Question

Consider a single-price monopolist. The monopolist's total cost function is given by TC=2Q². The demand curve for the monopolist's outputs is given by Q=300-0.25P. The market will have a deadweight loss of $____.

Answer 1

converting the demand curve to the inverse demand curve to find MR

Q=300-0.25P

0.25P=300-Q

P=1200-4Q

MR=1200-8Q ...... MR curves double sloped than an inverse linear demand curve

MC=change in total cost =first differentiation of cost function=dTC/dQ=4Q

the firm produces at MR=MC

1200-8Q=4Q

12Q=1200

Q=100

P=1200-4*100=800

MC=4*Q=4*100=400

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Social optimum is at MC=P

4Q=1200-4Q

8Q=1200

Q=150

P=4*150=600

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DWL=0.5*(P monopoly- MC monopoly)*change in Q

=0.5*(800-400)*(150-100)

=10000

The DWL is $10000