Demand function for each input, k and l

Question

Suppose the long-run production function for a competitive firm is f(x1,x2)= min {3x1,2x2}. 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: 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? C: Write down the formulas and draw the graphs of the average cost and marginal cost functions, as functions of y.

Answer 1

Question

Chapter 10, Problem 10.7P

a)

To determine

To find: Demand function for each input, k and l

b)

To determine

To know: Production function for q.

c)

To determine

To know: CES production function.

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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. .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.