Due February 10 Economics 2010d Spring 2014

Problem Set 2

1. Romer, Advanced Macro (4th ed.), problem 12.2

2. Romer, Advanced Macro (4th ed.), problem 12.3

3. Take the simple RBC model presented in Lecture 3. The budget constraint assumes that people know they cannot invest in capital, since the stock of capital is fixed. But this is not quite right if individuals are atomistic, since each one thinks she can buy as much capital as she wants at the going price. (However, the aggregate capital stock is still fixed at ,K so aggregate investment must always be zero.) a. Modify the budget constraint to allow for purchases of capital as well as riskless

bonds. Let the time-t price of capital relative to output be qt. The owner of a unit of capital gets paid R, where R is the marginal product of capital. Capital needs to be bought one period before any returns are received (one unit of capital purchased at time t yields the owner Rt+1).

b. What is the Euler equation for consumption if foregone consumption is used to purchase capital, which is held for one period? c. Is there a connection between the rate of return on capital, R, and the riskless interest rate r? What is it? d. In equilibrium, is the price of capital relative to output, qt always equal to 1, as in

the standard Ramsey model? Explain why or why not.

Due February 10 Economics 2010d Spring 2014 4. A growing literature in macroeconomics is suggesting that business cycles may be

driven by variations in the expected future level of technology, with no change in the current level of technology. (This hypothesis is appealing, because the expected future level of technology can change many times as new information becomes available, and contractions can occur if optimistic expectations are disappointed, without any actual decline in technology.) This is known as the news shocks hypothesis; the idea is often attributed to Pigou (1927).

Analyze a simple version of this hypothesis using a competitive RBC model where

the capital stock is constant for all time and production takes place with constant returns to scale. Assume that at time t, people in the model economy are told that technology will improve permanently starting at time t+1. However, technology today (Zt) does not change.

A. In your model, what happens to output, Y, consumption, C, and hours worked, L, in

response to this shock? Do these variables in the model commove in the way that they commove over the business cycle in the data?

B. This approach to business cycles has been criticized using the following intuition:

An improvement in future technology with no change in current technology is perceived today as an increase in lifetime wealth (an income effect) with no offsetting substitution effect. In response to such a shock, consumption and hours worked will move in opposite directions, and so this type of model could never explain business cycle facts. Is this critique correct in the simple model you analyzed? Explain why or why not.