Question 7 (10 points) You\'re a farmer trying to decide what to plant. You can

Question

Question 7 (10 points) You're a farmer trying to decide what to plant. You can plant either wheat or corn, but not both. You've been to see the county extension agent, who has estimated the relationship between the number of workers you employ and the yield of either wheat or corn. These are given below in Table 2. The extension agent predicts the price of wheat will be $20/ton, corn will sell for S15/ton, and agricultural workers will make S250/month. Table 2. Workcrs Tons of wheat/month Tons of corn/month 10 25 45 70 90 20 45 75 100 120 135 145 150 153 115 120 122 a.What's the profit maximizing work force if you plant wheat? What's the resulting profit if you plant wheat? What's the profit maximizing work force if you plant corn? d. What the resulting profit if you plant corn? Which crop will you plant if you wish to maximize your profit?

Explanation / Answer

MPL (nth unit) = Q (n units) - Q ((n-1) units)

MRPL = MPL x Price

a) Profit would be maximized where MRPLw >= wage rate for the last unit of worker employed.

L = 6 workers

Q = 105 tons

b) Profit = 105 x 20 - 6 x 250 = $600

c)

Profit would be maximized where MRPLc >= wage rate for the last unit of worker employed.

L = 5 workers

Q = 120 tons

d) Profit = 120 x 15 - 5 x 250 = $550

e) Wheat would yield a higher profit than corn.

L Qw (tons) MPLw MRPLw Qc (tons) MPLc MRPLc 0 0 0 1 10 10 200 20 20 300 2 25 15 300 45 25 375 3 45 20 400 75 30 450 4 70 25 500 100 25 375 5 90 20 400 120 20 300 6 105 15 300 135 15 225 7 115 10 200 145 10 150 8 120 5 100 150 5 75 9 122 2 40 153 3 45

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