Problem Set 1

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

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AAE 320 Farming Systems Management Problem Set #1 Due February 22, 2008 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 20.0 206.4 21.5 208.4 23.0 210.1 24.5 211.5 26.0 212.0 27.5 212.3 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? 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? 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.

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

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