Suppose the long-run production function for a competitive firm is f(L,K)= L 1/3 K 1/4 , where L is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of capital is r, which is the interest rate. Fixed costs are zero. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the L-y and K-y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs?
Suppose the long-run production function for a competitive firm is f(L,K)= L 1/3 K 1/4 , where L is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of capital is r, which is the interest rate. Fixed costs are zero.
.a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y.
.b. Draw the conditional input demand functions for labor and capital in the L-y and K-y spaces.
.c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs?
.d. Write down the formula and draw the graph of the average cost and marginal cost functions, as functions of y.
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.d. Write down the formula and draw the graph of the average cost and marginal cost functions, as functions of y.
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