INDUSTRIAL WATER USE In many countries, assuring an adequate water supply for economic development is a key concern, and this typically is thought of as water for industry. A growing economy and growing industrial output mean a greater need for water. The question: How does one calculate this need? How should water managers plan for future economic growth?Table 4. Manufacturing Water Intake in California and the Lower Colorado Region 1973 1983 Total Water Intake Total Water (billions of (gallon/$ Intake gallons) of value (billions of CALIFORNIA added) gallons) 20 Food and Kindred Products 137.4 74 57.7 24 Timber and Wood Products 34.6 196 16.2 26 Paper 48.2 311 42.5 28 Chemicals 39.2 62 25.0 29 Petroleum 112.8 200 74.7 32 Stone, Clay. Glass 18.6 41 16.1 33 Primary Metal Industries 11.0 49 NA 34 Fabricated Metal Products 5.2 13 5.7 35 Machinery 2.8 6 3.3 36 Electric, Electronics 4.4 4 5.3 37 Transportation Equipment 11.7 2 6.9 Other Manufacturing 4.5 12.5 Total Manufacturing 430.4 35 265.9 LOWER COLORADO REGION 20 Food and Kindred Products 2.2 41 1.0 28 Chemicals 3.1 132 1.0 32 Stone, Clay, Glass 0.9 34 0.8 33 Primary Metals 11.4 58 9.8 35 Machinery 0.4 2 0.3 36 Electric, Electronics 2.0 7 2.3 Other Manufacturing 4.5 6.1 Total Manufacturing 24.5 25 21.3 Source: Water Use in Manufacturing Special Report of 1972 and 1982 Censuses of ManufacturersI960 1966 1970 1975 1960 1966 1990 1996 Figure 4. U.S. water withdrawals by use category from 1960 1995.The first-order conditions for the profit maximization are: ()iifxpwx∂⋅=∂ 1,...,iN= These imply: (a) cost minimization ()()iijifxxwwfxx∂∂=∂∂ (b) profit maximizing choice of output ()cypy∂=∂SOME USEFUL PROPERTIES OF CONDITIONAL DEMANDS (1) (1,...,ini)xgw wy= depends essentially on RELATIVE input prices, 11,...,nnnwwww−. If all change in the 1,...,nww same proportion, every demand function remains unaffected. (...,)1,iixgw= ,nyw (2) (),0iigwyw∂≤∂ The own-price responsiveness must be non-positive. This is known as the “substitution effect.” (3) However, the cross-price derivatives can have either sign (),0ijgwyorw∂<>∂ (4) The absolute size of the cross-price derivatives depends on the ELASTICITY OF SUBSTITUTION between the pair of inputs, ix and jx, denoted ijσ. The elasticity of substitution varies INVERSELY with the curvature in isoquants between ix and jx.(5) The formula relating the elasticity of substitution to the cross price elasticity of demand is: ij j ijsεσ= where ()ln , / lniij jgwy wε≡∂ ∂ price elasticity of demand for ix with respect to jw and /jjjswx C≡ budget share -- expenditure on input ix as share of total expenditure on all inputs. (6) ijε and ijσ< / > 0 as inputs and are SUBSTITUTES /COMPLEMENTS. i j Not all inputs can be complements. (7) (),igwyy∂∂ < / > 0 according as ix is a NORMAL/INFERIOR input.. Not all inputs can be inferior. (8) Taking the derivative of the cost function with respect to an input price yields the conditional demand function for that input: ()(,,iicwygwyw∂=∂)