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monopoly1 - 11 Monopoly 11.1 Price discriminations Free to...

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11 Monopoly Free to set price-quantity combinations. py c ( y ) max p,y , s.t. D ( p ) = y. Alternatively p ( y ) y c ( y ) max y . FOC : p ( y ) + p 0 ( y ) y = c 0 ( y ) , SOC : 2 p 0 ( y ) + p 00 ( y ) y c 00 ( y ) 0 . Level of production is not e cient! Natural monopolies. Residual monopolies. 11.1 Price discriminations In general, monopoly can o ff er ( P, Q ), or even a sched- ule of o ff ers ( P j , Q j ), j J . 11.1.1 1 st Degree M. extracts full willingness to pay from the consumers. Did we solve the above problem correctly? Think about ( P, Q ): max P,Q P cQ, s.t. u ( Q ) P. Conditions: no resale, knowledge of the consumers, uniformity of the consumers(?).
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11.1.2 2 d Degree Consumers are di ff erent, M. cannot di ff erentiate between them. O ff ers a schedule of prices: depend on quantity of units purchased (non-linear prices, quantity discounts). 2 (rep) consumers: u 1 ( x ) < u 2 ( x ), u 0 1 ( x ) < u 0 2 ( x ). O ff er: ( P 1 , Q 1 ), ( P 2 , Q 2 ) . IR=Individual Rationality (participation) constraints: u 1 ( Q 1 ) P 1 0 , u 2 ( Q 2 ) P 2 0 . IC=Incentive Compatibility
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