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Unformatted text preview: EXCERCISES 2: TAXES Here are the solutions to the third exercise. I. A. Optimal (private) outcome. Set price equal to marginal cost. P = MC 120 Q = Q Q = 60 Or the optimal can be found by maximizing total surplus with respect to Q and setting it equal to zero. Total surplus is given by the area under the demand curve above the cost curve, or: TS = P(Q)dQ TC = 120Q-Q 2-Q 2 = 120Q - Q 2 dTS/dQ = 120 2Q = 0 Q = 60 Price is given by 120 Q = 120 60 = 60 Profit or producer surplus is P*Q Cost: PS = 120Q - Q 2 - Q 2 = 120Q 1Q 2 = 120(60) 1(60) 2 = 1800 Consumer surplus is the area under the demand curve, above price, or: CS = P(Q)dQ P*Q = 120Q-Q 2-120Q+Q 2 1 = Q 2 = 1800 Total surplus can be found by plugging Q into the equation above: TS = 120Q - Q 2 = 120(60) (60) 2 = 3600 Table 1 summarizes the answers. B. Unit tax of 40. The unit tax represents an additional cost to production of 40Q, or 40 at the margin. Set price equal to marginal cost, including the tax: P = MC + u 120 Q = Q + 40 Q = 40 P C = 120 Q = 80 P S = MC = Q = 40 TS = 120Q - Q 2 = 3200 CS = Q 2 = 800 PS = P S *Q-C = (40)(40) ()(40 2) = 800 The excess burden is the difference between the total surplus with the tax and the total surplus in the optimal case, or 400....
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- Fall '07