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A firms has the following weekly production function: Q = 20KL - 0.025KL2. Suppose the firm is in the short-run with K fixed at 20.

a. What is the equation for marginal product? Explain whether the production function is consistent with the Law of Diminishing Returns. (10)

b. Find the maximum weekly output the firm can produce in a week. (10)

c. If the firm pays workers $300 per week, i.e., MCL = 300), and its product sells in a competitive market for $15 per unit, find the optimal number of workers to hire. (Assume that material costs are $5 per unit.) (10)

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Irving Heathcote
Irving HeathcoteLv2
30 Sep 2019

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Each employer faces competitive weekly wages of $1,600 for blacks and $2,400 for whites. Suppose employers undervalue the efforts/skills of blacks in the production process. In particular, every firm is associated with a discrimination coefficient d, (0,1), such that, although a firm's actual production function is q=10(Eb+Ew), the firm manager acts as if its production function is q=10(1-d)Eb+10Ew. Every firm sells its output at a constant price of $280 per unit up to a weekly total of 150 units of output. No firm can sell more than 150 units of output without reducing its price to $0.

a) Describe the employment decision, output level and profits made by firms for which d = 0.25 and d = 0.75 respectively.

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2.What is the equilibrium condition for finding the optimal number of workers a perfectly competitive firm will hire? a. In the short-run. b. In the long-run.

3.A firm faces a perfectly elastic demand for its output for $6 per unit of output and each hour of labor produces five units of output. For L number of workers hired each hour and w hourly wage rate, the firm faces an upward-sloped labor supply curve of L = 20w - 120 and the firms face an upward-sloped marginal cost of labor curve is given as MC = 6 + 0.1L. How many workers should the firm hire each hour to maximize profits? What wage will the firm pay?

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