Remember Earl, who sells lemonade in Philadelphia? You met him in the chapter on cost functions. Earl’s production function is f(x1, x2) = x1/3 1 x21/3, where x1 is the number of pounds of lemons he uses and x2 is the number of hours he spends squeezing them. As you found out, his cost function is c(w1, w2, y) = 2w11/2 w21/2 y3/2, where y is the number of units of lemonade produced.
(a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the price of lemonade is p, Earl’s marginal cost function is MC(y) = _______ and his supply function is S(p) = _____. If lemons cost $4 per pound and the wage rate is $9 per hour, his supply function will be S(p) = ______.
(b) In general, Earl’s marginal cost depends on the price of lemons and the wage rate. At prices w1 for lemons and w2 for labor, his marginal cost when he is producing y units of lemonade is MC(w1, w2, y) = _______. The amount that Earl will supply depends on the three variables, p, w1, w2. As a function of these three variables, Earl’s supply is S(p,w1, w2) = ______.