Answer all parts. Suppose that a monopolist offers two different products with demand functions P1 = 56 – 4q, Р2 3D 48 — 2q2 The monopolist's joint cost function is C(41, 92) = qỉ + 5q192 + q3 %3D a. Write out the monopolist's profit function as a function of b. Differentiate the profit function with respect to q, and q2.Explain intuitively why we take the derivative of the function. c. Solve the first order conditions using Cramer's rule. d. Use the values that you found in part c to find the prices in each market and the profit that is made by the monopolist. e. Use the second order condition for a maximum to check whether or not the and 92. values that you have computed do represent a maximum.
Answer all parts. Suppose that a monopolist offers two different products with demand functions P1 = 56 – 4q, Р2 3D 48 — 2q2 The monopolist's joint cost function is C(41, 92) = qỉ + 5q192 + q3 %3D a. Write out the monopolist's profit function as a function of b. Differentiate the profit function with respect to q, and q2.Explain intuitively why we take the derivative of the function. c. Solve the first order conditions using Cramer's rule. d. Use the values that you found in part c to find the prices in each market and the profit that is made by the monopolist. e. Use the second order condition for a maximum to check whether or not the and 92. values that you have computed do represent a maximum.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Answer all parts.
Suppose that a monopolist offers two different products with demand functions
P1 = 56 – 4q,
Р2 3D 48 — 2q2
The monopolist's joint cost function is
C(41, 92) = qỉ + 5q192 + q3
%3D
a. Write out the monopolist's profit function as a function of
b. Differentiate the profit function with respect to q, and q2.Explain intuitively why
we take the derivative of the function.
c. Solve the first order conditions using Cramer's rule.
d. Use the values that you found in part c to find the prices in each market and
the profit that is made by the monopolist.
e. Use the second order condition for a maximum to check whether or not the
and
92.
values that you have computed do represent a maximum.
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