Answer to Question #286036 in Microeconomics for Etsub

Question

Suppose the production function a firm producing Q requires the use of only labor and

capital. The production function for the product is given by: Q-1/4K3/4. The amount of capital used is fixed at 5 units. Then,

A. Determine MPL and APL function

B. Determine MP and AP function

C. Compute MRTSKL & MRTS LK

Answer 1

Solution:

A.). Q = L^1/4K^3/4

MP_L = $\frac{\partial Q} {\partial L}$ = 0.25L^-0.25K^0.75

AP_L = $\frac{ Q} {L}$ = 0.25K^0.75 $\div$ L         

 

B.). MP_K = $\frac{\partial Q} {\partial K}$ = 0.75L^0.25K^-0.75

AP_K = $\frac{ Q} {K}$ = 0.25L^0.25 $\div$ K        

 

C.). MRTS_KL =  MP_L $\div$ MP_K = 0.25L^-0.25K^0.75 $\div$ 0.75L^0.25K^-0.75 = 0.3K^1.5 $\div$ L^0.5

MRTS_LK =  MP_K $\div$ MP_L = 0.75L^0.25K^-0.75 $\div$ 0.25L^-0.25K^0.75 = 3L^0.5 $\div$ K^1.5