Problem Set 3 - Labor Demand I 1 Suppose that labor is the...

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Labor Demand - I February 19, 2010 1. Suppose that labor is the only variable input in production and that an additional unit of labor increases total output from 65 to 73 units. If the product sells for $4 per unit in a perfectly competitive market, what is the Marginal Revenue Product (MRP) of this additional worker? Would the MRP be higher or lower than this amount if the firm were selling its product in a non-competitive goods market and had to lower its price to sell all 73 units? 2. What happens to employment in a competitive firm that experiences a technology shock such that at every level of employment its output is 100 units per hour greater than before? 3. Suppose that the hourly wage rate is $10 and the price of each unit of capital is $25. The price of output is constant at $50 per unit. The firm’s production function is f ( E, K ) = EK . Consider the short run problem where the amount of capital is fixed at ¯ K = 1600. (a) How much labor should the firm employ in the short run? (b) How much profit will the firm earn? 4. Table 1 shows the number of units of output that a firm could produce depending on the number of labor units it hires. Suppose that we are measuring labor is labor hours. The firm has a fixed unit of capital and the cost of capital is $10. The firm sells its output in a competitive market at $2 per unit. Assume that the labor market is competitive. Table 1: E 0 1 2 3 4 5 6 7 8 9 10 Q 0 11 27 47 66 83 98 111 122 131 138 (a) Compute the Marginal Revenue Product (MRP) associated with each unit of labor. (b) Compute the Average Revenue Product (ARP) associated with each unit of labor. (c) If the wage rate is $40 per hour how many workers should the firm hire? What is the output produced? What is the profit of the firm? 1
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(d) If the wage rate is $35 per hour how many workers should the firm hire? What is the output produced? What is the profit of the firm?
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