Question

onsider a government-controlled firm that produces output y according to the production function y = kal, where a > 1 is a parameter. Suppose the firm is directed to maximize output subject to meeting the cost constraint 2k l = 12. (a) Set up the Lagrangian.

Answer 1

The Lagrangian for the government-controlled firm can be set up as: L = y - λ(2kl - 12), where y is the output, k is the capital, l is the labor, and λ is the Lagrange multiplier. By maximizing this Lagrangian subject to the cost constraint, we can find the optimal values of capital and labor that maximize output.

Step-by-step explanation:

The Lagrangian for the government-controlled firm can be set up as:

L = y - λ(2kl - 12)

where y is the output, k is the capital, l is the labor, and λ is the Lagrange multiplier. By maximizing this Lagrangian subject to the cost constraint, we can find the optimal values of capital and labor that maximize output.