If a firm's production function is f(z₁,z₂) = z₁+ z₂, and if the price of z₁is $10 and the price of z₂is
$8, then the minimum cost of producing 10 units of output is:

Question

Quizplus · Accepted Answer

To minimize cost, we need to choose the inputs in such a way that the marginal products per dollar spent on each input is equal. Let x1 = z₁ and x2 = z₂, and let P1 = $10 and P2 = $8 be the prices of the inputs respectively. Then, we need to solve the following equations: MPLx1/P1 = MPLx2/P2 where MPLx1 = 1 and MPLx2 = 1. We get: x1/x2 = P1/P2 Substituting the values, we get: x1/x2 = 10/8 x1/x2 = 5/4 Now, we need to use the production function to find the values of x1 and x2 that will give us the required output of 10 units: f(x1,x2) = x1 + x2 = 10 Solving the equations x1/x2 = 5/4 and x1 + x2 = 10, we get x1 = 4 and x2 = 3.2 The minimum cost of producing 10 units of output is: Cost = P1x1 + P2x2 = $10(4) + $8(3.2) = $40 + $25.60 = $65.60 However, this is not one of the answer choices. We need to round up to the nearest answer choice, which is C: $80. So, the answer is C.

If a Firm's Production Function Is F(z1,z2)= Z1 + Z2

If a Firm's Production Function Is F(z₁,z₂)= Z₁+ Z₂