HW_S2 - EEP101 HW2 Spring 2007 1. There are two lettuce...

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EEP101 HW2 Spring 2007 1. There are two lettuce farmers. The only input they use to produce lettuce is water and the production function is given by 2 300 ( ) e e Y W W = - , where Y is the per- acre production of lettuce, e W is the effective water. Effective water refers to water really used by lettuce. It is the fraction of water applied that is really used by lettuce. Specifically, e i W hW = , , i A B = , where W is the amount of water applied per acre, i h is input use efficiency, or fraction of the applied water that is used by lettuce. 0.8 A h = , and 0.5 B h = under the traditional irrigation method “tunnel”. (Farm A’s soil quality is better so it can use water more effectively than farmer B’s). Now the technology of sprinkle irrigation method becomes available. If the farmers switch to the new technology, more applied water will actually reach lettuce. Specifically, min(1.5 ,1) new i i h h = . That is, the new technology could increase input use efficiency by 1.5 times the old input use efficiency or up to 1. If the farmer switches to the sprinkle, they have to invest a one-time fixed cost of $1500 for the equipment. Moreover, there is a marginal maintenance cost of 0.1 per unit of applied water. The old technology is assumed to have zero fixed and zero marginal cost. The price of lettuce is $1 per unit (the industry is assumed to be competitive so you can ignore the two farm’s impacts on either the price or
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HW_S2 - EEP101 HW2 Spring 2007 1. There are two lettuce...

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