A producer’s production function is q=6K^(1/3)L^(1/2). The market price for the firm’s output is p, the cost of capital is $4 per unit used and the cost of labor is $3 per unit.
a. Write an equation for the firm’s long-run profit.
b. Find the factor demands for the two inputs.
c. Find an equation for the supply function of the firm and graph it.
d. If the price of the firm’s output is p=2, what are the firm’s level of output and profit?