Question

2. A chair manufacturer hires its assembly-line labor for $20 an hour and calculates that the rental cost of its machinery is $30 per hour. Suppose that a chair can be produced using 4 hours of labor or machinery in any combination. a. What is the long-run total cost curve? b. What is the short-run total cost curve if capital is fixed at K?

Answer 1

In the long run the firm will be using the cost minimising choice of input. Since one chair can be produced by 4 hours of labour or 4 hours of capital in any combination, it is cheaper to use labour because its wage rate is less than the rental price of machinery. Hence the long-run total cost will be C = 20L where Q = 0.25L. this makes the long run total cost C = 20*4Q or C = 80Q

In the short run however the capital is fixed at K so the cost function will be C = 20L + 30K. The production function is Q = 0.25L + 0.25K where capital is fixed at K. Hence L = 4(Q - 0.25K) or L = 4Q - K. The cost function now becomes C = 80Q + 10K