Due February 3 Economics 2010d Spring 2014

Problem Set 1

1. Romer, Advanced Macro (4th ed.), problem 2.10 (skip parts d and f)

2. Romer, Advanced Macro (4th ed.), problem 2.11

3. Romer, Advanced Macro (4th ed.), problem 2.13

4. Suppose a representative consumer maximizes an additively separable utility function over consumption and leisure, as discussed in class. a. Use the first-order conditions to derive an Euler equation for leisure (relating leisure in t and t+1 as a function of wages and real interest rates). b. In the data, real wage changes appear permanent. Given this fact, how would the model of labor supply used here explain transitory changes in hours worked? c. Suppose there are fluctuations in the real interest rate, but not in real wages. Will movements in consumption and labor supply be positively or negatively correlated in response to these real interest rate changes? Explain.

5. The problem of getting labor supply to vary significantly with small changes in real

wages has been addressed by many macroeconomists. Some have suggested durability of leisure as a solution. Suppose the representative consumer maximizes

0

ln

t t t

tC V N

subject to a standard budget constraint. N is effective leisure, as defined below. V is a concave function. Real wages in this economy follow a predictable patternhigh one period, low the next, then high, then low and so on: wt = wH in all even periods and wt = wL in all odd periods. wH and wL are constants, and we know only that wH > wL. Assume that Ct is constant over time.

Due February 3 Economics 2010d Spring 2014

a. Suppose our usual specification: t tN L L , with standard notation. Can you say qualitatively or quantitatively how much labor is supplied in even (odd) periods? What parameters are important for your answer? b. Now suppose

11 12 2 t t tN L L L L . Explain why this specification is called durable leisure. Give an example supporting the idea that the utility from leisure may last more than one period. How much labor will be supplied in each even (odd) period? Does your answer depend on the form of V or the ratio of wH to wL? Explain. c. Does durable leisure help reconcile the micro-macro gap in labor economics (macro labor supply appears elastic, but micro estimates suggest that labor supply is inelastic with respect to the real wage)? Explain why or why not.