Question

The Production Function is Q = 300KL, the Price of Labor is PL=7, the Price of Capital is PK=12, and the budget to purchase labor and capital is TC = 100. Using the Lagrangian function maximize output subject to the TC function. Provide a graph inclusive of the optimum isoquant and the optimum TC function.

Answer 1

Answer: Q = 300KL

subject to constraint : 7* L + 12*K = 100

Lagrange: , differentiating w.r.t L, K and we get,

dividing eqn 1 by eqn 2 , we get,

, putting value of K = 7L/12 into eqn 3 , we get,

100 - 7L - 12 * (7L/12) = 0

14L = 100

L = 100/14 = 7.14

therefore , K = 7L/12 = (7/12) * 100/14 = 25/6 = 4.16