6. The short-run production function for a particular agricultural crop is critically dependent on the level of

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6. The short-run production function for a particular agricultural crop is critically dependent on the level of rainfall during the growing season, the relationship being Y ¼ 30 þ 3X .075X2

, where y is yield per acre in bushels, and x is inches of rainfall during the growing season.

(a) If the expected value of rainfall is 20 inches, can the expected value of yield per acre be as high as 70 bushels per acre? Why or why not?

(b) Suppose the variance of rainfall is 40 square inches.

What is the expected value of yield per acre? How does this compare to the bound placed on E(Y) by Jensen’s inequality?

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