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Created 8/24/1998
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ECONOMICS 202B

TTh 12:30-2:00 Evans 60
(Sections W 10-12 Evans 6, W 12-2 Evans 2)

Problem Set #1

Due 9/3/98


1. Shapiro-Stiglitz (Romer, 10.3). Consider the version of the Shapiro-Stiglitz model that David Romer presents in section 10.4 of his Advanced Macroeconomics.

(a) What happens to the equilibrium level of unemployment if workers become less "patient"--if their time discount rate rises? What happens to the equilibrium level of the wage?

(b) What happens to the equilibrium level of unemployment and to the equilibrium real wage if the job destruction rate b declines?

(c) What happens to the equilibrium level of unemployment and to the equilibrium real wage if the labor force grows?

d) What happens to the equilibrium level of unemployment and to the equilibrium real wage if the economy suddenly becomes twice as productive--if the amount of output produced by each input combination suddenly doubles?


2. Fair Wage (George Akerlof and Janet Yellen (1990)). Consider a representative firm in an efficiency wage model with profits given by:

F(eL) - wL

with w being the wage, L being the number of workers hired, and with the level of effort e satisfying:

e = w/w* if the actual wage w is less than or equal to some w*

e = 1 if the actual wage is greater than or equal to the same w*

Akerlof and Yellen think of w* as what workers consider to be the fair wage--and if they aren't paid what they regard as the fair wage, they reduce their effort. Suppose that w* depends on the state of the economy:

w* = w(avg) + a - bu

where a and b are parameters, u is the unemployment rate, and w(avg) is the average wage paid in the economy.

(a) Suppose that the representative firm takes w(avg) and u as given. What wage does the representative firm choose if it can choose w freely?

(b) Suppose that there are N such firms and L* workers who are willing to work for any positive wage. Under what conditions will equilibrium generate positive unemployment?

(c) Suppose that there are N such firms and L* workers who are willing to work for any positive wage. Under what conditions will the equilibrium generate full employment?


3. Unemployment in the City (John Harris and Michael Todaro (1970)). Suppose that there are two sectors: a city and a countryside. Jobs in the city pay U (urban); jobs in the countryside pay R (rural). Each workers gets to choose whether to stay in the countryside or move to the city: all workers who stay in the countryside get jobs. But employment opportunities in the city are limited: a fixed number NU of urban jobs are allocated at random among those workers who choose to move to the city.

Workers are risk neutral, and there is no disutility of working. Thus the expected utility of moving to the city is the urban wage U times the probability of getting an urban job.

(a) What is the equilibrium level of unemployment as a function of the parameters of the model and the size of the labor force?

(b) How does an increase in the number of urban jobs NU affect the level of unemployment? Why?

(c) Suppose that the unemployed living in the city receive an unemployment benefit of B. What happens to the level of unemployment as B changes?


4. Search. Suppose that there are a large number of firms in the economy, and that the wages they offer are uniformly distributed between two levels L and U. A worker can search for a job by spending a cost S (for search) and thus learning the wage level associated with one particular open job.

After learning about the wage level, the worker can (i) take the job, (ii) take another--earlier--job that he or she had already learned about, or (iii) spend another amount S and sample yet another job. The worker accepts or rejects jobs in order to maximize the expected value of w - nS, where w is the wage in the job that the worker finally accepts and n is the total number of jobs sampled.

(a) Under what conditions on the wage of a newly-sampled job will a worker accept the job?

(b) Would a worker ever go back and accept a previously-sampled job? Why (not)?


5. Efficiency of Search Equilibrium (Romer, 10.17). Consider the search model that David Romer presents in section 10.8 of his Advanced Macroeconomics. Suppose, for simplicity, that the interest rate is zero and that the representative firm is owned by a representative household to which belongs a representative worker--so that social welfare is simply the flow of profits per unit of time plus utility per unit of time: AE - (F+V)C. Letting N denote the total number of jobs, welfare is:

(*) W(N) = AE(N) - NC,

where E(N) gives equilibrium employment as a function of N.

(a) Use the matching function (10.68) and the steady-state condition (10.69) to derive the impact of a marginal change in the number of jobs N on the level of employment E(N).

(b) Substitute back into (*) to find how a marginal change in the number of jobs affects social welfare W(N).

(c) Under what circumstances will increasing the equilibrium number of jobs increase social welfare? Under what circumstances will increasing the equilibrium number of jobs decrease social welfare?


Professor of Economics J. Bradford DeLong, 601 Evans
University of California at Berkeley; Berkeley, CA 94720-3880
(510) 643-4027 phone (510) 642-6615 fax
delong@econ.berkeley.edu
http://www.j-bradford-delong.net/

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