John Hassler

Kjetil Storesletten

Åsa Johansson

March 21, 1997

**EXAM
Macroeconomics I
5 points**

As usual the exam consists of three parts, I Short Questions,
II Problem and III Essay. Choose 5 questions from part I, one
from part II and one from part III. A pass will require 60 points
(out of 100) and a pass with distinction 80 points. Make sure you
spend your time wisely. One of us will come down after 90
minutes, it is advisable that you read through the exam before
that.**I Short answers**

Choose 5 out of the following 6. 1 page per question should be more than enough for your answers. Worth 10 points each.

- Evaluate the following statement: "A temporarily high government spending, like a war, should be financed by temporarily high taxes."
- Evaluate the following statement: "Humans do not live for ever. The probability of dying implies that the Ricardian Equivalence theorem cannot hold."
- Is the following statement true, false or uncertain? "If an individual’s savings behavior is unaffected by risk one knows he is risk-neutral."
- In a standard Solow model, let
*Y=K**a**N*1-a with a =0.5. Let population growth rate be 0.02, the savings rate = 0.10 and depreciation 0.10. Compute the steady state consumption per capita. - The standard Ramsey model predicts convergence; production and consumption growth is higher in countries with low initial capital stocks. What would happen with that prediction if we considered a small open economy, with free flows of capital?
- Is the following statement true, false or uncertain? If the agent’s subjective discount rate is positive, then the steady state capital stock in a Ramsey model is always lower than the Golden Rule capital stock.

**II Problem**

Do one of the following two problems (choose 8 or 9). Provide a strict formal argument. Worth 25 points

7.* Taxation in the Ramsey model*

Consider n representative individual who solves

1

where *U *is a CARA type utility function, *f *is a
standard concave production function, *K *is the capital
stock, *c *is consumption and *T *is a tax.

- Set up the current value Hamiltonian with its necessary conditions for optimality.
- Express the optimality conditions and the transition
equation for
*K*as a system of two differential equations in*K*and*c.*(Hint; Take time derivatives of the condition for the maximum of the Hamiltonian). Present your results as a phase diagram in*K*and*C.*Make sure you indicate movements in the phase diagram in all areas and any potential saddle path. - What are the effects of an unexpected permanent increase in the tax rate. Indicate transitions and the long run effect in the phase diagram. Describe in words what is happening and provide intuitive economic explanations.
- Now consider an unexpected temporary increase in the tax
rate, between, say, time
*t*and*T.*Indicate transitions and the long run effect in the phase diagram. Describe in words what is happening and provide intuitive economic explanations. - Lastly, assume that at
*t*it is announced that at*T*the tax rate will permanently be raised at*T >t.*Describe in words what is happening and provide intuitive economic explanations.

8. *Intertemporal substitution of labor*

Assume that

- The agents have preferences over leisure
*l**t*and consumption*c**t*and maximize where*u*(.) is concave and increasing. - Markets are complete.
- Labor input is indivisible, i.e. one can work
*h*0 hours or not at all (so leisure is 1-*h*0 or 1, say).

- Show that aggregation holds in this economy in the sense that, by introducing a particular set of assets (lotteries), the aggregate outcomes could have been generated by a representative consumer (with preferences not necessarily the same as those of the underlying agents, see (b) below).
- Show that the preferences of the representative agent are linear in aggregate labor input, regardless of the concavity of u(.).
- What does the findings in (b) teach us about the willingness to substitute leisure across time for the representative agent versus the individuals in the economy? Explain why this can to some extent resolve the criticism levied against RBC theory.

**III Essay**

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

*9. Asset Pricing Models*

The standard and consumption based CAPM are two variants of assets pricing models? How do they differ in their assumptions and implications? Describe some empirical tests of the two models and discuss their relative performance. Provide some hypothetical explanations for the empirical findings.

10. *Real Business Cycle Models*

Discuss the criticisms against Real Business Cycle models as a theory for real-world fluctuations. Assess how reasonable the assumptions underlying the theory is and indicate why or why not a theory that relies on so strong assumptions can be useful. Emphasize what type of questions the simple versions of RBC theory we have seen in class can and cannot be used to address.

**Good Luck!**