A competitive firm uses two inputs and has a production function f(x1, x2)=8x.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)8(x1 + x2)y. B)2(y/8)2. C)(x1 + x2)/8. D)y/16. E)y₂/16.

Question

Quizplus · Accepted Answer

The cost of producing y units of output is determined by the cost function, which in turn is derived from the production function and the prices of inputs. Given the production function $f(x_1, x_2) = 8x_1^{0.25}x_2^{0.25}$ and the prices of both inputs being $1, the cost function can be found by solving for $x_1$ and $x_2$ that minimize the total cost subject to producing $y$ units of output. The correct answer, $2(y/8)^2$, is derived by inverting the production function to solve for $x_1$ and $x_2$ as functions of $y$, and then substituting these expressions into the total cost equation $w_1x_1 + w_2x_2$, given $w_1 = w_2 = 1$. This process involves using the properties of Cobb-Douglas production functions and their cost minimization conditions.

A Competitive Firm Uses Two Inputs and Has a Production