Question

given Q= 100K^0.5 L^0.5 w=50 r=40 show how to determine the amount of labor and capital that the firm should use in order to minimize the cost of producing 1,118 units of output. what is the minimum cost?

Answer 1

In this exercise we have to use the knowledge of function to write the minimum production cost, so we have to:

$K=13.975$

Thus writing the function that corresponds to this will be:

$MPK = Q'(K) = 50L^{0.5}/K^{0.5} = 25\\MPL = Q'(L) = 50K^{0.5}/L^{0.5} = 100$

Now calculating the minimum production cost we have:

$MPK/r = MPL/w\\MPK/40 = 100/50\\MPK =80\\MPK = 50L^{0.5}/K^{0.5} = 80\\K=(1.118/80)= 13.975$

See more about functions at brainly.com/question/14674614