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

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

Consumers Purchase goods and services Have preferences expressed by utility function Good 2 Good 1

Consumers Budget Consumers have a budget, expressed by a budget constraint Good 2 Good 1

Consumers Problem Purchase so that the ratio of marginal benefit (marginal utility) to marginal cost (price) is equal among all purchases The ratio (in dimensions of \$/unit or shadow price) is the Lagrange multiplier, the change in utility for a change in consumer income

Consumers Problem (2 goods) Solution: slope of budget line equals slope of indifference curve Good 2 Good 1

Demand Solution to Consumers Problem gives puschase amounts which aggregate to demand

Willingness-to-Pay Value - What is someone willing to pay? Suppose consumer is willing to pay: – \$38 for 1 st unit of water – \$26 for 2 nd unit of water – \$17 for 3 rd 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 – Consumers surplus is \$53 WTP = Gross Benefit = 93 CS = Net Benefit = 53 Total cost = 40 Price, p Quantity, q

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 output input 1 input 2

Production Function Y max = maximum yield (mt/ha) b 0 … b 8 = coefficients, x= irrigation water applied (mm) E max = Max ET (mm) s = irrigation water salinity (dS/m) u = irrigation uniformity

Profit Output Input Revenue Cost Profit

The Firms Problem

Revenue – Monopolistic Firm Revenue Marginal Revenue 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 (1)(2)

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

Example Linear demand function Marginal revenue –slope is twice that of demand Revenue

Firms Problem – 2 nd Way

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

Example – Competitive Firm How much water should a water company produce

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

Consumers' and Producers Surpluses Consumers' Surplus – amount consumer willing to pay minus amount actually paid, but didnt 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

Profit from agricultural demand sites = equal to crop revenue minus fixed crop cost, irrigation technology improvement cost, and water supply cost Benefit Function for Ag Water Use Aharvested area (ha) p crop price (US\$/mt) FC fixed crop cost (US\$/ha) TCtechnology cost (US\$/ha) C w water price (US\$/m3) w ag water delivered to demand sites in growing season (m3)

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\$), w muni,t municipal water withdrawal in period t(m3) w 0 maximum water withdrawal (m3) p 0 willingness to pay for additional water at full use (US\$) eprice elasticity of demand (estimated as -0.45) 1/e

Benefit Function for Hydropower The profit from power generation P t Power production for each period (KWh) w turbine,t Water passing turbines for each period (m 3 ) P power Price of paid for power (US\$/KWh) C p Cost of producing power (US\$/KWh)

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

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

Prices for Water LocationDateUS\$/m3 US\$/1000 gal Cario1993\$0.04 \$0.15 Syria NA\$0.07\$0.26 Egypt (Beheira)1993\$0.07\$0.26 Gaza City1998\$0.12\$0.45 Morocco (Meknes)2000\$0.20\$0.76 Algiers1998\$0.21\$0.79 Amman1999\$0.23\$0.87 Sana'a1999\$0.25\$0.95 Gaza (Khan Younis)1998\$0.29\$1.10 Tunisia1999\$0.32\$1.21 Lebanon1998\$0.32\$1.21 Morocco) Marrakech2000\$0.39\$1.48 Canada1999\$0.41\$1.55 US1999\$0.50\$1.89 Morocco (Safi)2000\$0.53\$2.01 Spain1999\$0.54\$2.04 Ramallah1994\$0.91\$3.44 UK1999\$1.15\$4.35 France1999\$1.17\$4.43 Netherlands1999\$1.19\$4.50 Denmark1999\$1.61\$6.09 Germany1999\$1.81\$6.85 Source: Worlds Water 2002-2003, Table 17.

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