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 competitive market quantity?

Question

Quizplus · Accepted Answer

To find the competitive market quantity, we need to equate the marginal cost (MC) to the marginal benefit (MB) which is the market price. In a perfectly competitive market, the market price is equal to the marginal revenue (MR), which is equal to the demand curve. MC = 1000 + 2Q_mill + (Q_mill)/5 MR = MB = P = 2000 - 0.01Q^d Setting MC = MR, we get 1000 + 2Q_mill + (Q_mill)/5 = 2000 - 0.01Q^d 2000Q_mill - Q_mill^2/100 - 10000 = 2Q_mill/5 Q_mill = 60000 Therefore, the competitive market quantity is 60,000.

Three Hundred Paper Mills Compete in the Paper Market