A manufacturing firm produces output using a single plant. The relevant cost function is C=500+5Q2. The firm's demand curve is P=600-5Q.
a) Find the level of output at which average cost is minimized. What is the minimum level of average cost? Find the firm's profit maximizing output and price. Find its profit.
b) Suppose the firm has in place a second plant identical to the first. Argue that the firm should divide production equally between the plants. Check that the firm maximizes profit at total output Q* such that MR(Q*)=MC1(Q*/2)=MC2(Q*/2