6. (20 pts) Suppose a competitive firm produces two products. Let Q represents the output level...
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6. (20 pts) Suppose a competitive firm produces two products. Let Q₁ represents the output level of the i-th product and let the prices of the products are denoted by P₁ and P₂. Since the firm is a competitive firm, it takes the prices as given. Accordingly, the firm's revenue function will be TR= P1Q1 + P2Q2 The firm's cost function is assumed to be C = 2Q+Q1Q2 +2Q²2. 1) Write down the firm's profit function. 2) The firm wants to maximize the profit by choosing the levels of Q1 and Q2. Please use Cramer's rule to find the optimal solution for this purpose. 3) Please use the Hessian matrix to check the solution does maximize. 4) Given the demand function Q, solved from part 2), find the price elasticity of demand for product 1 and interpret the answer, if p₁=2 and p2=4. 6. (20 pts) Suppose a competitive firm produces two products. Let Q₁ represents the output level of the i-th product and let the prices of the products are denoted by P₁ and P₂. Since the firm is a competitive firm, it takes the prices as given. Accordingly, the firm's revenue function will be TR= P1Q1 + P2Q2 The firm's cost function is assumed to be C = 2Q+Q1Q2 +2Q²2. 1) Write down the firm's profit function. 2) The firm wants to maximize the profit by choosing the levels of Q1 and Q2. Please use Cramer's rule to find the optimal solution for this purpose. 3) Please use the Hessian matrix to check the solution does maximize. 4) Given the demand function Q, solved from part 2), find the price elasticity of demand for product 1 and interpret the answer, if p₁=2 and p2=4.
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Answer rating: 100% (QA)
1 Write down the firm s profit function ANS WER Pro fit TR C Pro fit P 1 Q 1 P 2 Q 2 2 Q 1 Q 1 Q 2 2 ... View the full answer
Related Book For
Microeconomics An Intuitive Approach with Calculus
ISBN: 978-0538453257
1st edition
Authors: Thomas Nechyba
Posted Date:
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