Consider a firm with the production function ƒ(x1, x2) = x₁/²x2. The price of the two inputs is w₁ = 2 and w₂ = 1. When the firm is minimizing costs, how many dollars will it spend on input 2 for every dollar spent on input 1? How many units of input 2 will the firm use for every unit of input 1? Suppose the firm produces a total quantity of q=108 at minimal cost. What is x1? Suppose the firm produces a total quantity of q=108 at minimal cost. What is x2?

Microeconomic Theory
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ISBN:9781337517942
Author:NICHOLSON
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Chapter10: Cost Functions
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Problem 10.6P
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Consider a firm with the production function f(x₁, x₂) = x1²2. The price of the
two inputs is w1 = 2 and w₂ = 1.
When the firm is minimizing costs, how many dollars will it spend on input 2 for
every dollar spent on input 1?
How many units of input 2 will the firm use for every unit of input 1?
Suppose the firm produces a total quantity of q=108 at minimal cost. What is
x1?
Suppose the firm produces a total quantity of q=108 at minimal cost. What is
x2?
Transcribed Image Text:Consider a firm with the production function f(x₁, x₂) = x1²2. The price of the two inputs is w1 = 2 and w₂ = 1. When the firm is minimizing costs, how many dollars will it spend on input 2 for every dollar spent on input 1? How many units of input 2 will the firm use for every unit of input 1? Suppose the firm produces a total quantity of q=108 at minimal cost. What is x1? Suppose the firm produces a total quantity of q=108 at minimal cost. What is x2?
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