A firm produces its output using the following production function: f(x₁, x₂) = √√√x₁ - 1 + 4x2 where x₁ denotes the amount of factor 1 and x2 denotes the amount of factor 2. The market price of factor 1 is $4, and the market price of factor 2 is $10. (a) To produce y = 8 units of output with the lowest cost, how much factor 1 and factor 2 should the firm use? Find the optimal bundle of inputs and calculate the minimal cost.
A firm produces its output using the following production function: f(x₁, x₂) = √√√x₁ - 1 + 4x2 where x₁ denotes the amount of factor 1 and x2 denotes the amount of factor 2. The market price of factor 1 is $4, and the market price of factor 2 is $10. (a) To produce y = 8 units of output with the lowest cost, how much factor 1 and factor 2 should the firm use? Find the optimal bundle of inputs and calculate the minimal cost.
Chapter1: Making Economics Decisions
Section: Chapter Questions
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(b) Now, suppose the
Transcribed Image Text:A firm produces its output using the following production function:
f(x1, x₂) = √√√x₁ −1+ 4x₂
where x₁ denotes the amount of factor 1 and X2 denotes the amount of factor 2. The market price of factor 1 is $4, and the market
price of factor 2 is $10.
(a) To produce y =
8 units of output with the lowest cost, how much factor 1 and factor 2 should the firm use? Find the optimal
bundle of inputs and calculate the minimal cost.
Transcribed Image Text:(c) Suppose the firm utilizes a new technology to produce output. According to the new production function, factors 1 and 2 must
be combined in fixed proportions. To produce 2 units of output, the firm needs to combine 3 units of factor 1 with a unit of factor
2.
If the price of factor 1 is $2 a unit and the price of factor 2 is $4 a unit, draw an isocost representing the lowest cost of producing 2
units of output.
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