Production Functions and Cost Functions in the short run and in the long run Consider the production function Q=KL. The firm needs to produce 64 units of output. The price of capital is R=$16 and the price of labor is W=$4 a. In the short run, the firm's capital is fixed at K=16. How much labor will it use? What is its short run total cost? Hint: Solve it for a generic Q and plug Q=64 only at the very end b. Find the firm's short run total cost, average total cost, and marginal cost curves. Hint: If you are trying to find cost curves, Q is unknown. c. Set up a Lagrangian to find the firm's optimal inputs in
Production Functions and Cost Functions in the short run and in the long run Consider the production function Q=KL. The firm needs to produce 64 units of output. The price of capital is R=$16 and the price of labor is W=$4 a. In the short run, the firm's capital is fixed at K=16. How much labor will it use? What is its short run total cost? Hint: Solve it for a generic Q and plug Q=64 only at the very end b. Find the firm's short run total cost, average total cost, and marginal cost curves. Hint: If you are trying to find cost curves, Q is unknown. c. Set up a Lagrangian to find the firm's optimal inputs in
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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Production Functions and Cost Functions in the short run and in the long run Consider the production function Q=KL. The firm needs to produce 64 units of output. The price of capital is R=$16 and the price of labor is W=$4 a. In the short run, the firm's capital is fixed at K=16. How much labor will it use? What is its short run total cost? Hint: Solve it for a generic Q and plug Q=64 only at the very end b. Find the firm's short run total cost,
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