problem is not well defined.
(b) Using the monopolists FOC , pm= ■ CC , we get qm CC
Consumer surplus given price p: S(p) = x°°x(t)dt = ^H-JJ . The deadweight welfare loss can be calculated by subtracting from the consumer surplus under competitive pricing, the consumer surplus plus profits under monopoly pricing:
DL = Te^TT " (F^Tir^J ' " = l=e[e=l ' [l c
(c) After some messy algebra one can show that the deadweight welfare loss is
decreasing in c (i.e. dDHc)/dc < 0). As e increases the demand becomes more elastic without changing the size of the market, which forces the monopolist to price closer and closer to the competitive price. In the limit as c the deadweight welfare loss goes to zero and the monopolist charges the competitive price.
Was this article helpful?