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A firm with market power faces the demand curve Q = 400 – P/4 and a...

A firm with market power faces the demand curve Q = 400 – P/4 and a marginal cost of MC = 2Q. Calculate the area of the deadweight loss triangle.

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Answer #1

Answer
the firm produces at MR=MC
the inverse demand curve is
Q=400-P/4
Q+P/4=400
P/4=400-Q
P=1600-4Q
MR=1600-8Q ....... the MR curve is double sloped than the demand curve
MC=2Q
equating both
1600-8Q=2Q
10Q=1600
Q=160
P=1600-4*160=960
MC=2*160=320
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an efficient quantity is produced at MC=P
1600-4Q=2Q
6Q=1600
Q=1600/6=266.666667
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DWL=0.5*(P-MC)*(efficient quantity-Q of monopoly)
=0.5*(960-320)*(266.666667-160)
=34133.3334
the DWL is $34133.3334

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