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A firm produces twogoods in pure competition and has the following total revenue andtotal cost functions: TR =P1Q1 +P2Q2 and TC =2Q12 +Q1Q2 +2Q22 Where,P1 = 12 and P2 = 1

A firm produces twogoods in pure competition and has the following total revenue andtotal cost functions: TR =P1Q1 +P2Q2 and TC =2Q12 +Q1Q2 +2Q22 Where,P1 = 12 and P2 = 1

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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A firm produces twogoods in pure competition and has the following total revenue andtotal cost functions:

TR =P1Q1 +P2Q2 and

TC =2Q12 +Q1Q2 +2Q22

Where,P1 = 12 and P2 = 18.

Form the profit function and identity the critical valueQ1*.

Identity the critical value Q2*.

Construct the Hessian matrix and calculate the value of|H1|.

Calculate the value of |H2|.

Based on the values of Hessian, what can you say about theprofit?

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