### Long-run equilibrium market price-quantity of lumber

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The lumber industry (lumber is wood used in manufacturing) in a city is a perfectly competitive industry. The long-run cost function for a lumber firm is C(q)^2 +1000 where q is a standardized amount of lumber. The market demand in the city is ,000-20*P.

a. Find the long-run equilibrium market price and quantity of lumber. How many firms will be in the market?

b. The government decides to impose a per-unit quantity tax of on the suppliers; if a firm sells one unit they must pay 50 to the government. Find the short-run equilibrium price and quantity after the tax is imposed. What is the profit of each firm? Note: to keep things simple, assume an individual firm's long-run marginal cost is the same as their short-run marginal cost.

c. Now find the new long-run equilibrium price and quantity with the tax. How many lumber firms will be in the market? Draw a diagram comparing the equilibrium price and quantity in the three situations: 1) before the tax 2) the short-run after the tax 3) the long-run after the tax.

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