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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.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Lotal, 9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC = 10Q, +Q0, +10Q, where O, and O, denote the quantity of items of goods 1 and 2, respectively that are produced. If Pi and P2 denote the corresponding prices then the demand equations are P = 50– Q +Q, 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. I
Transcribed Image Text:Lotal, 9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC = 10Q, +Q0, +10Q, where O, and O, denote the quantity of items of goods 1 and 2, respectively that are produced. If Pi and P2 denote the corresponding prices then the demand equations are P = 50– Q +Q, 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. I
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