WheatStorageHW - Lyon Wheat Storage Home-Work Problem This...

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Lyon Wheat Storage Home-Work Problem 1. This is a wheat storage problem. Even though, it is incomplete, it is complicated enough for a home-work problem. We are working with a closes economy with perfect forsight. We start the problem at t = 0 with the harvest of the wheat crop just completed and the wheat in storage. Another wheat harvest will take place at the beginning of one year. For now we will not model the planting, growing, harvesting, and transporting of the wheat to storage. Instead we will assume that the volume harvested and placed in storage at t = 1 is known to be x 1 . We do this because 8 * (1) depends upon the harvest, x 1 , and the carryover. Any wheat that is carried over into the next time period will have the same value as newly harvested wheat that is in storage. Note that the time line is viewed as Time Period 0 = (0, 1] , Time Period 1 = (1, 2] , etc. with potential discontinuities between each of these time periods. The harvest coming in instantaneously is the main source of the discontinuities. Max: W = m 0 1 e ! rt [ m 0 y(t) D(v) dv C(y(t), x(t))]dt + e r S(x(1)+x 1 ) (1) S.t: dx dt ))) = y(t)
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WheatStorageHW - Lyon Wheat Storage Home-Work Problem This...

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