Monopolies and - UNC-Wilmington Department of Economics and Finance ECN 321 Dr Chris Dumas Monopoly(single seller and Monopsony(single buyer

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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 + - =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/22/2009 for the course ECN 321 taught by Professor Dumas during the Fall '08 term at University of North Carolina Wilmington.

Page1 / 6

Monopolies and - UNC-Wilmington Department of Economics and Finance ECN 321 Dr Chris Dumas Monopoly(single seller and Monopsony(single buyer

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online