Lizzie sells lemonade in a competitive market on High street in the

university area. Her production function is f(x1, x2)=x1^1/3 X2^1/3, where output is measured in

gallons, x1 is the number of pounds of lemons, and x2 is the number of hours of labor spent

squeezing lemons.

(a) Does Lizzie's production function exhibit increasing, decreasing, or constant returns

to scale?

(b) If w1 is the cost of a pound of lemons, w2 is the wage rate of lemon-squeezers,

marginal product of x1 is MP1= 1/3X1^-2/3 X2^1/3 and marginal product of x2 is MP2= 1/3X1^1/3 X2^2/3, what is the cheapest way for Lizzie to produce lemonade in terms of hours of labor per pound of

lemons? (Hint: TRSslope of the isocost line)

(c) If Lizzie wants to produce y gallons of lemonade in the cheapest way possible, then

how many pounds of lemons will she use?

(d) If Lizzie wants to produce y gallons of lemonade in the cheapest way possible, then

how many hours of labor will she use?

(e) What is Lizzie's minimum cost as a function of output and factor prices (cost

function)?

(f) What is Lizzie's average cost function, AC(y)?

(g) What happens to Lizzie's average cost function when output y increases?

(h) How is your response in part (g) related to your response in part (a)?