Question

Suppose you have the following production function , Q=f(L,k)=10L1/2K1/2. In addition the price of labor is$1and the price of capital is$4. So what is the optimal amount of labor and capital if you want to produce 20 units?

Answer 1

$\frac{МРL}{МРK} =\frac{1}{4}$

$\frac{ΔK }{ΔL} = \frac{1}{4}$

К= 0.25L

$10=10L^{0.5}K^{0.5}$

$1=L^{0.5}K^{0.5}$

$1=L^{0.5}(0.25L)^{0.5}$

L=2

$К= 0.25L=0.25\times2=0.5$