Suppose the long-run production function for a competitive firm is f(x1,x2)= min {x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. .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 x1-y and x2- 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(x1,x2)= min {x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2.
.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
.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 function, as a function of y.
.e. Write down the formula and draw the graph of the marginal cost function, as a function of y.
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.d. Write down the formula and draw the graph of the average cost function, as a function of y.
.e. Write down the formula and draw the graph of the marginal cost function, as a function of y.
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