A firm hires two inputs, input 1 and input 2, to make output. Unfortunately, for every unit of input 1 that the firm hires, 1 - a units turn out to be defective, where 1 > 1 - only a fraction a of purchased units of input 1 actually contributes to producing output y. Let x₁ and x₂ be the quantities that are not defective and can be employed towar production. If rounding is needed, please round your answers to 3 decimal places. Suppose the firm's production function is such that x₁ and x₂ are perfect substitutes: each unit of output can be made with either one unit of x₁ or units of x₂. Suppose W₂ = 9. It is optimal for the firm to hire only input 1 (and hire 0 units of input 2) if a > Suppose the firm's production function is such that x₁ and x₂ are perfect complements: the firm needs 1 unit of x₁ and 4 units of x₂ to make each unit of output. Find the producing 3 units of output when w₁ = W₂ = 1 and a = 0.7.
A firm hires two inputs, input 1 and input 2, to make output. Unfortunately, for every unit of input 1 that the firm hires, 1 - a units turn out to be defective, where 1 > 1 - only a fraction a of purchased units of input 1 actually contributes to producing output y. Let x₁ and x₂ be the quantities that are not defective and can be employed towar production. If rounding is needed, please round your answers to 3 decimal places. Suppose the firm's production function is such that x₁ and x₂ are perfect substitutes: each unit of output can be made with either one unit of x₁ or units of x₂. Suppose W₂ = 9. It is optimal for the firm to hire only input 1 (and hire 0 units of input 2) if a > Suppose the firm's production function is such that x₁ and x₂ are perfect complements: the firm needs 1 unit of x₁ and 4 units of x₂ to make each unit of output. Find the producing 3 units of output when w₁ = W₂ = 1 and a = 0.7.
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.4P
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H10.
![A firm hires two inputs, input 1 and input 2, to make output. Unfortunately, for every unit of input 1 that the firm hires, 1 - a units turn out to be defective, where 1 > 1 − a > 0. That is,
only a fraction a of purchased units of input 1 actually contributes to producing output y. Let x₁ and x₂ be the quantities that are not defective and can be employed towards
production.
If rounding is needed, please round your answers to 3 decimal places.
Suppose the firm's production function is such that x₁ and x₂ are perfect substitutes: each unit of output can be made with either one unit of x₁ or units of x2. Suppose 1 = 1 and
W₂ = 9. It is optimal for the firm to hire only input 1 (and hire 0 units of input 2) if a ≥_
Suppose the firm's production function is such that x₁ and x₂ are perfect complements: the firm needs 1 unit of x₁ and 4 units of x₂ to make each unit of output. Find the total cost of
producing 3 units of output when w₁ = W₂ = 1 and a =
= 0.7.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88ca4c30-51fe-4a55-ab57-9e8751f53a24%2F4f63854f-ebc5-4064-97d2-85069d213217%2Fi434iuj_processed.png&w=3840&q=75)
Transcribed Image Text:A firm hires two inputs, input 1 and input 2, to make output. Unfortunately, for every unit of input 1 that the firm hires, 1 - a units turn out to be defective, where 1 > 1 − a > 0. That is,
only a fraction a of purchased units of input 1 actually contributes to producing output y. Let x₁ and x₂ be the quantities that are not defective and can be employed towards
production.
If rounding is needed, please round your answers to 3 decimal places.
Suppose the firm's production function is such that x₁ and x₂ are perfect substitutes: each unit of output can be made with either one unit of x₁ or units of x2. Suppose 1 = 1 and
W₂ = 9. It is optimal for the firm to hire only input 1 (and hire 0 units of input 2) if a ≥_
Suppose the firm's production function is such that x₁ and x₂ are perfect complements: the firm needs 1 unit of x₁ and 4 units of x₂ to make each unit of output. Find the total cost of
producing 3 units of output when w₁ = W₂ = 1 and a =
= 0.7.
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