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Show where each D^ is written as function of the gross output vector X^, X2, . . . XIi. Function ( 2) says that if % increases, ceteris paribus with respect to all the other final demand items, then income will increase and, therefore, economic welfare will have been improved. While the form of ( 2) emphasizes the direct relationship between the index of welfare and the final demand items, it will be convenient for what follows shortly to use the inverse form of the arguments of ( 2), i. e., make each output, Xj, a function of the final demand vector Dj., D2, * . ., Dn. In other words, given the level of income Y, there is a unique relationship between the gross output vector and the final demand vector. The operational form of the welfare function is then: ( 3) YCXi ( Pi, D2, . . ., Dn), X2 ( Pu Da Dn), . • *, Xn( Di, D2, . . ., Dn) J. The economic resources of a region consist of water, land, labor, knowledge, and capital. All of these are constraints on the arguments or determinants of ( 3)* For our purposes, however, we treat water as the only constraint, and assume that the other factors are always available in sufficient quantity to just supply their demand requirements. It is also to be noted that, unlike the factor " labor," the cost of storing and transporting the factor " water" will enter explicitly into the analysis. Not that the supplying cost of labor is zero in terms of resources allocated to this activity, but it is a " private" cost born by either the firm or the householder involved, whereas the cost of water transport and storage facilities is mostly ( but not exclusively) a " public" cost. In other words, we do not take into consideration the resources embodied in the transportation service that a worker 10 |