4. 1/3 1/3 is w2. A firm uses two factors x₁ and x2 for production y = x1 x2 The price of the product is 2. The price of x1 is w1. The price of X2 The firm is endowed with one unit of x2. (a) In the short run, the firm can not adjust x2, and x2 = 1. Write down the short-run profit-maximizing problem. What is the profit-maximizing output? What is the factor demand curve of x1? (b) In the long run, the firm can adjust x2. Write down the long-run profit- maximizing problem. What is the profit-maximizing output when w₁ = 1 and w2 = 1? (c) Is the production function constant returns to scale, increasing returns to scale, or decreasing returns to scale? Prove it.
4. 1/3 1/3 is w2. A firm uses two factors x₁ and x2 for production y = x1 x2 The price of the product is 2. The price of x1 is w1. The price of X2 The firm is endowed with one unit of x2. (a) In the short run, the firm can not adjust x2, and x2 = 1. Write down the short-run profit-maximizing problem. What is the profit-maximizing output? What is the factor demand curve of x1? (b) In the long run, the firm can adjust x2. Write down the long-run profit- maximizing problem. What is the profit-maximizing output when w₁ = 1 and w2 = 1? (c) Is the production function constant returns to scale, increasing returns to scale, or decreasing returns to scale? Prove it.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:4.
1/3 1/3
is w2.
A firm uses two factors x₁ and x2 for production y = x1 x2
The price of the product is 2. The price of x1 is w1.
The price of X2
The firm is endowed with one unit of x2.
(a) In the short run, the firm can not adjust x2, and x2 = 1. Write down the
short-run profit-maximizing problem. What is the profit-maximizing output?
What is the factor demand curve of x1?
(b) In the long run, the firm can adjust x2. Write down the long-run profit-
maximizing problem. What is the profit-maximizing output when w₁ = 1
and w2 = 1?
(c) Is the production function constant returns to scale, increasing returns
to scale, or decreasing returns to scale? Prove it.
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