Labor Market with Monopsony
A company is the sole employer in a small town. The labor supply curve is given by W = 10 + 2L, where W is the wage and L is the number of workers. The marginal revenue product of labor (MRPL) is constant at $50 per worker. The company currently employs 10 workers and pays a wage of $30. A union is considering negotiating a higher wage.
1. Determine the profit-maximizing level of employment and wage for the monopsonist. Show your calculations.
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For a monopsonist, the marginal cost of labor (MCL) is derived from the labor supply curve. Total labor cost = W*L = (10 + 2L)L = 10L + 2L^2. MCL = d(TC)/dL = 10 + 4L. The firm hires where MRPL = MCL: 50 = 10 + 4L => 4L = 40 => L = 10. The wage is determined by the supply curve at L=10: W = 10 + 210 = $30. So the firm maximizes profit by employing 10 workers at $30, which is the current situation.
2. If the union successfully negotiates a wage of $40, what will be the level of employment? Is this outcome efficient? Explain.
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At a wage of $40, the firm will hire workers according to the labor supply curve. Set W = 40 in the supply equation: 40 = 10 + 2L => 2L = 30 => L = 15. So employment will be 15 workers. This outcome is more efficient than the monopsony outcome because it is closer to the competitive equilibrium where MRPL = supply. The competitive equilibrium would be where MRPL = W: 50 = 10 + 2L => 2L = 40 => L = 20, W = $50. At L=15, the marginal revenue product ($50) exceeds the wage ($40), so there is still some monopsonistic exploitation, but less than before. The outcome is not fully efficient because employment is below the competitive level, but it is an improvement.