Question

Assume the production of a good, X, follows the Cobb-Douglas function Q=40K0.3 L0.7. If w= $10 and r= $4, use Excel's optimizer to minimize costs if Q=500. In Solver, select the “Evolutionary” method.

Answer 1

The Cob Douglas production function is of the form,
Q = c.K^a*L^b
Where c is total factor productivity, k is capital, a is output elasticity of capital, L is labor and b is output elasticity of labor

TC = K*4+L*10
By minimizing TC and setting Q = 500, running the solver using Evolutionary solver method we get, L=12.48 and K =12.49 units

Solver Parameters Set Objective SLS12 OYalue of 500 By Changing Variable Cells: $J$12:$K$12 Subject to the Constraints: I$12 500 TC 175 500 12 12 Add Change Delete Reset Al Make Unconstrained Variables Non-Negative Select a Solving Method: Evolutionary Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve