for ever. The probability of dying implies that the Ricardian Equivalence theorem cannot hold."

3. Is the following statement true, false or uncertain? "The price of a risky asset is a random walk with drift, so its return is unpredictable."

4. Is the following statement true, false or uncertain? "Under full liquidity constraints the marginal propensity to consume out of current income is generally at least as large as under no liquidity constraints."

5. Is the following statement true, false or uncertain? "Fluctuations in labor input in a RBC model, not caused by real wage fluctuations, should be negatively correlated with consumption."

**II Problems**

Choose 1 out of the following 2. Provide a strict formal argument. Worth 25 points.

7. Consider a continuous-time model of a closed economy
without population growth or technical progress. Production per
capita, at date *t*, is given by

7.1

where *k *denotes capital per capita and *A *is a
productivity parameter. Capital depreciates at the rate *d**t*,
where *d**t*
is a convex function of aggregate capital *K**t*:
with *B**K**, B**KK*
>0.

Consumers save in the form of capital; the representative consumer chooses an optimal consumption plan, so as to maximize

where *c *is consumption per capita and *r *is the rate of time preference.

a) What will the representative firm be paying to rent capital from consumers in equilibrium at a competitive capital market, where each firm takes aggregate capital as given?

b) Write down the consumer’s budget constraint and characterize the solution to her intertemporal maximization problem.

c) Consider the full competitive market equilibrium in this
economy; normalize the constant labor force to unity such that *k**t*=*K**t*
at all *t.* Characterize the equilibrium dynamics of *c**t** *and *k**t*,
both algebraically and in a common diagram! Does this economy
converge to a steady state from any initial capital stock *k*0?

d) Is the private market equilibrium socially efficient from
the viewpoint of a social planner that seeks to maximize the
representative consumer’s utility function ? Explain why or
why not, by analyzing the solution to for *c *and *k*
in the social planner’s problem!

8. Consider an economy where the log of per capita consumption follows an AR(1) process with i.i.d. normal innovations,

8.1

where the last line of the previous equation says that the
distribution of *e*_{t+1 }conditional
on information known in *t* equals in distribution a normal
with variance *s*^{2}.^{
}Now assume that all agents are identical and maximize

8.2

a) What is the mean, variance and distribution of and ?

b) Recall that if *x *is normal with mean and variance *s*2 then the
expected value *.
*Use this to show that

8.3

We are now opening markets for a few different assets in this economy. We make sure that the net supply of each asset is zero. Your task is to calculate the prices of these assets.

c) Is the net supply assumption important? Why or why not?

d) Calculate the price of a bond that returns 1 SEK the next
period for sure. Explain in a few words how it depends on *a*, *b, s,* *r*
and *c**t*!

e) Let *pt *be the price calculated under d). Define the
riskless rate of return as -ln*p**t*.*
*What is the time average of the riskless rate of return.
Explain in a few words how it depends on *a*,
*b, s,* *r* and *c**t*!

f) Calculate the price of the following stochastic asset. The period after the asset is bought a dice is thrown (en tärning kastas). The holder of the asset receives the same number of SEK as the number of eyes the dice shows. Explain your results!

g) Calculate the price of a stochastic asset that pays if bought at *t.*
Does this asset give a higher or lower return than the previous
assets? Explain your results!

**III Essay**

Choose 1 out of the following 2. Emphasize discussion rather than formalism. Worth 25 points.

9. *Growth Differences*

Describe the stylized facts regarding differences across
countries and time in the rate of growth in GDP per capita!
Discuss both the methodology and the most important result in the
*empirical *literature that seeks to explain these
differences! What are the strong points and weak points of this
work, in your view?

10.* Asset Pricing Models*

Discuss the empirical success and failures of the standard and consumption based CAPM? Indicate possible explanations to the problems you mention.

A pass will require 60 points (out of 100) and a pass with distinction 80 points.

**Good Luck!**