Earl sells lemonade in a competitive market on a busy street corner in Philadelphia. His production function is f(x1, x2) = x11/3 x21/3, where output is measured in gallons, x1 is the number of pounds of lemons he uses, and x2 is the number of labor-hours spent squeezing them.
(a) Does Earl have constant returns to scale, decreasing returns to scale, or increasing returns to scale?
(b) Where w1 is the cost of a pound of lemons and w2 is the wage rate for lemon-squeezers, the cheapest way for Earl to produce lemonade is to use w1/w2 hours of labor per pound of lemons.
(c) If he is going to produce y units in the cheapest way possible, then the number of pounds of lemons he will use is x1(w1, w2, y) = ______ and the number of hours of labor that he will use is x2(w1, w2, y) = ______.
(d) The cost to Earl of producing y units at factor prices w1 and w2 is c(w1, w2, y) = w1x1(w1, w2, y)+w2x2(w1, w2, y) = _____.