Suppose output for a simple production process is given by Q = K + L, where K denotes capital, and L denotes labor. The price of labor is $2 per unit and the price of capital is $4 per unit. What would be the minimum costs of producing 10 units of output?

Question

Quizplus · Accepted Answer

To find the minimum costs of producing 10 units of output, we need to find the combination of K and L that minimizes the cost of producing 10 units of output. Since Q = K + L, we can rewrite the production function as L = Q - K.

The cost of producing 10 units of output can now be written as C = 4K + 2L = 4K + 2(Q - K) = 2Q + 2K.

To minimize cost, we need to minimize this expression subject to the constraint that Q = 10.

Minimizing 2Q + 2K subject to Q = 10 gives us K = 0 and L = 10.

The minimum cost of producing 10 units of output is therefore 2(10) + 4(0) = $20.

Suppose Output for a Simple Production Process Is Given by Q