Suppose the marginal product of labor in the economy is given by MPN = 200 - 0.5 N, while the supply of labor is 100 + 4w
(a) Find the market-clearing real wage rate.
(b) What happens if the government imposes a minimum wage of 40? Is there involuntary unemployment?
(c) What happens if the government imposes a minimum wage of 60? Is there involuntary unemployment?
(a) The market-clearing real wage rate equates the demand and supply of labor. Setting w = MPN = 200 - 0.5 N and solving for N gives N = 400 - 2w, which represents labor demand. Equating labor demand to labor supply gives 400 - 2w = 100 + 4w, or 300 = 6w, or w = 50.
(b) A minimum wage of 40 has no effect, as it is below the market wage, so involuntary unemployment is 0.
(c) A minimum wage of 60 is binding, as it is above the market wage. At w = 60, labor demand is 400 - (2 × 60 ) = 280, while labor supply is 100 + (4 × 60 ) = 340. So unemployment is 60 workers.
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