APPENDIX A
 Economic and Statistical Model Formulation

 The purpose of this appendix is to summarize economic (the-
oretical and statistical) models upon which the analysis was
based. The economic model is discussed first.


Economic Theory of Derived Demand
 Assume the following production function for an individual
firm:
 q=f (x, x2, ...,x) (A.1)
where
 q= quantity of the good or service produced
 xj=the amount of input j (such as water) used, j=l,.. m.
If a cross-sectional aggregation of all firms having a similar
production process were made, and if it were assumed these
firms faced different prices for inputs, then variation in use of
these inputs between the firms will exist. This variation in input
use is described by the theory of derived demand.1
 A long run derived demand for any input k can be developed
by maximizing the following expression:


 Max = pq rix (A.2)
 j=1

and solving the first order conditions simultaneously for the xj
to yield demand curves of the following general form (for each
input k):
 xa=g (rk, ri, p) (A.3)
where
 x1= demand for input k;
 rk= price for input k;'
 ri= price (a vector of input prices) of all other variable inputs
 j k, j= 1, 2,.. ., m, and
 p= price of the good or service produced.
 As shown in Equation (A.3), the demand for any input k is a
 function of the price of that input, the price of the output, and

 IMore detailed explanations of the theory of derived demand may be
 found in Mosak [22, pp. 761-87] and Ferguson [7, pp. 175-89].