Suppose that a certain factory output is given by the Cobb-Douglas production function Q(K, L) = 60K¹/3 [2/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory's output. (a) Determine whether the Cobb-Douglas production function is concave, convex, strictly concave, strictly convex or neither. If a unit of labour costs $100, unit of capital $200, and $200,000 is budgeted for production (b) Formulate the problem as a constrained optimization problem. (c) Write down the Lagrange function.
Suppose that a certain factory output is given by the Cobb-Douglas production function Q(K, L) = 60K¹/3 [2/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory's output. (a) Determine whether the Cobb-Douglas production function is concave, convex, strictly concave, strictly convex or neither. If a unit of labour costs $100, unit of capital $200, and $200,000 is budgeted for production (b) Formulate the problem as a constrained optimization problem. (c) Write down the Lagrange function.
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.5P
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