Q1. Consider a monopolist which produces two different products, each having the following demand functions: 91 = 14-701₁ 92 = 24 - P2₁ where 9₁ and 92 represent the output levels of product 1 and product 2 and p₁ and p₂ represent their prices. The monopolist's joint cost function is given as C (91, 92) = 91 +59192 +93.

Microeconomic Theory
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ISBN:9781337517942
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Chapter14: Monopoly
Section: Chapter Questions
Problem 14.9P
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Q1. Consider a monopolist which produces two different products, each having the following
demand functions:
91 = 14-
-P₁,
92 = 24 - 12/212₂2
P2,
where 9₁ and 92 represent the output levels of product 1 and product 2 and p₁ and p2
represent their prices.
The monopolist's joint cost function is given as
C (91, 92) = 91 +59192 +9²/2.
Show the Hessian, H, for this problem. What does the second order condition
require for this problem? Show if it is satisfied.
Transcribed Image Text:Q1. Consider a monopolist which produces two different products, each having the following demand functions: 91 = 14- -P₁, 92 = 24 - 12/212₂2 P2, where 9₁ and 92 represent the output levels of product 1 and product 2 and p₁ and p2 represent their prices. The monopolist's joint cost function is given as C (91, 92) = 91 +59192 +9²/2. Show the Hessian, H, for this problem. What does the second order condition require for this problem? Show if it is satisfied.
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