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Carl the clothier owns a large garment factory on an isolated island. Carls factory is the only source of employment for most of the islanders, and thus Carl acts as a monopsonist. The supply curve for garment workers is given byl = 80w,wherel is the number of workers hired and w is their hourly wage. Assume also that Carls labordemand (marginal revenue product) curve is given byl = 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 garmentworkers. How many workers will Carl now hire, and how much unemployment will there beif the minimum wage is set at $4 per hour?c. Graph your results.d. How does a minimum wage imposed under monopsony differ in results as compared with a minimum wage imposed under perfect competition? (Assume the minimum wage is above themarket-determined wage.)
Solution:- a) L=400-40MVPL MVPL = 10 1/40L MVPL=MRPL=MFCL>AFCL implies MVPL=MEL 10-1/40L = 1/40L L= 200 Supply curve for government workers :- L = 80W 200=80w W=200/80=2.5 b) The government implements a minimum wage law covering all government workers. For Carl, the MEL now equals the minimum wage and in equilibrium the MEL will equal the MRPL. MVPL=MRPL=MEL=Wm i) If the minimum wage is set at $# per hour. MVPL = MEL = Wm = 3 L=400-40MVPL L=400-40(3)=280 L=80W= L=80*3=240 Carls demand = L=280 Supply= L=240 Demand>supply ii) If the minimum wage is set at $3.33 per hour Carls demand:- L=400-40MVPL L=400-40(3.33)…

67 Carls Supply:- L=80W L==80*3.33 L=267 Demand = supply iii) If the minimum wage is set at $4 per hour Carls demand:- L=400-40*4 L=240 Carls Supply:- L=80W L=80*4 L=320 Supply>demand c) d) Under perfect competition, a minimum wage means higher wages but fewer workers employed. Under monopsony, a minimum wage may result in higher wages and more workers employes as shown by some of the cases studied in part b.

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