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1. A firm is a monopolistic producer of two goods. The prices are related to quantities Q1 and Q2 according to the demand functions P = 50- Q1 and P2 95 -3Q2. If the total cost function is TC = Q? + 3Q,Q2 + Q², i) Find the firm's total revenue function. ii) Find the firm's total profit function. iii) Calculate the values of Q1 and Q2 which maximize profit. iv) Using the second order condition (SOC), prove that the profit level is at a maximum.

1. A firm is a monopolistic producer of two goods. The prices are related to quantities Q1 and Q2 according to the demand functions P = 50- Q1 and P2 95 -3Q2. If the total cost function is TC = Q? + 3Q,Q2 + Q², i) Find the firm's total revenue function. ii) Find the firm's total profit function. iii) Calculate the values of Q1 and Q2 which maximize profit. iv) Using the second order condition (SOC), prove that the profit level is at a maximum.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. A firm is a monopolistic producer of two goods. The prices are related to quantities Q1 and Q2 according to the demand functions P = 50 – Q, and P = 95 – 3Q2. If the total cost function is TC = Qf + 3Q,Q2 + Qź, i) Find the firm's total revenue function. ii) Find the firm's total profit function. iii) Calculate the values of Q, and Q2 which maximize profit. iv) Using the second order condition (SOC), prove that the profit level is at a maximum.
Transcribed Image Text:1. A firm is a monopolistic producer of two goods. The prices are related to quantities Q1 and Q2 according to the demand functions P = 50 – Q, and P = 95 – 3Q2. If the total cost function is TC = Qf + 3Q,Q2 + Qź, i) Find the firm's total revenue function. ii) Find the firm's total profit function. iii) Calculate the values of Q, and Q2 which maximize profit. iv) Using the second order condition (SOC), prove that the profit level is at a maximum.
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