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A monopolist produces a single good X but sells it in two separate markets. The dem function for each market is P, = 50 – 4Q, and P2 = 80 – 3Q2 where P, and Q,, Pz and Q2, are the price and quantity in market 1 and 2, respectiv The cost function is TC = 120 + 8Q, + 8Q2. (a) Find the total revenue for the firm in terms of Q, and Q2. (b) Find the profit function in terms of Q, and Q2. (c) Write down the first and second order partial derivatives, using the function in (b) (d) Solve the system of equations ən :0 and = 0 "de zde (e) Show that the point (Q1.Qz) is a maximum. (1) Find the maximum profit.

A monopolist produces a single good X but sells it in two separate markets. The dem function for each market is P, = 50 – 4Q, and P2 = 80 – 3Q2 where P, and Q,, Pz and Q2, are the price and quantity in market 1 and 2, respectiv The cost function is TC = 120 + 8Q, + 8Q2. (a) Find the total revenue for the firm in terms of Q, and Q2. (b) Find the profit function in terms of Q, and Q2. (c) Write down the first and second order partial derivatives, using the function in (b) (d) Solve the system of equations ən :0 and = 0 "de zde (e) Show that the point (Q1.Qz) is a maximum. (1) Find the maximum profit.

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter14: Monopoly
Section: Chapter Questions
Problem 14.1P
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A monopolist produces a single good X but sells it in two separate markets. The dema function for each market is P, = 50 – 4Q1 and P2 = 80 – 3Q2 where P, and Q1, P2 and Q2, are the price and quantity in market 1 and 2, respective The cost function is TC = 120 + 8Q1 + 8Q2. (a) Find the total revenue for the firm in terms of Q1 and Q2- (b) Find the profit function in terms of Q, and Q2. (c) Write down the first and second order partial derivatives, using the function in (b) (d) Solve the system of equations дл = 0 and = 0 aQ2 "de (e) Show that the point (Q1.Qz) is a maximum. (f) Find the maximum profit.
Transcribed Image Text:A monopolist produces a single good X but sells it in two separate markets. The dema function for each market is P, = 50 – 4Q1 and P2 = 80 – 3Q2 where P, and Q1, P2 and Q2, are the price and quantity in market 1 and 2, respective The cost function is TC = 120 + 8Q1 + 8Q2. (a) Find the total revenue for the firm in terms of Q1 and Q2- (b) Find the profit function in terms of Q, and Q2. (c) Write down the first and second order partial derivatives, using the function in (b) (d) Solve the system of equations дл = 0 and = 0 aQ2 "de (e) Show that the point (Q1.Qz) is a maximum. (f) Find the maximum profit.
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