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Consider the following monopoly with P = 30.5 -2.75 Q and the marginal cost curve is...

Consider the following monopoly with P = 30.5 -2.75 Q and the marginal cost curve is MC=4.5Q; a.Calculate the consumer surplus under the monopoly. b. Calculate the producer surplus under the monopoly. c. Calculate the deadweight loss.

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Answer #1

Demand is given by P = 30.5 – 2.75Q. This implies MR = 30.5 – 5.5Q. Marginal cost MC = 4.5Q. Hence we have

MR = MC or 30.5 – 5.5Q = 4.5Q. This gives Q = 30.5/10 = 3.05 units and P = 30.5 – 2.75*3.05 = 22.1125

CS = 0.5*(30.50 - 22.1125) = 4.19375

PS = 0.5*(13.725 - 0)*3.05 + (22.1125 - 13.725)*3.05 = 46.5125

DWL = 0.5*(22.1125 - 13.725)*3.05 = 12.79

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