The Total and Marginal Cost Functions for a Typical Soft

Essay

The total and marginal cost functions for a typical soft coal producer are:
TC = 75,000 + 0.1Q² and MC = 0.2Q
where Q is measured in railroad cars per year. The industry consists of 55 identical producers. The market demand curve is:
Q_D = 140,000 - 425P,
where P is the price per carload. The market can be regarded as competitive.
a. Calculate the short run equilibrium price and quantity in the market. Calculate the quantity that each firm would produce. Calculate producer surplus, consumer surplus, and total surplus at the equilibrium values. Calculate the firm's profit (or loss).
b. The Federal government is considering the imposition of a $15 per carload tax on soft coal. Calculate the short-run equilibrium price and quantity that would exist under the tax. What portion of the tax would be paid by producers and what portion by consumers? Calculate the producer and consumer surplus under the tax and analyze the efficiency consequences of the tax. Calculate the firm's profit (or loss) under the tax. Could the tax be justified despite its efficiency implications?