In the 1930s a prominent economist devised the following demand function for cor

Question

In the 1930s a prominent economist devised the following demand function for corn:

6,600,000 q1.3 In the 1930s a prominent economist devised the following demand function for corn: where q is the number of bushels of corn that could be sold at p dollars per bushel in one year. Assume that at least14,000 bushels of corn per year must be sold. How much should farmers charge per bushel of corn to maximize annual revenue? How much corn can farmers sell per year at that price? What will be the farmers' resulting revenue?

Explanation / Answer

a)
Revenue = pq = [6,600,000/q^1.3] q
Revenue = 6,600,000 q^(-0.3)

R = 6,600,000 q^(-0.3)
ln (R) = 6,600,000 -0.3q
differentiate both sides with respect to q
(1/R) dR/dq = 6,600,000 -0.3
dR/dq = R [6 599 999.7] = 0

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