A firm uses capital and labor to produce output according to the production function q =4 rad(KL) , for which MP L= 2 rad(K/L) and MP K= 2 rad(L/K) .
a. If the wage w=$1/labor-hr. and the rental rate of capital r=$4/machine-hr., what is the least expensive way to produce 16 units of output?
b. What is the minimum cost of producing 16 units?
c. Show that for any level of output, q, the minimum cost of producing q is $q.
d. Explain how a 10% wage tax would affect the way in which the firm chooses to produce any given amount of output.