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For a monopolist's products A and B, the joint-cost function is c(qA9B) = 2(9A + 9B +qA9B), and the demand functions are 9A=20-PA. 9B = 10 - PB. Find the values of p, and p, that maximize profit. What are the quantities of A and B that correspond to these prices? What is the total profit?

For a monopolist's products A and B, the joint-cost function is c(qA9B) = 2(9A + 9B +qA9B), and the demand functions are 9A=20-PA. 9B = 10 - PB. Find the values of p, and p, that maximize profit. What are the quantities of A and B that correspond to these prices? What is the total profit?

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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1. The algorithm for local extrema of f(x,y) 1.1. 1.2. 1.3. 1.4. Calculate the first derivatives: ах' ду af Find the critical points: (xo. Yo) = 0,= (xo.Yo) = 0 a²fa²fa²f Calculate the second derivatives: дх2 дугдхду For every critical point: 1.4.1. Calculate the Hessian: H(x, y) = (x,y) x(x,y) - ( dx dy 1.4.2. If H(xo, Yo) = 0 the test is inconclusive, stop 1.4.3. If H(xo, Yo) < 0 the critical point is a saddle, stop 1.4.4. If Əx² 1.4.5. If (xo. Yo) > 0 or minimum (xo. Yo) >0 then U, the extremum is a local Əy² 8²1 -(xo. Yo) <0 or (xo. Yo) <0 then n, the extremum is a local ax² maximum
Transcribed Image Text:1. The algorithm for local extrema of f(x,y) 1.1. 1.2. 1.3. 1.4. Calculate the first derivatives: ах' ду af Find the critical points: (xo. Yo) = 0,= (xo.Yo) = 0 a²fa²fa²f Calculate the second derivatives: дх2 дугдхду For every critical point: 1.4.1. Calculate the Hessian: H(x, y) = (x,y) x(x,y) - ( dx dy 1.4.2. If H(xo, Yo) = 0 the test is inconclusive, stop 1.4.3. If H(xo, Yo) < 0 the critical point is a saddle, stop 1.4.4. If Əx² 1.4.5. If (xo. Yo) > 0 or minimum (xo. Yo) >0 then U, the extremum is a local Əy² 8²1 -(xo. Yo) <0 or (xo. Yo) <0 then n, the extremum is a local ax² maximum
For a monopolist's products A and B, the joint-cost function is c(qA9B) = 2(9A + 9B +9A + 9B), and the demand functions are 9A = 20-PA. 9B = 10 - PB. Find the values of p, and pe that maximize profit. What are the quantities of A and B that correspond to these prices? What is the total profit?
Transcribed Image Text:For a monopolist's products A and B, the joint-cost function is c(qA9B) = 2(9A + 9B +9A + 9B), and the demand functions are 9A = 20-PA. 9B = 10 - PB. Find the values of p, and pe that maximize profit. What are the quantities of A and B that correspond to these prices? What is the total profit?
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