Labor Economics 5th Edition by George Borjas

Exercise 15

Consider two identical jobs, but some jobs are located in Ashton while others are located in Benton. Everyone prefers working in Ashton, but the degree of this preference varies across people. In particular, the preference (or reservation price) is distributed uniformly from $0 to $5. Thus, if the Benton wage is $2 more than the Ashton wage, then 40 percent (or two-fifths) of the worker population will choose to work in Benton. Labor supply is perfectly inelastic, but firms compete for labor. There are a total of 25,000 workers to be distributed between the two cities. Demand for labor in both locations is described by the following inverse labor demand functions:
Ashton: w A = 20 - 0.0024 E A.
Benton : w B = 20 - 0.0004 E B.
Solve for the labor market equilibrium by finding the number of workers employed in both cities, the wage paid in both cities, and the equilibrium wage differential.