Problem

The Harris-Torero model. (Harris and Tovar, 1970.) Suppose there are two sectors. Jobs in the primary sector pay w_p; jobs in the secondary sector pay w_s. Each worker decides which sector to be in. All workers who choose the secondary sector obtain a job. But there are a fixed number, N_p, of primary sector jobs. These jobs are allocated at random among workers who choose the primary sector. Primary-sector workers who do not get a job are unemployed, and receive an unemployment benefit of b. Workers are risk-neutral, and there is no disutility of working. Thus the expected utility of a primary sector worker is qw_p+(1 - q)b, where q is the probability of a primary sector worker getting a job. Assume that b < w_s < w_p, and that N_p / N‾ < (w_s -b) / w_p - b).

(a) What is equilibrium unemployment as a function of w_p, w_s, N_p, b and the size of the labor force N‾?

(b) How does an increase in N_p affect unemployment? Explain intuitively why, even though unemployment takes the form of workers waiting for primary-sector jobs, increasing the number of these jobs can increase unemployment.

(c) What are the effects of an increase in the level of unemployment benefits?