Earl sells lemonade in a competitive market on a busy street corner in Philadelp

Question

Earl sells lemonade in a competitive market on a busy street corner in Philadelphia. His production function is f(x_1,x_2) = x_1^1/3x_2^1/3, where out-put is measured in gallons, x_1 is the number of pounds of lemons he uses, and x_2 is the number of labor-hours spent squeezing them. (i) Does Earl have constant, decreasing, or increasing returns to scale? (ii) Let w_1 and w_2 denote the cost of a pound of lemon and the wage rate for lemon squeezers, respectively. Write down Earl's cost minimization problem. (iii) Solve Earl's cost minimization problem. (iv) What is Earl's cost function?

Explanation / Answer

(i) To find out returns to scale.

SHortcut is to add the powers of the two inputs: 1/3 + 1/ 3 = 2/3

Since 2/3 > 1 DECREASING RETURNS TO SCALE

(ii) Cost minimization"

min(X1 + X2) W1X1 + W2X2

(iii) Cost function

C = W1X1 + W2X2

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