Question

A ?firm's technology requires it to combine 4 labor hours with 3 machine hours to produce 1 unit of output. So capital and labor are perfect complements. So the production function is f(E,K) = min(E/4,K/3). The ?firm wants to produce q units of output, where q > 0 is some number. Suppose the price of capital is $10 per machine per hour. What combination of inputs will the ?firm use if the wage rate is $10 per hour? What combination of inputs will the ?firm use if the wage rate is $15 per hour? What if one of the inputs (but not both) is free?

Answer 1

If the wage rate is Dollar 10 per hour then the combination of inputs in the firm is equal proportion of labor and capital. Because the price for capital and labor is Dollar 10 per hour. So the firm use same proportion of labor and capital to produce more output.

If the wage rate is $15 per hour then the firm use more capital and less labor inputs for production. Because the labor is more expensive than capital. The price of capital is $10 and the price of labor that is the wage is $15. So the use of labor inputs in production is more expensive than the use of capital in production. Then the firm can produce exist output with less cost.

If the one of the input is not free, then the firm use more of available input. If the capital is available then the firm use more capital. If the labor is available then the firm use more labor. Because the productivity of capital and labor is more or less same. Because a labour needs 4 hours for an output and the capital needs 3 hours for an output.