Three hundred paper mills compete in the paper market.The total cost of production (in dollars)for each mill is given by the formula TC = 1,000Q_mill + (Q_mill)²,where Q_mill indicates the mills annual production in thousands of tons.The marginal external cost of a mill's production (in dollars)is given by the formula MEC = 200 + 2Q_mill.Finally,annual market demand (in thousands of tons)is given by the formula Q^d = 200,000 - 100P.What is the efficient quantity?

Question

Quizplus · Accepted Answer

The efficient quantity is found where the marginal social cost (MSC) equals the marginal benefit (demand). MSC is the sum of marginal cost (MC) and marginal external cost (MEC). MC is derived from TC as MC = d(TC)/dQ = 1,000 + 2Q. Thus, MSC = MC + MEC = 1,000 + 2Q + 200 + 2Q = 1,200 + 4Q. Setting MSC equal to the price from the demand curve, P = (200,000 - Q^d)/100, and solving for Q gives the efficient quantity.

Three Hundred Paper Mills Compete in the Paper Market