2. A competitive firm uses k and I to produce output q. Its production function is q = f(l, k) = l³k³. Wk = w₁ = $1. 1 1 a. Suppose that the output price is $2. Find the firm's demand for k and I that would maximize its profit. Find how many units of output it would produce and how much profit it would make. b. Now suppose the market price is unknown, but the firm wants to produce 144 units of output, and everything else remains the same. Find the firm's conditional factor demands that would minimize the cost. Also, calculate the associated total cost and the profit. c. Continuing the situation in part (b), what should be the minimum output price for the firm to continue to operate in the market?
2. A competitive firm uses k and I to produce output q. Its production function is q = f(l, k) = l³k³. Wk = w₁ = $1. 1 1 a. Suppose that the output price is $2. Find the firm's demand for k and I that would maximize its profit. Find how many units of output it would produce and how much profit it would make. b. Now suppose the market price is unknown, but the firm wants to produce 144 units of output, and everything else remains the same. Find the firm's conditional factor demands that would minimize the cost. Also, calculate the associated total cost and the profit. c. Continuing the situation in part (b), what should be the minimum output price for the firm to continue to operate in the market?
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:2. A competitive firm uses k and I to produce output q. Its
production function is q = f(l, k) = l³k³. Wk = w₁ = $1.
1 1
a. Suppose that the output price is $2. Find the firm's
demand for k and I that would maximize its profit. Find
how many units of output it would produce and how much
profit it would make.
b. Now suppose the market price is unknown, but the firm
wants to produce 144 units of output, and everything else
remains the same. Find the firm's conditional factor
demands that would minimize the cost. Also, calculate the
associated total cost and the profit.
c. Continuing the situation in part (b), what should be the
minimum output price for the firm to continue to operate in
the market?
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