Answer the Constrained Optimization: Cobb-Douglas Production Function: 3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product of Capital (MPK) 4. Using your knowledge of the tangency condition in Producer’s theory, find the combination of K and L that the firm should use to produce the maximum possible output. Do not solve the problem using the Lagrangian method. Note: The tangency conditions just states that the slope of the production function must be equal to the slop
Answer the Constrained Optimization: Cobb-Douglas Production Function: 3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product of Capital (MPK) 4. Using your knowledge of the tangency condition in Producer’s theory, find the combination of K and L that the firm should use to produce the maximum possible output. Do not solve the problem using the Lagrangian method. Note: The tangency conditions just states that the slope of the production function must be equal to the slop
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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Question
Answer the Constrained Optimization: Cobb-Douglas Production Function:
3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product of Capital (MPK)
4. Using your knowledge of the tangency condition in Producer’s theory, find the combination of K and L that the firm should use to produce the maximum possible output. Do not solve the problem using the Lagrangian method.
Note: The tangency conditions just states that the slope of the production function must be
equal to the slope of the isocost function.
5. What is the maximum possible output that the firm could earn given the constraint it faces
Transcribed Image Text:A firm operates with a Cobb-Douglas Production function:
Q = 12K0.4L0.4
where K is units of capital, and L is number of laborers. To produce an output, the firm must pay
$40 per unit of capital, and $5 per laborer. However, the firm has a budget of $800 only to spend
for labor cost and capital cost.
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