Question

1. Consider a steel firm that faces a convex isoquant production function where the inputs are labor and capital. The production function yields constant returns to scale. The firm is currently at a cost-minimizing combination of labor and capital for the desired level of output. Suppose the capital used in the production process emits low amounts of polluted wastewater into a nearby river. In order to promote the use of the environmentally friendly capital the government provides a unit subsidy on the use of each unit of capital used by the firm.

a. Explain and graphically illustrate the impact of the unit subsidy on the firm’s cost minimizing decision. Explain in economic terms how the firm adjusts its production process given the necessary conditions.

b. As a result of the subsidy, what happens to the expansion path and the long run average costs? Graph the general relationships. Explain in the context of the necessary conditions and how costs are determined by the cost minimizing decisions of the firm.

2. Consider a firm that faces a Cobb-Douglas production function: q = 2L.5K.5 where L is labor hours used by the production process and K is machine hours used. The wage is $360 per labor hour and the price of capital per machine hour is $40.

a. Find the cost minimizing combination of labor hours and machine hours for a desired level of output of 7200. Show how you arrived at your answer. Calculate the total cost using this combination.

b. Consider that the firm desires to increase output to 10900 but holds the level of machine hours constant at the amount you found in part a. What would be the total cost of producing this level of output?

c. Given your answer to parts a and b and given that the firm desires to increase its scale of operations to 10900, in terms of total costs, what should the firm do? Show numerical evidence of your answer in terms of average costs. Explain why the solution you propose yields lower total costs. Graphically illustrate the general result.

Answer 1

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