Carl the clothier owns a large garment factory on an isolated island. Carl’s fac

Question

Carl the clothier owns a large garment factory on an isolated island. Carl’s factory is the only source of employment for most of the islanders, and this Carl acts as a monopsonist. The supply curve for garment workers is given by:
L=80w
Where L is the number of workers hired and w is their hourly wage. Assume also that Carl’s labor demand (marginal revenue product) curve is given by:
L=400-40MRPL
a. How many workers will Carl hire to maximize his profits and what wage will he pay?
b. Assume now that the government implements a minimum wage law covering all garment workers. How many workers will Carl now hire and how much unemployment will there be if the minimum wage is set at $4 per hour?
c. How does a minimum wage imposed under monopsony differ in results as compared with a minimum wage imposed under perfect competition (assuming the minimum wage is above the market-determined wage)?

Explanation / Answer

a. L = 80w Expressing total wage as a function of L , we have, wL = L^2/80 Marginal Expense= ME = dwL/dL = 2L/80 = L/40 now, L=400-40MRPL L = 400 - 40 x L/40 L = 400 - L 2L = 400 L = 200 Number of employees = L = 200 wages = W = 200/80 = 2.5 dollars b. now, w = 4 we have, now 500 = 4 x L L = 125 workers Unemployment = 200 - 125 = 75 c. a minimum wage imposed under monopsony is lower as compared with a minimum wage imposed under perfect competition

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