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.
Constrained Optimization: Cobb-Douglas Production Function
A firm operates with a Cobb-Douglas Production function:
Q = 12K 0.4L 0.4
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.
1. 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.
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