Problem Set 1 Key

# Problem Set 1 Key - AAE 320 Farming Systems Management...

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AAE 320 Farming Systems Management Problem Set #1 Answer Key 1) You are a crop consultant helping a grain farmer in the Central Sands of Wisconsin determine his economically optimal irrigation level. Using his records for different fields over the last 4 years, you calculated his average yield for different levels of total water (from irrigation and rainfall) the corn received during the growing season. There has never been a year when the corn has received enough water from rainfall only (he always has to pump some). Fill in the table below and answer the following questions. Water Received (inches) Average Corn Yield (bu/ac) Marginal Product (bu/ac) Value of the Marginal Product (\$/ac) 17.0 201.0 18.5 204.0 2.00 10.00 20.0 206.4 1.60 8.00 21.5 208.4 1.33 6.67 23.0 210.1 1.13 5.67 24.5 211.5 0.93 4.67 26.0 212.0 0.33 1.67 27.5 212.3 0.20 1.00 The marginal product is the change in output over the change in input use, which here is calculated as the differences. As a result, there is no marginal product for the first row. The first entry is (204.0 – 201.0)/(18.5 – 17) = 2.00 bu/ac. The calculations for the remaining rows are reported in the table above. The value of this marginal product depends on the input price. The numbers in the table are calculated assuming a corn price of \$5/bu in the last column. The first entry is \$5/bu time 2.00 bu = \$10.00. The calculations for the remaining rows are reported in the table above. a) When he plants, he forward contracts his corn at a price of \$5.00/bu. The cost of pumping one acre inch of water is \$6.00 per acre inch. How much water should he plan on making sure his corn has? For economically optimal input use, the value of the marginal product (VMP) should equal the cost of the marginal input. In this table, \$6.00/acre-inch cost matches the VMP somewhere between 21.5 and 23 inches, closer to 23 inches, or at about 22.5 inches. b) In the early summer, his old irrigation pump fails and he replaces it with a new, more energy efficient pump. His pumping costs fall to \$4.50 per acre inch. How much water should he plan on making sure his corn has? The VMP’s are reported in the table match the pumping cost of \$4.50/acre-inch somewhere between 24.5 and 26 inches, much closer to 24.5 than 26 inches, so about 24.75 or 25 inches is the economically optimal water for the crop.

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2 c) Because his new pump has a pumping cost that is 25% lower, he wants to increase his pumping to make sure his corn has 25% more water. Use the table above to explain to him why this is not a profitable plan. Give an intuitive explanation of what the table above means in normal language, not “econ-speak.” A short paragraph of a few sentences and some dollar amounts should suffice. The key to note is that he says he is going to maximize profit per acre.
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## This note was uploaded on 08/08/2008 for the course AAE 320 taught by Professor Mitchell during the Spring '08 term at University of Wisconsin.

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Problem Set 1 Key - AAE 320 Farming Systems Management...

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