Solving Cobb-Douglas production function to find the optimal combination of cpital and labor.
Assume that a firm wants to produce 40 units of a product. The firm's production function is the following Cobb-Douglas production function
Q= K1/2 L1/2,
Where Q is the level of output and L represents labor, and K represents capital.
Where PL= $12 is the price of labor that is wages, and Pk= $3 is price of capital.
a) Describe the optimal combination of capital and labor that this company should employ?
b) Illustrate what is the associated minimum cost incurred by the firm?
c) Find and interpret the value of the lagrange multiplier λ?
d) Check if the necessary condition for this cost minimization problem hold or not, and give economic interpretation?
e) Derive the isoquant and isocost functions?