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Monopolies and Monopsonies - UNC-Wilmington Department of...

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UNC-Wilmington ECN 321 Department of Economics and Finance Dr. Chris Dumas Monopoly (single seller) and Monopsony (single buyer) Example Problems Monopoly (single seller) Example Problem Assumptions: A single producer is producing product Q using two inputs, L and K The market for Q is a monopoly (the producer has market power in the market for Q; thus, P Q is a choice variable for the producer). Suppose a market research study finds that consumers’ demand function for product Q is given by: Q = 4P Q -2 . (Note that the demand function can also be written as P Q = 2Q -1/2 .) The markets for L and K are perfectly competitive (the producer does NOT have market power in the markets for L and K; thus, P L and P K are given constants for the producer) In this example, suppose that the producer uses an imperfect substitutes technology to produce product Q from inputs L and K. Suppose that the producer’s production function is: Q = 10L 1/2 K 1/4 . Set up the optimization problem: subject to: 4 1 2 1 K L 10 Q = , technology Q = 4P Q -2 , consumer demand Replace TR and TC with their definitions, and re-write consumer demand as P Q = 2Q -1/2 . subject to: 4 1 2 1 K L 10 Q = technology P Q = 2Q -1/2 consumer demand (re-written) Substitute consumer demand for P Q in the profit function (notice that P Q then disappears from the list of choice variables). subject to: 4 1 2 1 K L 10 Q = technology Simplify the profit function by combining the factors that contain Q (that is, add the exponents on the Q’s): subject to: 4 1 2 1 K L 10 Q = technology 1 ( 29 K P L P Q P ofit Pr K L Q Q P , Q , K , L max + - = TC TR ofit Pr max Q P , Q , K , L - = ( 29 K P L P Q ) Q 2 ( ofit Pr K L 2 / 1 Q , K , L max + - = - ( 29 K P L P Q 2 ofit Pr K L 2 / 1 Q , K , L max + - =
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UNC-Wilmington ECN 321 Department of Economics and Finance Dr. Chris Dumas
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