he cost functions of a competitive firm are: TC = 40 + 2.5Q^2 where TC is total cost and marginal cost and q is the firm's total output. The marginal cost function is MC = 5Q. There are currently 200 identical firms in the industry. (NOTE: All firms produce exactly the same product.) The demand function is P = 1600/Q, where P is the price per unit and Q is the aggregate quantity demanded.
a. Find the market equilibrium price and quantity. Explain.
b. Calculate the profit of a firm at the point of equilibrium. Is this longrun equilibrium? Explain.
c. A new regulation requires each firm to pay an annual license fee of $22.50. Find the market equilibrium price and quantity after the implementation of tax. (In your answer distinguish between the short-run and long-run equilibrium.) Explain.
d. Suppose that instead of an annual fee, the government imposes a tax on the consumption of this product. The tax is $t per unit. Show graphically the market equilibrium price and quantity after the implementation of the tax. Explain. (In your answer distinguish between the short-run and long-run equilibrium.)