Water Resource Economics

1. Water Resource Economics Water Resources Planning and Management Daene C. McKinney

2. Consumers • Purchase “goods” and “services” • Have “preferences” expressed by “utility” function Good 2 Good 1

3. Consumer’s Budget • Consumers have a “budget”, expressed by a budget constraint Good 2 Good 1

4. Consumer’s Problem 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

5. Consumer’s Problem (2 goods) Good 2 Good 1 Solution: slope of budget line equals slope of indifference curve

6. Demand • Solution to Consumer’s Problem gives puschase amounts which aggregate to demand

7. CS = Net Benefit = 53 WTP = Gross Benefit = 93 Total cost = 40 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 Quantity, q

8. Willingness-to-Pay

9. 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

10. Firms • Firms produce outputs from inputs (like water) • Firm objective: maximize profit input 2 output input input 1

11. Production Function Ymax = maximum yield (mt/ha) b0… b8 = coefficients, x = irrigation water applied (mm) Emax = Max ET (mm) s = irrigation water salinity (dS/m) u = irrigation uniformity

12. Profit • Output • Input • Revenue • Cost • Profit

13. The Firm’s Problem

14. Revenue – Monopolistic Firm Revenue • Marginal Revenue (1) (2) • Increase in output (dy) has two effects • (1) Adds revenue from sale of more units, and • (2) Causes value of each unit to decrease

15. Revenue – Competitive Firm Revenue • Competitive firm: p is constant • Marginal Revenue • derivative WRT y

16. Example Linear demand function • Revenue • Marginal revenue • slope is twice that of demand

17. Firm’s Problem – 2nd Way

18. Cost Functions Total Cost (fixed and variable costs) Average cost (cost per unit to produce y units) Marginal cost (cost to produce additional unit)

19. Example – Competitive Firm • How much water should a water company produce

20. Example – Monopolistic Firm • Firm influences market price • Choose production level and price to maximize profit

21. Consumers' and Producers’ Surpluses • Consumers' Surplus • amount consumer willing to pay minus amount actually paid, but didn’t have to • Reflects benefit to consumer • Producers' Surplus • amount producer would have been willing to accept (cost of production) plus additional amount from consumer • Reflects benefit to producer

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

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

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

25. Objective Function • Maximize economic profit from water supply for irrigation, M&I water use, and hydroelectric power generation, subject to institutional, physical, and other constraints

26. Pricing • Demand affected by price of water • price elasticity of demand: • %change in demand for %change in price • Conservation • Non-Price methods (education, etc.) • Price methods • “declining block rates” - the more water used, the lower the price for the last units of use (discourages conservation) • “alternative rate structures” - encourage users to reduce their consumption • Increasing (or inverted) block: Rates increase at set usage level intervals • Seasonal block: Two different rate structures are set (one in the summer and one in the winter) • Baseline block: A baseline usage water usage amount is set based on a customer's winter use and a surcharge is then imposed for any use over the baseline during the summertime Price $3/1,000 gallons = 174 gal/day/person = 870 million gal/day Dallas-Fort Worth area (5 million) Elasticity In Texas elasticity = -0.32 Consumption will decline 3.2% for every 10% rise in price

27. Prices for Water Source: World’s Water 2002-2003, Table 17.