A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC=10Q1+Q1Q2+10Q2where Q1and Q2 denote the quantity of items of goods 1and 2, respectively that are produced. If P1 and P2 denote the corresponding prices then the demand equations areP1=50-Q1+Q2P2=30+2Q1-Q2Using 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.

The total cost is given as The inverse demand function is given as The firm is contracted to produce…

Answered: A monopolistic producer of two goods, 1…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter14: Monopoly

Section: Chapter Questions

Problem 14.9P

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A monopolistic producer of two goods, 1 and 2, has a joint total cost function

TC=10Q₁+Q₁Q₂+10Q₂

where Q₁and Q₂ denote the quantity of items of goods 1and 2, respectively that are produced. If P₁ and P₂ denote the corresponding prices then the demand equations are

P₁=50-Q₁+Q₂

P₂=30+2Q₁-Q₂

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.

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