A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC = 10Q, +Q,Q2+10Q, where O, and Q, denote the quantity of items of goods 1 and 2, respectively that are produced. If Pı and P2 denote the corresponding prices then the demand equations are R = 50-Q+Q2 P = 30+20, - Q, Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.

A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC = 10Q, +Q,Q2+10Q, where O, and Q, denote the quantity of items of goods 1 and 2, respectively that are produced. If Pı and P2 denote the corresponding prices then the demand equations are R = 50-Q+Q2 P = 30+20, - Q, Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter14: Monopoly

Section: Chapter Questions

Problem 14.5P

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