Consider a monopolist with the (inverse) demand function: Pb = 120 - 5 Qb. Given an...

Consider a monopolist with the (inverse) demand function: Pb = 120 - 5 Qb. Given an increasing marginal cost: mc = 11 + 3 Q, how much CS do consumers lose because of the monopoly ? (Assume fixed costs = 10

Expert Solution

the firm produces at MR=MC

MR=120-10Q ....... An MR curve is double sloped than an inverse linear demand curve
MC=11+3Q
equating both
120-10Q=11+3Q
13Q=109
Q=8.38461538
P=120-5*8.38461538
P=78.0769231
MC=11+3*8.38461538
MC=36.1538461
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An efficient output is at MC=P
equating both equations
11+3Q=120-5Q
8Q=109
Q=109/8
Q=13.625
P=MC=11+3*13.625=51.875

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Reduction in the consumer surplus because of monopoly is the area between monopoly price and efficient output price. And also between quantities and below the demand curve and above perfect competitive price.
Loss in consumer surplus =0.5*(Monopoly price -perfect competition price)*(efficient output -monopoly output)
=0.5*(78.0769231-51.875)*(13.625-8.38461538)
=68.6540774
the loss in consumer surplus is $68.65

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Rahul Sunny answered 1 year ago

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