Assume that a firm's only variable input is labor. When 50 workers are used, the average product of labor is 50 and the marginal product of labor is 75. The wage rate is $80 and the total cost of the fixed input is $500.
a) Assume the firm has typical u-shaped cost functions. If the firm is operating in a competitive industry and the market price of the good they’re producing is $1.25 per unit, are they at an optimum? If not, what should the firm do? If the answer is indeterminate, explain why. If you back up your explanation with a graph, be sure to label everything clearly and completely.
b) Demonstrate that your answer from part (a) holds, looking at things from the input side as well (that is, using MRP and ARP and w).