A competitive firm uses two inputs and has a production function f(x1, x2)  23x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1  w2  $1.The cost of producing y units of output for this firm is

A) 23(x1  x2) y.
B) y/46.
C) (x1  x2) /23.
D) 2(y/23) 2.
E) y₂/46.

Question

Curtis Nagel · Accepted Answer

Final Answer : D, Explanation :   The cost of producing y units of output involves finding the cost function that relates the output level to the total cost. Given the production function   f ( x 1 , x 2 ) = x 1 0.25 x 2 0.25 f(x_1, x_2) = x_1^{0.25}x_2^{0.25} f ( x 1 ​ , x 2 ​ ) = x 1 0.25 ​ x 2 0.25 ​   and factor prices   w_1 = w_2 = $1  , the cost of producing y units is not directly given by the production function. However, the correct approach involves minimizing the cost subject to the production function, which typically results in a cost function related to the output level. Option D,   2 ( y / 23 ) 2 2(y/23)^2 2 ( y /23 ) 2  , is a plausible representation of such a cost function, assuming specific derivations and optimizations have been made based on the given production function and factor prices.

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