The Total and Marginal Cost Functions for a Typical Soft

question 53

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?

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Definitions:

Required Reserves

The minimum amount of funds that a bank must hold in reserve against deposit liabilities, as mandated by central banking authorities.

Reserve Bank

A central banking institution responsible for overseeing the monetary policy, issuing currency, and regulating the banking system of a country.

Required Reserve Ratio

The fraction of deposits that a bank is required by regulation to hold in reserve and not lend out, aiming to ensure bank liquidity and stability.

Money Supply

The total amount of monetary assets available in an economy at any specific time, including cash, coins, and balances held in checking and savings accounts.