Two hundred paper mills compete in the paper market. The total cost of productio

Question

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 = 500Qmill+ (Qmill)2where Qmillindicates the mills annual production in thousands of tons. The marginal cost of production is MC = 500 + 2Qmill. The external cost of a mill’s production (in dollars) is given by the formula EC = 40Qmill+ (Qmill)2and the marginal external cost of production is MEC = 40+ 2Qmill. 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.

Explanation / Answer

Competetive equillibrium is where MR = MC. In order to calculate MR , first convert the demand function to inverse demand function and multiply the same with Q. After doing this equate MR to MC, You will get answers as Q= 495 and P = 1495. In order to calculate the efficient quantity, MR should be equated to MEC +MC,. This is because external costs must also be included to arrive at the socially efficient answer. Hence solving for the above equation you get Q= 313 and P = 1496.87

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