Question

Suppose the market demand function is given by Q = 200 - 2p. The monopolist has the following cost function TC = 100 + 0.5Q2 (MC = 0.5 + Q) (a) find profit maximizing p and Q for the monopolist (b) suppose regulation was implemented and the regulator "coerced" the monopolist to behave as "a competitive firm would(e.g., p=MC)". Find this p and Q. (c) calculate the size of the (dead weight) welfare loss triangle; (d) how much of this (answer to (d) is from buyers and how much is from the seller? (d) calculate the size of the transfer from buyers to seller

Answer 1

A) Take Inverse demand as 2P = 200 - Q or P = 100 - 0.5Q. MR = 100 - Q. MC = Q. This gives MR = MC or 100 - Q = Q or Q = 50. Price = 100 - 50*0.5 = $75.

b) Now suppose regulation was implemented and the regulator "coerced" the monopolist to behave as "a competitive firm which implies it uses the rule P = MC or 100 - 0.5Q = Q. This gives Q = 66.67 and P = 66.67.

c) DWL = 0.5*(75 - 50)*(66.67 - 50) = 208.375

d) Buyer's burden of DWL = 0.5*(75 - 66.67)*(66.67 - 50) = 69.43

Sellers burden of DWL = 0.5*(66.67 - 50)*(66.67 - 50) = 138.95