Suppose a monopoly supplied its market from two plants, with cost functions: C₁-18 q₁ and C₂ (92) — 392. The monopolist faces a linear demand p = 238 - 5 Q, where is the amount sold in this market, which is the total amount produced by both plants. Find the quantities produced at each plant to maximize the monopolist's profit. 91 · 92 Number Number Now check the second order conditions:

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter14: Monopoly
Section: Chapter Questions
Problem 14.9P
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The principal minors are H₁ =
absin (a)
ab
sin (a)
8
di
8
di
f
f
Therefore the Hessian is positive definite
8
8
R
R
Ω
Ω
and
m
the solution is a maximum.
A2
P
and H₂=
Transcribed Image Text:The principal minors are H₁ = absin (a) ab sin (a) 8 di 8 di f f Therefore the Hessian is positive definite 8 8 R R Ω Ω and m the solution is a maximum. A2 P and H₂=
Suppose a monopoly supplied its market from two plants, with cost functions:
C₁ = 18 q₁ and C₂ (92) = 392.
The monopolist faces a linear demand p = 238 - 5 Q, where Q is the amount sold in this market, which is the total amount produced by both plants.
Find the quantities produced at each plant to maximize the monopolist's profit.
91
Number
Number
Now check the second order conditions:
The Hessian is
b
sin (a)
da
f
8
a
Ω
B
A₂
Transcribed Image Text:Suppose a monopoly supplied its market from two plants, with cost functions: C₁ = 18 q₁ and C₂ (92) = 392. The monopolist faces a linear demand p = 238 - 5 Q, where Q is the amount sold in this market, which is the total amount produced by both plants. Find the quantities produced at each plant to maximize the monopolist's profit. 91 Number Number Now check the second order conditions: The Hessian is b sin (a) da f 8 a Ω B A₂
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