Suppose that a firm's only variable input is labor. When the 50 workers are used, the marginal product of labor is 75 and the average product of labor is 50. The total cost of the fixed input is $500 and the wage rate is $80.
1. Suppose 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 forming is $1.25 per unit, are they at an optimum? If not, explain 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.
2. Show that your answer from part (a) holds, looking at the things from the input side as well (that is, using MRP and ARP and w).