Two hundred paper mills compete in the paper market. The total cost of production (in dollars) for each mill is given by the formula TC=500Q^mill + (Q^mill)^2 where Q^mill indicates the mill's annual production in thousands of tons. The marginal cost of production is MC=500 + 2Q^mill. The external cost of a mill's production (in dollars) is given by the formula EC=40Q^mill + (Q^mill)^2 and the marginal external cost of production is MEC=40+2Q^mill. Finally, annual market demand (in thousands of tons) is given by the formula Qd=150,000 - 100P where P is the price of paper per ton. Using algebra, find the competitive equilibrium price and quantity, as well as the efficient quantity. Calculate the magnitude of the deadweight loss resulting from the externality. Illustrate your solution with graphs.
Two hundred paper mills compete in the paper market. The total cost of production (in dollars) for each mill is given by the formula TC=500Q^mill + (Q^mill)^2 where Q^mill indicates the mill's annual production in thousands of tons. The marginal cost of production is MC=500 + 2Q^mill. The external cost of a mill's production (in dollars) is given by the formula EC=40Q^mill + (Q^mill)^2 and the marginal external cost of production is MEC=40+2Q^mill. Finally, annual market demand (in thousands of tons) is given by the formula Qd=150,000 - 100P where P is the price of paper per ton. Using algebra, find the competitive equilibrium price and quantity, as well as the efficient quantity. Calculate the magnitude of the deadweight loss resulting from the externality. Illustrate your solution with graphs.
