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Show provides for himself when he drives his automobile to and from his place of employment; but we can, if he rides a commercial or municipal bus. In the case of water, however, the resources embodied in aquaducts, irrigation canals, dams and reservoirs, are explicitly taken into account in the theoretical considerations of this section. Our complete model can now be formalized. We have a welfare function ( 3), which is to be maximized subject to a water constraint and a constraint on the amount of resources the community has alloted to water supplying facilities. In Lagrangian terminology, we want to maximize: ( 4) Y[ Xi( Di, . . ., Dn), . . ., Xn ( Dl, . . ., Dn)]+ XEW - Jj> Wj ( XjH + rcc - 2 » Cj ( wp], where the first term is the welfare function ( 3), the second term is the water constraint with Wj a function of X;, and the third term is the resources ( in dollars) constraint on water facilities with C; a function of W.. Equation ( 4) is a •* J general equilibrium representation of the economy of Utah. As such, it will reflect all of the interactions involved in a change in one of its arguments. It is necessary to keep this in mind, if what follows is to make any sense. Equation ( 4) will be maximized when the following first- order conditions hold: 8 / e^ 3Y dXi ,£- 3Wi dXi c" SCi 3Wi dXi rt , i dXj ^ 3Wj dXj AaCj dWj dXj 2L Ixl d57 *? W\ dDi fcdWi lX\ dDi Rearranging ( 5) gives: o The system is open with respect to the household. It is assumed stable. 11 |
