Question

Earnie sells lemonade at a busy street corner in Rollaville. His production function is f(x,y) = x^1/4*y^1/2 where output is measured in gallons, x is the number of pounds of lemons he uses, and y is the number of labor-hours spent squeezing them. The price of a pound of lemons is $1 and the wage rate for the lemon-squeezer (Earnie’s best friend, Bert) is also $1. While Earnie can hire Bert for any amount of time, he has only three choices of amount of lemons available to him: 1 pound, 16 pounds, and 81 pounds.

(a) Does Earnie’s production process exhibit increasing, decreasing, or constant returns to scale? SHOW your work.

(b) Suppose that Earnie has decided to use exactly one pound of lemons. What are his average cost and marginal cost? Denote them as AC1 and MC1, respectively. Find the minimum point of AC1. (REMINDER: If the total cost function is given by c(q) = Aq2 +B, where A and B are constants, then the marginal cost is MC(q) = 2Aq.)

(c) Repeat with 16 pounds of lemons and find AC16 and MC16. Find also the minimum point of AC16.

(d) Repeat with 81 pounds of lemons and find AC81 and MC81. Find also the minimum point of AC81.

(e) Find the range of output (lemonade) where AC16 is the smallest of the three average costs.

(f) Find the range of output (lemonade) where AC81 is the smallest of the three average costs.

(g) Use your answers to (b)–(f), draw average costs and marginal costs. In addition, indicate Earnie’s “long-run” average cost curve when only these three different amounts of lemons are available to Earnie. Make sure your graphs contain (1) minimum values of each of the three short-run average costs and (2) output quantities that you found in (e) and (f).

Specifically need E, F, & G. Thank you in advance.

Answer 1