lecture 18

# lecture 18 - Economics 100A Lecture#18 Tuesday Mar 30 1 2 3...

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Economics 100A Lecture #18: Tuesday, Mar. 30 1) Multi-plant monopoly and cartels 2) Capturing surplus using monopoly power 3) Price discrimination: defns, examples, types 4) 1 st degree price discrimination 5) 3 rd degree price discrimination

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(1) Multi-plant monopoly Firms produce product from many locations: National firms have geographically disperse plants, e.g., Anheuser-Busch has 12 plants in U.S. Multinationals often operate domestic and foreign sites, e.g., Japanese auto makers Can assume … The product is same from any plant Costs of plants are different due to transportation, local wage rates, regulations, etc.
Multi-plant monopolist problem How should monopolist allocate production across plants? Suppose two plants with different costs: C 1 (q 1 ) and C 2 (q 2 ) To minimize cost of any quantity, allocate so same marginal costs: MC 1 (q 1 ) = MC 2 (q 2 ) Why? How much should the monopolist produce? maximize: (q 1, q 2 ) = P(q 1 +q 2 )(q 1 +q 2 ) – [C 1 (q 1 )+C 2 (q 2 )] solution: MR(q 1 + q 2 ) = MC T (= MC 1 (q 1 ) = MC 2 (q 2 ) ) Why?

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Quantity Price MC 1 MC 2 MC T Multi plant cost function
Q P MC T Demand MR Q* 1 Q* 2 Q* T P* MC 1 MC 2 Multi plant monopoly solution

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Linear example Plant #2 is more efficient than plant #1 MC 1 (q 1 ) = 1 + q 1 MC 2 (q 2 ) = 1 + q 2 /2 Linear demand MR = 24 – 2(q 1 + q 2 ) Solution: 1 + q 1 = 1 + q 2 /2 q 2 = 2 q 1 MR = 24 – 6q 1 = 1 + q 1 = MC T q 1 = 23/7 and q 2 = 46/7 More produced at plant #2 than plant #1. Why? Yet “inefficient” plant #1 still produces. Why? q q MC q MC all for ) ( ) ( } 2 1
Cartel as a multi-plant monopoly Different producers seek to maximize joint profits Just like a monopolist with many plants Could be multiple firms or countries (e.g., OPEC) Assumes Each member obeys joint profit max rule Every producer joins the cartel, and no entry or exit Cartel solution Market marginal revenue = cartel’s marginal cost Recall multi-plant monopolist: MR(q 1 + q 2 ) = MC 1 (q 1 ) = MC 2 (q 2 )

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Q P MC T Demand MR Q* 1 Q* 2 Q* T P* MC 1 MC 2 Cartel solution
Cartel vs. multi-plant monopoly Similarities Different sources of the good have different costs Both have stake in overall profits Differences Each cartel member highly interested in its own profit, whereas plant can be “cost center” Each plant supposedly under full control of monopolist, whereas cartel member independent

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## This note was uploaded on 04/21/2010 for the course ECON 100A taught by Professor Woroch during the Spring '08 term at Berkeley.

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lecture 18 - Economics 100A Lecture#18 Tuesday Mar 30 1 2 3...

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