Optimizing Water Resource Management through Economic Analysis

Economic Analysis of Alternative Water Plans: Water Resource Economics Water Resources Planning and Management Daene C. McKinney

River Basin Planning ? ? ? ? ??,? ??,? ??,? ??,? ??,? ??,? ??,? ??,? ??,? ???????? ? = ?? + ?? + ?? ?=? S.T. ??+?= ??+ ?? ?? ?? ? Inflow Qt Reservoir St K1 Municipal Water Supply Benefits: Try to meet targets Irrigation Water Supply Benefits: Try to meet targets Hydropower Benefits: Try to meet targets Rt Municipal Losses Gains Irrigation Environmental Flow wM wI wP TM,t monthly target for municipal demand TI,t monthly target for irrigation demand TP,t monthly target for recreation weight for Municipal demand weight for Irrigation demand weight for Recreation ZI penalty for missing target in month t minimum XI,t TI,t target release

Decision Making Developing and managing water resources systems involves making decisions. Modeling and data management tools can contribute to the information needed to make informed decisions. Decisions in water resources management inevitably involve making tradeoffs compromising among competing opportunities, goals or objectives. One of the tasks of water resources system planners or managers involved in evaluating alternative designs and management plans or policies is to identify the tradeoffs, if any, among competing opportunities, goals or objectives. It is then up to a largely political process involving all interested stakeholders to find the best compromise decision.

System Performance Criteria Measures indicating just how well different management plans and policies serve the interests of all stakeholders are typically called system performance criteria B/C framework Convert impacts into a single monetary metric Find the plan that maximizes benefits vs costs. Does not address distributional issues of who benefits and who pays, and by how much. Water resources planning and management takes place in a multi-criteria environment Stakeholders individuals or interest groups who have an interest in the outcome of any plan Quantification of an objective is the adoption of some quantitative scale that provides an indicator for how well the objective would be achieved

Economic Criteria Water resources system development and management is often motivated by economic criteria. Two economic concepts: scarcity and substitution. Scarcity - supplies of natural, synthetic and human resources are limited. Hence people are willing to pay for them. They should therefore be used in a way that generates the greatest return, i.e. they should be used efficiently. Substitution - individuals, social groups and institutions are generally willing to trade a certain amount of one objective value for more of another

Objective for Ag, Muni and Hydropower Water Use Maximize economic profit from water supply for irrigation, M&I water use, and hydroelectric power generation, subject to institutional, physical, and other constraints Z = AG(wag)+ [Muni(wmuni,t)+Power(wpower,t)] t

Objective for Agricultural Water Use Profit from agricultural demand sites = equal to crop revenue minus fixed crop cost, irrigation technology improvement cost, and water supply cost Ag(wag,t)= A pY( wag,t )-FC-TC -Cw wag,t t t A p FC TC Cw wag harvested area (ha) crop price (US$/mt) fixed crop cost (US$/ha) technology cost (US$/ha) water price (US$/m3) water delivered to demand sites in growing season (m3)

Objective for Municipal Water Use Benefit from industrial and municipal demand sites is calculated as water use benefit minus water supply cost -Cwwmuni,t a wmuni,t w0 Muni(wmuni,t)=w0p0 +2a+1 (1+a) Muni(w) wmuni,t w0 p0 e benefit from M&I water use (US$), municipal water withdrawal in period t(m3) maximum water withdrawal (m3) willingness to pay for additional water at full use (US$) price elasticity of demand (estimated as -0.45) 1/e

Objective Function for Hydropower Water Use The profit from power generation ( ) Pt(wturbine,t) t Power(wturbine,t)= Ppower-Cp Pt wturbine,t Ppower Cp Power production for each period (KWh) Water passing turbines for each period (m3) Price of paid for power (US$/KWh) Cost of producing power (US$/KWh)

Consumers Purchase goods and services Have preferences expressed by utility function = x ( , ,..., ) x x n x 1 2 = x ( ) ( , ,..., ) u u x x n x 1 2 x2 Good 2 Indifference curve ) , ( 2 u x 1x Better Bundles Increasing utility Worse Bundles u x1 Good 1

Consumer s Budget Consumers have a budget , expressed by a budget constraint m x p x p + 2 2 1 1 x2 Good 2 Unaffordable bundles m/p2 Budget line p1x1+p2x2=m Slope = -p1/p2 Affordable bundles m/p1 x1 Good 1

Consumer s Problem x Maximize ( ) u subject to x p m x 0 L u = = = , 0 ,..., 1 p k K K k x x = + x x = k ( , ) ( ) L u m p kx k k k 1 K L = = = k 0 m p x k k 1 u u = x k = = ,..., 1 k K m p k The ratio (in dimensions of $/unit or shadow price) is the Lagrange multiplier, the change in utility for a change in consumer income Purchase so that the ratio of marginal benefit (marginal utility) to marginal cost (price) is equal among all purchases

Consumer s Problem (2 goods) Maximize ( , ) u x x 1 2 subject to Good 2 + = x2 p x p x m 1 1 1 1 Indifference curve slope = MRS12 u = 0 p Optimal choice MRS12 = -p1/p2 1 x 1 u Budget line slope = -p1/p2 = 0 p x2* 2 m x 2 Increasing utility + = ( ) 0 p x p x 1 1 2 2 x1* Good 1 x1 u u x x 1 2 = = p p Solution: slope of budget line equals slope of indifference curve 1 2

Demand Solution to Consumer s Problem gives puschase amounts which aggregate to demand Price, p Maximize u(x) subject to p x m x 0 Demand curve x(p,m) ( ) x = x p * * , m Quantity, x

Willingness-to-Pay Value - What is someone willing to pay? Suppose consumer is willing to pay: $38 for 1st unit of water $26 for 2nd unit of water $17 for 3rd unit of water And so on If we charge p* = $10 4 units will be purchased for $40 But consumer is willing to pay $93 Consumer s surplus is $53 Price, p Price, p 40 38 CS = Net Benefit = 53 30 26 WTP = Gross Benefit = 93 20 17 Total cost = 40 12 p*=10 Quantity, q 1 2 3 4 5 Quantity, x

Willingness-to-Pay

Market Prices Revealed WTP Some goods or services are traded in markets Value can estimated from consumer surplus (e.g., fish, wood) Ecosystem services used as inputs in production (e.g., clean water) Value can be estimated from contribution to profits made from the final good Some services may not be directly traded in markets But related goods that can be used to estimate their values are trade in markets Homes with oceanviews have higher price People will take time to travel to recreational places Expenditures can be used as a lower bound on the value of the view or the recreational experience

Firms Firms produce outputs from inputs (like water) Firm objective: maximize profit Input, x2 input 2 y output Production function y = f(x) Isoquant 0 = x ( ) f y y2 y1 Slope = df/dx Increasing output y0 Input, x1 x input input 1

Production Function max Y = + + [ ( / ) ln( / )] Y a a x E a x E 0 1 max 2 max Ymax b0 b8 x Emax s u = maximum yield (mt/ha) = coefficients, = irrigation water applied (mm) = Max ET (mm) = irrigation water salinity (dS/m) = irrigation uniformity = = = + + + + + + a a a b b b b b b u u u b b b s s s 0 0 1 2 1 3 4 5 2 6 7 8 8.00 II III I Output, y (ton/ha) 6.00 4.00 2.00 0.00 0 5,000 10,000 15,000 20,000 Input, x (m3/ha)

Profit Output Input Revenue Cost y = (x ) f x R = py N = = n C w 1 nx n = R C Profit N = (x = n ) pf w 1 nx n

The Firm s Problem N Maximize p(p,w)= pf(x1,...,xn)- wnxn n=1 f Isoprofit line = py wx slope = w/p y = = = 0 , ,..., 1 p w n N n x x n n df/dx= w/p w f n = = ,..., 1 n N y* x p n Prod. Fcn. y = f(x) slope = df/fx /w x* x

Revenue (1) Price-setting Firm R = py Revenue dR R R dp dp = + = + p y Marginal Revenue dy y p dy dy (1) (2) Increase in output (dy) has two effects 1. (1) Adds revenue from sale of more units, and 2. (2) Causes value of each unit to decrease

Revenue (2) Price-taking Firm R = py Revenue Competitive firm: p is constant ( ) dR d py Marginal Revenue derivative WRT y = = p dy dy

Example p Marginal Revenue = a 2by Revenue py = ay by2 Demand function p = a - by Linear demand function by a y p = ) ( a a b 2b y* a/b y y a/2b y p Marginal Revenue = a 2by Revenue py = ay by2 Demand function p = a - by Revenue R = a a 2 = py ay by b 2b y* a/b y y a/2b y Marginal revenue slope is twice that of demand dR 2 = b p Marginal Revenue = a 2by Revenue py = ay by2 Demand function p = a - by a a a by 2b dy y* a/b y y a/2b y

Cost Functions N = Minimize w x n n 1 n subject to 0 = ( ,..., ) f x x y 1 N L f = = = 0 ,..., 1 w n N n x x n n L 0= = 0 f y f w x m m = f w n x n

Cost Functions Total Cost (fixed and variable costs) + ) x = = w x ( ) min = : ( TC y y f ( ) ( ) TC y FC VC y Average cost (cost per unit to produce y units) ( ) TC y = AC y Marginal cost (cost to produce additional unit) dTC dVC = = MC dy dy

Example (1) Price-taking Firm How much water should a water company produce Cost Price & MC = Maximize ( ) ( ) y py TC y d dp dTC AC = 0 = + y p dy dy dy p = MC p* = = ( ) ( ) MR y p MC y p = MC y* Product y

Example (2) Price-setting Firm Firm influences market price Choose production level and price to maximize profit Price & Cost = Maximize ( ) ( ) y py TC y MC Demand MR d dp dTC = 0 = + y p AC pm dy dy dy p = MC p* dp = + = ( ) ( ) MR y y p MC y MR = MC dy = ( ) ( ) MR y MC y ym y* y

Objective Function for Agricultural Water Use Profit from agricultural demand sites = equal to crop revenue minus fixed crop cost, irrigation technology improvement cost, and water supply cost Ag(wag,t)= A pY( wag,t )-FC-TC -Cw wag,t t t A p FC TC Cw wag harvested area (ha) crop price (US$/mt) fixed crop cost (US$/ha) technology cost (US$/ha) water price (US$/m3) water delivered to demand sites in growing season (m3) Y(wag)=Ymax[a0+a1(wag/Emax)+a2ln(wag/Emax)]

Objective Function for Municipal and Industrial Water Use Benefit from industrial and municipal demand sites is calculated as water use benefit minus water supply cost -Cwwmuni,t a wmuni,t w0 Muni(wmuni,t)=w0p0 +2a+1 (1+a) Muni(w) wmuni,t w0 p0 e benefit from M&I water use (US$), municipal water withdrawal in period t(m3) maximum water withdrawal (m3) willingness to pay for additional water at full use (US$) price elasticity of demand (estimated as -0.45) 1/e

Objective Function for Hydropower Water Use The profit from power generation ( ) Pt(wturbine,t) t Power(wturbine,t)= Ppower-Cp Pt wturbine,t Ppower Cp Power production for each period (KWh) Water passing turbines for each period (m3) Price of paid for power (US$/KWh) Cost of producing power (US$/KWh)

Combined Objective Function for Ag, M&I and Hydropower Water Use Maximize economic profit from water supply for irrigation, M&I water use, and hydroelectric power generation, subject to institutional, physical, and other constraints Z = AG(wag)+ [Muni(wmuni,t)+Power(wpower,t)] t