A competitive firm has a production function described as follows. "Weekly out put is the square root of the minimum of the number of units of capital and the number of units of labor employed per week." Suppose that in the short run this firm must use 16 units of capital but can vary its amount of labor freely.
a. Write down a formula that describes the marginal product of labor in the short run as a function of the amount of the labor used.
MP=1/(2Lsubscript of1/2) if L<16, MP =0 if L>16.
b. If the wage is w=$1 and the price of output is p=$4, how much labor will the firm demand in the short run? Hint: Solve for L in p*MP=w using the given values for p,w and MP.
c. What if w=$1 and p=$10?
d. Write down an equation for the firm's short-run demand for labor(L) as a function of w and p.