Question

The production function for Superlite Sailboats, Inc., is
Q = 20K 0.5 L 0.5
with marginal product functions
MPK = 10 (L/K) 0.5 and MPL = 10(K/L) 0.5
If the price of capital is $5 per unit and the price of labor is $4 per unit, determine the path for the firm.
The firm currently is producing 200 units of output per period using input rates of L = 4 and K = 25. Is this an efficient input combination? Why or why not? If not, determine the efficient input combination for producing an output rate of 200.

Answer 1

$С=25*5+4*4=141$; C-cost

We have a an efficient input combination when C=min. It is impossible if MPK=MPL

$10*(\frac{L}{K})^{0.5}=10*(\frac{K}{L})^{0.5}$

$K=L$

$200=20*K^{0.5}*K^{0.5}$

$K=L=10$

$C=10*5+10*4=90$