Question

# Suppose the market demand function is given by Q = 200 - 2p. The monopolist has...

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

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

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