Market mechanisms and the efficient allocation of surface water resources in southern Alberta

Socio-Economic Planning Sciences 36 (2002) 25–49

Market mechanisms and the efficient allocation of surface water resources in southern Alberta$ Robert C. Mahana, Theodore M. Horbulykb, John G. Rowsec,* a TransAlta Energy Marketing, Calgary, Canada Department of Economics, University of Calgary, Canada c Department of Economics, University of Calgary, 2500 University Drive NW Calgary, AB Canada T2N 1N4 b

Abstract Population growth and economic expansion increasingly are stressing water resources in southern Alberta, Canada. Adopting market mechanisms may improve water use efficiency. Utilizing a novel network model of an entire river basin, we quantify the short-run efficiency gains (over one growing season) from reallocating surface water. Employing a standard welfare maximizing objective, and observing essential institutional and hydrologic structures, we find the relative efficiency gains from introducing market pricing to be under 3% for a year of surplus water flows, about 6% for a mean flow year, and more than 15% for a drought flow year. Although such gains exclude the costs of the current water allocation policy, as well as those of moving to market pricing, results tend to support the present cautious approach by the Alberta government to modify the mechanisms for allocating surface water. r 2002 Elsevier Science Ltd. All rights reserved.

1. Introduction Population growth and economic expansion increasingly are stressing water resources in southern Alberta, Canada. Improving efficiency in water use, such as by adopting market mechanisms, may reduce this stress. If the locations and users of surface water diversions change as a consequence, however, there could be widespread effects on many rural and urban users. Economic modeling of surface water uses and values for an entire river basin is a comprehensive and rational way to examine alternative allocative methods.

$

Financial support for this research was provided by Environment Canada under the University-Based Research Program on Economic Instruments. *Corresponding author. Tel.: +1-403-220-5857. E-mail address: [email protected] (J.G. Rowse). 0038-0121/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 8 - 0 1 2 1 ( 0 1 ) 0 0 0 1 3 - 1

26

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

Utilizing a nonlinear programming model that maximizes conventionally defined social welfare (consumers’ plus producers’ surplus) while observing essential institutional and hydrologic structures, we quantify the short-run efficiency gains (over one growing season) from reallocating scarce surface water. Such reallocations would be consistent with basin-wide policy reforms implementing perfectly functioning water markets. In contrast, the status quo allows unlimited and unpriced water diversions to holders of historical water rights. For our work, we develop a novel network model representing: flows in four river sub-basins; explicit conversion of untreated water into treated potable water, and of treated waste water to untreated surface water; pricesensitive water demands and exogenous choke prices; a cropping sub-model to estimate irrigation demands; and the ability to represent different hydrologic circumstances. (A ‘choke price’ for water is the price at which the quantity of water demanded shrinks to zero because all demand shifts to a substitute for water.) Previewing our base case results, the relative welfare gains from introducing market pricing in southern Alberta are under 3% for a year of surplus water flows, about 6% for a mean flow year, and more than 15% for a drought flow year. In absolute terms, the gain in a drought year could represent as much as $85 million per season. (This gain and others reported below are measured in 1995 Canadian dollars, for which the 1995 exchange rate was approximately $1.00 Cdn=$0.70 US.) Sensitivity analysis shows the results to be quite robust to alternative specifications for irrigated crop prices, own-price demand elasticities, demand choke prices, water (supply) flow volumes, and future water demand growth. The paper is organized as follows. The water allocation model and a representative farms submodel are introduced next, then the base case solutions are tabulated and discussed. Sensitivity analyses are subsequently reported and interpreted. Concluding remarks comprise the final section.

2. The water allocation model 2.1. Preliminary remarks Historically, surface water rights have not been tradable in Alberta. Hence, the potential reallocation of water rights is simulated by deterministic mathematical optimization. A nonlinear model estimates the social welfare gains from establishing active trade in untreated surface water in the South Saskatchewan River Basin. Our approach draws on previous research, including Flinn and Guise [1], Vaux and Howitt [2], Marin and Smith [3], Enright and Lund [4], Booker and Young [5,6] and Lo [7]. Principal assumptions are: the time frame is short run; water markets are perfectly competitive; water demand and supply are deterministic; and equilibria are partial. Water flows and uses are represented for the period of May through SeptemberFone growing season. The study area is shown in Fig. 1. It consists of four sub-basins in southern Alberta: the Red Deer River, the Bow River, the Oldman River and the South Saskatchewan River. Fig. 2 depicts this river network. Sixteen activity nodes represent potential sources or diversions of surface water. Seven rivers provide flows. Eighteen demand sinks represent consumptive water uses for urban (domestic and general) uses, irrigation, industrial use and hydroelectric generation. Certain in-stream flows are also maintained for interprovincial water sharing.

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

27

Fig. 1. Map of study area.

Our model is sufficiently specialized in terms of geography and water uses that a compact algebraic representation is not possible. To avoid a prohibitively long presentation, part of the model is formulated explicitly and the rest is simply described. Mahan [8] presents the complete model and its formulation in the GAMS modeling language [9]. We frequently use GAMS notation for convenience. Table 1 lists set definitions for the activity nodes, usage types, gauging stations and hydrologic regimes. 2.2. The objective function and its interpretation The model objective function, O; measures social welfare as the sum of the areas under the inverse demand curves (i.e., total benefits) less the sum of the areas under the inverse supply curves (i.e., total costs). At the optimum, O is the sum of consumers’ plus producers’ surpluses from water market transactions. Because each demand function has constant own-price elasticity and water demands are inelastic, a choke price is specified to estimate consumption benefits. All marginal costs are constant and all decision variables are non-negative. Thus, the objective function is:  XXX X X Z UL Fqu ðqdÞ dqd þ CPqu Qdminqu  Costquk Qquk ; ð1Þ O¼ q

u

LL

q

u

k

where q, u and k index the nodes, usage types and types of water treatment, respectively, and Fqu(qd) is the inverse demand function for water consumption qd. Fqu(qd) is integrated from lower limit LL=Qdminqu (a parameter) to upper limit UL=Qdqu (a variable). The corresponding exogenous choke price is CPqu and Qdminqu is consumption level Fqu(CPqu). Parameters Costquk

28

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

Fig. 2. Schematic diagram of the South Saskatchewan river basin.

and variables Qquk denote, respectively, the unit cost of water treatment and the quantity of water at the kth stage of conversion (described further, below). A constant-elasticity demand function has the form Qd=aPe, where Qd is quantity demanded, P is the price, a is a parameter and e is the absolute price elasticity. The inverse demand function is

29

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49 Table 1 Set definitionsa Activity node

Node (q)

Usage type

Red Deer Urban/Industrial Bow River Hydro City of Calgary urban/Industrial Western Irrigation Region Bow River Irrigation Region Eastern Irrigation/Industrial Region Lethbridge Northern Irrigation Region City of Lethbridge Urban Canal Headworks Mountain View, Aetna, United, Leavitt Irrigation Region Raymond & Magrath Irrigation Region St. Mary River Irrigation RegionFWest Taber Irrigation Region St. Mary River Irrigation RegionFEast Confluence City of Medicine Hat Urban/Industrial Apportionment

R1 B1 B2 B3 B4 B5 O1 O2 C0 C1 C2 C3 C4 C5

urban & indust hypow urban & indust agri agri agri & indust agri urban

S1 A

agri agri agri agri agri urban & indust

Economic usage type indices (u) Irrigation Domestic use General use Industrial Hydro Domestic & general use consumption

irrig dom gen ind hydro toturb

Gauging station indices (g) Red Deer River Bow River Elbow River Oldman River Headwaters of St. Mary, Belly and Waterton Rivers

1 2 3 4 5

Hydrologic regime (level) Long-term mean flow Drought flow Surplus flow

base drought surplus

a Note: Sets and set elements use GAMS notation. Nodes are indexed by q, and node R1, for example (see Fig. 2), represents City of Red Deer Urban/Industrial uses. Such uses are specified in GAMS as urban and indust, respectively. The set of urban use nodes is R1, B2, O2 and S1, and the set of industrial use nodes is R1, B2, B5 and S1. Other sets represent agricultural use (agri) and hydropower use (hypow). In addition, six economic usage types (indexed by u) are associated with these four sets. For instance, irrig is water use associated with agri; dom and gen are water uses associated with urban, etc. Gauging stations and hydrologic regimes are straightforward.

30

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

RQ P(Qd)=(a/Qd)1/e and the gross surplus (GS) of consuming Qd is GSðQd Þ ¼ 0 d PðqÞ dq: For 0oeo1 (price-inelastic demand), this integral does not converge. To cope with this complication, we assume that a water source exists that can provide unlimited supplies at a price called the backstop price, which serves as a choke price. (Backstop price and choke price are concepts also used in nonrenewable resources. See, for instance, Hartwick and Olewiler [10, p. 289].) Because a choke price is likely far above any price paid previously, a choke price is conjectural. Specifying choke price CP generates quantity Qdmin from the demand function and, hence, for all Qd X Qdmin=a(CP)e: 11=e

GSðQd Þ ¼ a1=e ½Qd

 Qdmin11=e =½1  1=e þ CP  Qdmin:

ð2Þ

The composite term in this expression is the definite integral in (1). Fig. 3 depicts the gross surplus or benefit of water consumption level Q*, corresponding to price * P . Effectively, the inverse demand function consists of the horizontal line segment at choke price CP extending from Qd=0 to the point of intersection of CP with P(Qd), then the curve P(Qd) for Qd X Qdmin. Gross surplus of consumption Q*, the shaded area in Fig. 3, consists of the rectangle CP  Qdmin plus the definite integral of P(Qd) from Qdmin to Q*. This area is specified precisely by GS(Q*) using (2). Several points should be noted. First, the interpretation of gross benefit using Fig. 3 is correct as long as CP exceeds the model-determined price P*. This condition is easily verified after model solution. Second, the portion of P(Qd) for prices above CP is not relevant to the model; only if choke price CP is raised (as in one sensitivity analysis below) does a different portion of P(Qd)

Fig. 3. Gross benefit of water consumption.

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

31

become relevant. Third, as indicated by the double sum of the first term in (1), many markets are modeled, not just one. Equilibrium pairs (Q*, P*) are determined for all markets simultaneously. Finally, because supply costs in (1) are deducted from the gross benefits of consumption, O measures the net benefits of water consumption.1 2.3. Balance constraints, supply equations and other constraints Balance constraints equate total inflows to outflows and are defined for each sub-basin and node, q. Higher values of q denote nodes further downstream. Specifically: flowðqÞ ¼ flowðq  1Þ þ inflowðqÞ þ adjustðqÞ þ totuseðqÞ for all q;

ð3Þ

where flow(q) measures total flow leaving q, inflow(q) measures tributary inflow to q, adjust(q) measures minor adjustment between nodes, and totuse(q) measures water lost through the conversion process. Supply equations set inflows at specified nodes to tributary inflows: inflowðqÞ ¼ gaugeðg; levelÞ;

qAfR1; B1; B2; 01; C0g:

ð4Þ

Parameter gauge(g, level) measures natural flow level at gauging station g for one of three hydrologic regimes; i.e., level A {base, drought or surplus}. Included in the model, but not specified here, are several other constraints. Flow adjustment equations allow return flows to reenter at locations other than diversion points; variables adjust(q) represent these effects. Total use equations define each totuse(q) variable as diversion flow less return flow. With few exceptions, return flows reenter at the point of diversion. Finally, a confluence equation defines the South Saskatchewan River flow as the sum of flows leaving the tributary Bow and Oldman Rivers. 2.4. Apportionment and in-stream flow constraints An interprovincial agreement on surface water apportionment limits Alberta’s water consumption in the entire South Saskatchewan River Basin. The combined flow into the downstream province of Saskatchewan from the Red Deer and South Saskatchewan Rivers must be no less than (the lesser of) one half of the natural flow or 1500 cubic feet per second 1

It is tempting to try to portray (Q*, P*) in Fig. 3 as occurring at the intersection of a demand curve and a supply curve, but deriving this portrayal is complex. All marginal costs are constant and water supply curves might plausibly be thought of as horizontal straight lines. Yet in the water network the supply curve for one market is not a horizontal line at a given marginal cost. With constant-elasticity demand functions and a constraint on total water use in the network, all water available to the network will be consumed and incremental water will have a positive scarcity value (shadow price). Thus, supplying more water to one market (say market 1) than Q* requires other markets to give up that water. All other market prices must rise to conserve water use, simultaneously boosting the scarcity value of incremental water to the network. The supply price in market 1 captures this scarcity value and rises too. This supply price rises as more water is diverted to market 1. Conversely, if less water is provided to market 1 than Q*, the unused water will be absorbed by other markets only if their prices decline, in turn reducing the scarcity value of water to the network. The less water supplied to market 1, the less the network scarcity value and the smaller the supply price in market 1. Clearly, the water supply curve for market 1 exhibits an upward slope at the equilibrium quantity-price pair. But, the nature of this curve can only be found after model solution using extensive parametric analysis. Graphing the supply curve for a single market is an onerous task.

32

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

(42.5 m3/s). Thus: flowð‘R1’Þ þ flowð‘S1’ÞXminlevel;

ð5Þ

where minlevel is a flow that depends on the hydrologic regime. Following GAMS notation, quotation marks around a name specify a set element; e.g. ‘R1’ and ‘S1’ are set elements indexed by q (see Table 1). Referring to Fig. 2, this constraint requires combined outflows from the nodes representing the cities of Red Deer and Medicine Hat to meet or exceed parameter minlevel. Minimum levels of in-stream flow must also be maintained for recreation and riparian uses, including fish habitat. These requirements are implemented by in-stream flow constraints. Diversion constraints represent actual 1995 consumption levels or licensed flow quantities under the institutional allocation structures modeled. Such constraints help to specify the amount of trade allowed among usage types, and within and among sub-basins. 2.5. Constraints representing the transformation processes Each water usage type has a transformation process to convert untreated water into treated water. For irrigation, untreated water is diverted and transported in canal networks. The ‘commodity’ valued is usable crop water after accounting for transportation losses and deep drainage losses. For each element of set agri, three equations represent the conversion process: RWDIVðagri;‘irrig’Þ ¼ RWðagri;‘irrig’Þ;

ð6Þ

Qdðagri;‘irrig’Þ ¼ RWDIVðagri;‘irrig’Þð1:0  lossðagri;‘ir d’ÞÞ;

ð7Þ

RTFLWðagri;‘irrig’Þ ¼ Qdðagri;‘irrig’Þð1:0  lossðagri;‘ir r’ÞÞ:

ð8Þ

Eq. (6) is an accounting equation specifying untreated water diverted. Eq. (7) defines irrigation water as what remains after losses from transportation and deep drainage (seepage). Water that is lost is assumed not to reenter any sub-basin during the growing season. Eq. (8) defines water returned for downstream use as what remains after consumption losses. For urban consumption, untreated water is diverted to a municipal utility for filtration, treatment, pressurization and conveyance. After consumption, waste water is captured by the sewer system for further treatment. The ‘commodity’ valued is potable water from the faucet. For each element of set urban, six equations represent the conversion process: RWDIVðurban;‘toturb’Þ ¼ RWðurban;‘toturb’Þ;

ð9Þ

Qtrtðurban;‘toturb’Þ ¼ RWDIVðurban;‘toturb’Þð1:0  lossðurban;‘trt’ÞÞ;

ð10Þ

Qdistðurban;‘toturb’Þ ¼ Qtrtðurban;‘toturb’Þð1:0  lossðurban;‘dist’ÞÞ;

ð11Þ

Qdistðurban;‘toturb’Þ ¼ Qdðurban;‘dom’Þ þ Qdðurban;‘gen’Þ;

ð12Þ

Qeffðurban;‘toturb’Þ ¼ ðQdðurban;‘dom’Þð1:0  lossðurban;‘dom c’ÞÞÞ þðQdðurban;‘gen’Þð1:0  lossðurban;‘gen c’ÞÞÞ; RTFLWðurban;‘toturb’Þ ¼ Qeffðurban;‘toturb’Þð1:0  lossðurban;‘wwt’ÞÞ:

ð13Þ ð14Þ

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

33

Eq. (9) is an accounting equation while (10) defines treated water as what remains after treatment losses (back-flushing filters, plant leakage, reservoir evaporation). Eq. (11) defines treated water distributed to consumers as what remains after distribution losses (evaporation, system leakage, maintenance losses). Eq. (12) defines the total amount of treated water as that consumed by

Fig. 4. The urban water transformation process.

34

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

domestic and general use consumers. Eq. (13) defines the amount of effluent water stemming from consumption and (14) defines water returned for downstream uses after effluent treatment. The data used to calibrate the model exhibit sizeable losses for conversion for urban usage (see Fig. 4): 4% in production (Eq. (10)), 8% in distribution (11), 15% in domestic use and 25% in general use (12). For industrial use, the conversion process is similar but consumption losses vary by type of consumer. Water used for hydropower generation is physically non-consumptive, but, because water is stored in reservoirs during the irrigation season for use in winter, hydropower use is represented as consumptive.

3. The representative farms sub-model A stand-alone sub-model estimates irrigation demands and values, which form inputs to the main allocation model. In practice, agricultural demands for surface water are for irrigation, stock watering and rural household uses. Historically, the latter two uses have been small and we thus ignore them. Thirteen irrigation districts (legal jurisdictions) are grouped into nine irrigation regions (geographic areas) based on water source and agro-climatic zone, while individual crops are aggregated into six representative crop groups. Crop group definitions are based on similarities in evapotranspiration rates, yields, market values and nutritional requirements. A representative crop is chosen for each group. Representative crops selected are soft wheat, hard spring wheat, barley, canola, potatoes and alfalfa. Soil moisture consists of moisture available at the start of the growing season plus effective precipitation and effective irrigation during the season. Total precipitation consists of rainfall and snowfall in-season, from which 10% deep drainage losses are subtracted to yield effective precipitation. Irrigation demand depends inversely on spring soil moisture and effective precipitation. Ten percent deep drainage losses are subtracted from total irrigation to give effective irrigation. Nitrogen fertilizer use is an important determinant of crop yield, and so the optimal use of such fertilizer is linked explicitly in the farm sub-model to soil moisture availability, and thus to effective irrigation. Although the quantity of soil moisture is important, the timing of that moisture also bears on crop yield. For all crops, a critical time for sufficient moisture is early in the growing season. During the season, the importance of water supply varies by crop. We implicitly assume that water is allocated optimally within the growing season. Drawing upon Kulshreshtha and Tewari [11,12], we model each crop as being produced by a representative profit-maximizing farm. Our representative farm practices monoculture on a 56hectare farm and irrigates with a center-pivot sprinkler. Two notable characteristics of the submodel are the water-yield function and the water-fertilizer function. The former function relates actual yield to effective irrigation while the latter function relates fertilizer application to effective irrigation. By assuming that spring soil moisture and effective precipitation are fixed at a given level, effective irrigation becomes the independent variable determining representative crop yield. Farm profits consist of revenues less costs. Revenues are determined by the price of the representative crop, the growing area and crop yield, the latter derived from the water-yield function. Numerous costs are included, of which pumping charges, fertilizer inputs and harvesting/field cultivation costs vary with effective irrigation. Some on-farm costs are deemed to

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

35

Table 2 Aggregate inverse demand functionsa 2 R%

Node index

Irrigation region

Double-log linear inverse demand functionb

B3 B4 B5 O1 C1

Western Irrigation Region (WIR) Bow River Irrigation Region (BRIR) Eastern Irrigation Region (EIR) Lethbridge Northern Irrigation Region (LNIR) Mountain View, Aetna, United, Leavitt Irrigation Region (MAULR) Raymond & Magrath Irrigation Region (RMR) St. Mary River Irrigation RegionFWest (SMRIRFW) Taber Irrigation Region (TIR) St. Mary River Irrigation RegionFEast (SMRIRFE)

P=(0.174/Q)1/1.619 P=(6.170/Q)1/1.253 P=(1.348/Q)1/1.703 P=(0.863/Q)1/1.521 P=(0.014/Q)1/1.768

0.84 0.81 0.88 0.87 0.91

P=(0.035/Q)1/1.979 P=(3.400/Q)1/1.226 P=(4.704/Q)1/1.056 P=(6.725/Q)1/1.286

0.86 0.80 0.72 0.68

C2 C3 C4 C5

a Note: The demand function can be represented by: Q=dPe. Therefore, the inverse demand function can be represented by: P=(d/Q)1/e. b Price is in dollars/m3 and quantity is in millions of m3 per season.

be incurred once a commitment is made to seed a crop. These costs are treated as fixed and independent of the costs or application rate of water for irrigation. Fixed costs are incurred for seed, equipment fuel, chemicals, pivot operation, machinery operation, operating interest, hail and crop insurance and repairs to machinery and buildings. Profits are maximized subject to an irrigation water constraint, which specifies effective irrigation water available. The inverse demand schedule for irrigation water is derived by solving the sub-model for various water constraint levels to determine the constraint shadow prices, each of which constitutes a marginal value of water. Inverse irrigation water demand functions are then derived by fitting regression equations to the derived inverse demand schedules. A weighted multiple of these equations is then used to derive aggregate inverse demand schedules from which aggregate inverse demand functions are estimated econometrically.2,3 Table 2 displays our estimated aggregate inverse demand functions. Because the farm submodel estimates the value of effective irrigation water, namely, water available for irrigation after transportation and deep drainage losses, the main model incorporates a process to convert untreated water to effective irrigation water. Fifteen percent of diverted water is assumed lost in canal and on-farm delivery systems, and 90% of water delivered is consumed.

2

For each irrigation region, the aggregate inverse irrigation demand function is derived as follows. First, for each representative crop, 50 price-quantity pairs are estimated by varying the constraint on water availability. (Each price used is the shadow price of the water availability constraint.) Then, irrigation water quantities for each representative crop are multiplied by a weighting factor based on that crop’s share of total hectares irrigated in a region. Then, the crop-specific weighted demand schedules are horizontally aggregated into one irrigation water demand schedule for that region. Mahan [8] illustrates these aggregate demands for water in the nine irrigation regions, which are based on expected crop prices and a 50% effective precipitation probability level. 3 Four functional forms were estimated econometrically: linear, double-log linear (constant own-price elasticity), quadratic and reciprocal. In general, the double-log linear specification dominates in adjusted R2 and is employed here. Marin and Smith [3] also use double-log linear functions to represent irrigation demands.

36

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

4. Data sources and model implementation Surface water flows are projected using reports by Alberta Environment [13] and Alberta Environmental Protection [14,15]. Consumption data are compiled from reports of Alberta Agriculture [16], Alberta Environment [17], irrigation districts [18–22] and municipal utilities [23– 27]. A range of non-consumptive use values is plausible. Drawing on figures used by Alberta Environmental Protection, Lo [7] develops in-stream flow requirements as lower bounds on residual channel flows in each sub-basin. We adopt the Lo [7] in-stream flow values, and treat them as institutional constraints to be satisfied. To derive urban water demands, each municipal utility’s demand function is estimated, then augmented with information about the water transformation process and supply costs. Utilities supply water for various uses: domestic, general-use (commercial, industrial) and other consumption (public use, fire fighting). Rate schedules are structured such that different consumer types pay different rates. Using rate schedules, municipal demand is classified as domestic use or general use, and reference prices are specified by summing water utility and sewage charges. Each price represents marginal water value at the reference quantity. Reference quantity is the gross volume of treated water consumed, and for each usage type is the estimated consumption for May through September, 1995. Each demand function has constant price elasticity, which, for each usage type in each urban area, is 0.5.4 Water supply costs for urban consumers are for water treatment and distribution as well as for administration, salaries, repairs and maintenance, energy, chemicals, taxes, insurance and debt servicing. Short run variable production costs are for utility operation and maintenance. Costs such as administrative overhead, depreciation and debt financing are assumed fixed. Industrial users include petroleum refining, manufacturing, fertilizer production and mining. Common uses are for cooling, condensing, processing and sanitation. Industrial demands are derived similarly to urban demands, and constant own-price elasticity demand functions are used. Demand price elasticities and consumptive-use ratios are taken from Tate et al. [29]. Their price elasticities range from 0.354 to 1.202. Hydro reservoirs are presently operated to optimize hydro-electric generation in winter. All electric utilities are assumed to purchase water during May through September and store it for winter use. In the base case, hydropower use can vary from zero to 100 million m3 of Bow River licensed volumes. In modeling the status quo institutional structure, 100 million m3 of water per season must be used for hydropower. In the other cases examined, hydropower use of water is variable and competes with other uses. Demand functions for hydro generation are derived using an avoided cost approach, the next best alternative being coal-fired thermal. Water value estimates for power generation range from $0.002/m3 to $0.022/m3, the latter being the short-run value when fixed costs of power generation are excluded. This short-run value is adopted, and water demand is restricted not to exceed 4 Other assumptions are plausible. McNeill and Tate [28] find that own-price elasticity of domestic demand falls between 0.1 and 1.0 with a median value of 0.25. The own-price elasticity of demand for general use is in the range of 0.05 to 1.0, with an average value of 0.5. The backstop priceFand, hence, the choke priceFdiffers by water use since the assumed quality of treated water differs by use. In $/m3, the assumed choke prices are: irrigationF1.50, domestic useF5.00, general useF3.50 and industrial useF2.50.

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

37

100 million m3 per season. This range of water value for hydropower highlights very different opinions about the value of water for power use. Historically, electricity prices have not been determined in competitive markets, although electricity market deregulation is currently in progress. Our model employs some stringent assumptions. The deterministic orientation and short-run time frame restrict choices open to economic agents; e.g., capital stocks for all agents are fixedFonly the intensities of use can be varied. Further, new technologies or new conservation techniques cannot be adopted, and certain inputs are pre-committed to farming. At the outset, all agents are aware of such factors as: surface water flows, spring soil moisture, forthcoming seasonal precipitation, input costs and output prices. All marginal costs are constant and all fixed costs are sunk and excluded from O: Utility and irrigation capital stocks can accommodate optimal allocations, as can the water-using capital stocks of all users. Rivers flow with no net evaporative or seepage loss except following diversion from a water course; seepage and evaporative losses are reflected in the conversion processes. In markets for agricultural inputs and outputs, as in all markets for water, transactions costs are nil.5 When water market mechanisms and trading are introduced, transactions costs may well be large but they ought to decline with trading experience. Assuming transactions costs are zero leads changes in O to measure the largest gains possible. The model incorporates numerous choices to represent economic agents and how they interact. However, alternate configurations and choices are possible and plausible; for instance, more demand nodes could be represented and some return flow locations could be altered. Model development followed a modular approach. Each module was assembled and exercised and, where possible, its results assessed for plausibility and (broad) consistency with historical uses. Testing was also conducted on the full model to ensure coherency of the components.6

5. Base case findings We consider three scenarios, each characterizing a potential role for water markets. Scenario 1 represents the historical institutional structure prohibiting water trade. Scenario 2, intra-regional trade, allows water trade among all consumptive uses within a sub-basin but not among subbasins. Scenario 3, inter-regional trade, allows water trade within and among sub-basins. For all cases studied, the Red Deer River sub-basin is prohibited from trading with the other sub-basins. While there is no natural channel linking the Red Deer River sub-basin with the others, water trade could be modeled by allowing trade in apportionment flows. Lo [7] allows the Red Deer sub5

According to Young [30, p. 1145]: The resources required to establish, operate and enforce a system to govern resource allocation are termed ‘‘transaction costs’’. These include costs of obtaining information (such as knowledge about the needs and attitudes of other participants), contracting costs (resources required to reach agreements) and policing (the costs of enforcing rules)... 6 During development, each module was modified to improve representation of the process(es) modeled. In several cases, interviews were conducted with industry experts to understand better the processes involved. Data problems have plagued our work: some data are incomplete, some absent and some inconsistent. Data rectification consumed much effort.

38

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

basin to participate in inter-regional trade in this way. For our base case, these scenarios are modeled with surface water flows at long-term mean levels. Scenario 1 represents historical water uses, so model restrictions fix consumption at each node to its estimated 1995 consumption level. Total net benefit O is $608 million per season. To illustrate model outputs, Table 3 lists equilibrium (treated) water quantities and marginal values. With two caveats marginal values may be interpreted as (constrained) equilibrium prices consistent with historical allocations: neither markets nor prices are presently used to allocate surface water, and unit values are not directly comparable across uses because of conversion costs and systems losses. (Horbulyk [31] provides a review of water pricing practices in Canada.) Even so, the widely divergent tabulated water values suggest trade gains may occur by reallocating water from low-value uses to high-value uses. Shadow prices (not shown) are an important part of the optimal solution. In particular, each diversion constraint has a shadow price measuring the marginal value of untreated water; the shadow prices of these constraints will be equated among all uses engaged in trade. In Scenario 1, however, all such shadow prices differ because all consumption levels are fixed at historical levels. Scenario 2 simulates outcomes when water trades are allowed within, but not among, subbasins. Total diversion of untreated water from each sub-basin is required not to exceed its Scenario 1 amount. Total net benefit is $643 million per seasonFa $35 million (5.8%) rise from Scenario 1. Table 4 shows that shifting water from low-value uses to high-value uses occurs. For example, in the Bow River sub-basin, water is transferred from the Western Irrigation Region to the Bow River Irrigation Region and to urban and industrial consumers. One price (the common shadow price) for untreated water is paid by all users within a sub-basin. In general, with water trade, high shadow prices fall and low shadow prices rise. Hydropower use also vanishes. In Scenario 3, the total amount of water available is limited to total basin diversion amounts from Scenario 1. Total net benefit is $646 million per season, a $38 million (6.3%) rise from Scenario 1, and a more modest $3 million (0.5%) rise from Scenario 2. Table 5 lists the equilibrium prices and quantities for treated water. Again, there are transfers from low-value uses to high-value uses. The untreated water price (unlisted) is $0.040/m3 for all users in all sub-basins except Red Deer River. This price underpins the common price of $0.047/m3 (listed) for irrigation water and the higher prices for non-irrigation water uses. In both Scenarios 2 and 3, there is no hydropower use because the equilibrium price of untreated water exceeds its value in power generation ($0.022/m3). The model assumes that there are no (positive or negative) externalities associated with this action, but recreationalists could be adversely affected by the lower hydro reservoir levels in summer that allow the higher in-stream flows. In all three scenarios, potential water trades are limited to historical quantities of surface water diverted. Thus, the base case gains could be larger if, instead, trades were limited only by available physical flows. Optimized diversion volumes maximize O but not necessarily the welfare of individual consumers, or of consuming classes. Table 6a lists net benefits by sub-basin and percentage shares of net benefits among sub-basins. The estimated benefits of a move to Scenario 2 or 3 are greatest for the Bow River sub-basin. Some 92% of the gains achievable by moving from Scenario 1 to Scenarios 2 and 3 are due to intra-regional trade alone; i.e., Scenario 1 to Scenario 2. Moreover, the existing allocation structure (Scenario 1) yields 94% of maximum welfare (Scenario 3).

Node index

R1 B1 B2 B3 B4 B5 O1 O2 C1 C2 C3 C4 C5 S1

Activity type

City of Red Deer Urban/Industrial Bow River Hydro City of Calgary Urban/Industrial Western Irrigation Region Bow River Irrigation Region Eastern Irrigation Region (Irrigation/Industrial) Lethbridge Northern Irrigation Region City of Lethbridge Urban/Industrial Mountain View, Aetna, United & Leavitt Irrigation Region Raymond & Magrath Irrigation Region St. Mary River Irrigation RegionFWest Taber Irrigation Region St. Mary River Irrigation RegionFEast City of Medicine Hat Urban/Industrial Total

Irrigation

Urban

P

Domestic use P Q 0.983 1.229

Q

0.029 0.053 0.038 0.036

52.53 245.95 361.36 135.30

0.026

9.38

0.038 0.053 0.061 0.056

22.34 123.81 89.76 276.03

1316.5

Industrial

Hydropower

General use P Q

P

Q

P

Q

2.18

0.963

2.04

0.957

30.00 0.022

100.00

47.69

1.215

24.79

1.160

27.59

1.161

4.13

0.737

13.69

1.088

6.60

1.071

7.19

0.777

3.46

0.763

3.86

59.9

37.9

75.4

100.0

a Note: (a) Each Price, P, is in dollars per cubic meter and each quantity, Q, is in millions of cubic meters per season. (b) Price and quantity values for urban and industrial consumers represent values for treated water. (c) It is assumed that irrigation and hydropower water uses do not incur conveyance and conversion costs. (d) Consumption figures are for the time period May to September.

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

Table 3 Equilibrium prices and quantities for Scenario 1a

39

40

Node index

R1 B1 B2 B3 B4 B5 O1 O2 C1 C2 C3 C4 C5 S1

Activity type

City of Red Deer Urban/Industrial Bow River Hydro City of Calgary Urban/Industrial Western Irrigation Region Bow River Irrigation Region Eastern Irrigation Region (Irrigation/Industrial) Lethbridge Northern Irrigation Region City of Lethbridge Urban/Industrial Mountain View, Aetna, United & Leavitt Irrigation Region Raymond & Magrath Irrigation Region St. Mary River Irrigation RegionFWest Taber Irrigation Region St. Mary River Irrigation RegionFEast City of Medicine Hat Urban/Industrial Total

Irrigation

Urban

P

Domestic use P Q 0.936 0.310

Q

0.042 0.042 0.042 0.051

29.18 325.18 294.46 80.61

0.051

2.79

0.051 0.051 0.051 0.051

12.92 131.62 109.51 311.05

1297.3

Industrial

Hydropower

General use P Q

P

Q

P

Q

2.24

0.916

2.09

0.960

29.90 0.022

0.00

95.02

0.296

50.26

0.324

52.22

0.325

6.48

0.751

13.48

0.424

10.58

0.407

11.66

0.735

3.56

0.721

3.97

111.4

68.0

102.1

0.0

a Note: (a) Each Price, P, is in dollars per cubic meter and each quantity, Q, is in millions of cubic meters per season. (b) Price and quantity values for urban and industrial consumers represent values for treated water. (c) It is assumed that irrigation and hydropower water uses do not incur conveyance and conversion costs. (d) Consumption figures are for the time period May to September.

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

Table 4 Equilibrium prices and quantities for Scenario 2a

Node index

R1 B1 B2 B3 B4 B5 O1 O2 C1 C2 C3 C4 C5 S1

Activity type

City of Red Deer Urban/Industrial Bow River Hydro City of Calgary Urban/Industrial Western Irrigation Region Bow River Irrigation Region Eastern Irrigation Region (Irrigation/Industrial) Lethbridge Northern Irrigation Region City of Lethbridge Urban/Industrial Mountain View, Aetna, United & Leavitt Irrigation Region Raymond & Magrath Irrigation Region St. Mary River Irrigation RegionFWest Taber Irrigation Region St. Mary River Irrigation RegionFEast City of Medicine Hat Urban/Industrial Total

Irrigation

Urban

P

Domestic use P Q 0.936 0.314

Q

0.047 0.047 0.047 0.047

24.87 287.32 248.88 91.46

0.047

3.23

0.047 0.047 0.047 0.047

15.23 145.73 119.54 346.10

1282.4

Industrial

Hydropower

General use P Q

P

Q

P

Q

2.24

0.916

2.09

0.960

29.90 0.022

0.00

94.38

0.300

49.91

0.328

51.88

0.329

6.45

0.330

26.21

0.420

10.62

0.403

11.72

0.314

5.45

0.300

6.15

112.8

69.9

114.4

0.0

a Note: (a) Each Price, P, is in dollars per cubic meter and each quantity, Q, is in millions of cubic meters per season. (b) Price and quantity values for urban and industrial consumers represent values for treated water. (c) It is assumed that irrigation and hydropower water uses do not incur conveyance and conversion costs. (d) Consumption figures are for the time period May to September.

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

Table 5 Equilibrium prices and quantities for Scenario 3a

41

42

Table 6 Scenario 1

(a) Net benefits by sub-basina Red Deer Riverb Bow River Oldman River South Saskatchewan River

50.76 (8.3%) 373.07 (61.3%) 145.63 (24.0%) 38.77 (6.4%)

50.76 (7.9%) 405.29 (63.0%) 148.60 (23.1%) 38.78 (6.0%)

50.76 (7.9%) 401.34 (62.1%) 152.15 (23.5%) 42.23 (6.5%)

Total

608.23

643.43

646.48

Node

Sub-basin

Scenario 1

(b) Net benefit by consumptive usage typec Irrigation region B3 Western B4 Bow River B5 Eastern O1 Lethbridge Northern C1 Mountain View, Aetna, United & Leavitt C2 Raymond & Magrath C3 St. Mary RiverFWest C4 Taber C5 St. Mary RiverFEast

R1 B2 O2 S1

Scenario 2 (millions of dollars/season)

Scenario 3

Scenario 2 (millions of dollars/season)

Scenario 3

3.82 (2.07%) 42.31 (22.94%) 31.38 (17.01%) 12.90 (6.99%) 0.54 (0.29%)

3.01 (1.62%) 46.04 (24.87%) 28.72 (15.51%) 10.58 (5.72%) 0.31 (0.17%)

2.82 (1.52%) 44.36 (24.01%) 26.70 (14.45%) 11.11 (6.01%) 0.33 (0.18%)

1.71 (0.93%) 22.06 (11.96%) 21.60 (11.71%) 48.13 (26.10%)

1.30 (0.70%) 22.47 (12.14%) 22.69 (12.26%) 49.99 (27.01%)

1.41 (0.76%) 23.15 (12.53%) 23.18 (12.55%) 51.70 (27.98%)

Total irrigation

184.45

185.11

184.76

Urban City of City of City of City of

11.19 (3.74%) 230.82 (77.09%) 38.69 (12.92%) 18.71 (6.25%)

11.24 (3.43%) 256.07 (78.22%) 41.25 (12.60%) 18.81 (5.75%)

11.24 (3.43%) 256.02 (78.01%) 41.26 (12.57%) 19.66 (5.99%)

Red Deer Calgary Lethbridge Medicine Hat

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

Sub-basin

R1 B2 B5 S1

a

299.41

327.37

328.18

Industrial City of Red Deer City of Calgary Eastern City of Medicine Hat

39.57 (32.39%) 54.15 (44.33%) 8.38 (6.86%) 20.07 (16.43%)

39.52 (30.18%) 62.27 (47.56%) 9.18 (7.01%) 19.97 (15.25%)

39.52 (29.59%) 62.26 (46.63%) 9.18 (16.90%) 22.57 (29.59%)

Total industrial

122.17

130.94

133.53

Hydropower Bow River

2.20

0.00

0.00

Note: Percentage figures listed for each scenario represent the contribution of each sub-basin to total net benefit. Net benefits for the Red Deer River are listed at 50.76 millions of dollars/season for all three scenarios, implying that there are no gains from Scenario 1 to each of the other two scenarios. However, at more than two places of decimal, reallocations between consumers in the Red Deer River sub-basin generate positive welfare effects. To six places of decimal, net benefit values are 50.758139, 50.760488, and 50.760488 for Scenarios 1, 2, and 3, respectively. c Note: Percentage figures listedFfor each Scenario and consumptive usage typeFrepresent the contribution of each node to total net benefit. b

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

B1

Total urban

43

44

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

Table 6b lists net benefits by type of water use. Under intra-regional trade, net benefits rise by 9.3% and 7.2% in the urban and industrial sectors, respectively, whereas net benefits for irrigation rise only by 0.4%. Moving from intra-regional trade to inter-regional trade results in slight losses for the irrigation sector and small gains for the urban and industrial sectors. Our model can also be used to examine the distribution of gains and losses under alternative property rights regimes for surface water. For example, the gains from intra- or inter-regional trade are shared differently when water is priced volumetrically in each scenario as opposed to a command and control approach in which government decrees how water is allocated, and at a price of zero for some or all users. Results are reported in Mahan [8].

6. Sensitivity analysis Base case findings depend upon numerous modeling and data assumptions. As noted earlier, key assumptions involve crop prices, demand price elasticities, choke prices, water (supply) flow volumes, and the future growth of water demand. In this section, we examine the importance of these assumptions to our findings. Crop prices drive agricultural activity and irrigation water demands. Suppose that crop prices are either 20% higher or lower than those used in the base case. From Table 7, net benefits without water trade are lower by about 2% or higher by about 6%, if crop prices are lower or higher, respectively. Welfare gains from water trade are higher in percentage terms when crop prices are low, but the overall pattern of results is not much influenced by these variations. As we vary crop prices and move from Scenario 1 to Scenario 2 or 3, percentage gains lie within 6% of base case values. Price elasticities for water demand may play an important role in market allocations, especially when demands are modeled with constant price elasticity. Suppose that the (absolute values of )

Table 7 Net benefits for the sensitivity analysesa Sensitivity analysis

Scenario 1

Base case Decreased crop prices Increased crop prices Less elastic demands More elastic demands Decreased choke prices Increased choke prices Drought flows Surplus flows Projected 2010 Demands (Long-term mean flows)

608.23 595.32 645.89 625.05 592.95 405.32 754.79 572.65 615.88 753.96

a

Scenario 2 Scenario 3 (millions of dollars/season) 643.43 630.52 681.46 654.51 634.38 440.52 789.99 651.06 630.87 801.02

(5.79%) (5.91%) (5.51%) (4.71%) (6.99%) (8.69%) (4.66%) (13.69%) (2.43%) (6.24%)

Note: Figures in parentheses measure percentage net benefit gains from Scenario 1.

646.48 633.73 684.23 657.46 637.53 443.57 793.04 657.28 632.04 804.35

(6.29%) (6.45%) (5.94%) (5.19%) (7.52%) (9.44%) (5.07%) (14.78%) (2.62%) (6.68%)

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

45

price elasticities are lower or higher by 20%. For example, if price elasticities for domestic and general-use consumers are changed from 0.50 to 0.40, there is less quantity-responsiveness by domestic water users to a price change in the short runFdemand is less elastic. In contrast, the move from 0.50 to 0.60 signifies more elastic demand. From Table 7, the potential relative gains from reallocation are greater when demands are more price-elastic, although the overall pattern of gains differs little from the base case. When water demands have constant price elasticity, the choke price may be an important determinant of Scenario 1 benefits because it defines the benefits received from infra-marginal units of water consumed. A choke price might represent the cost of a backstop supply source, such as pumped groundwater. Altering a choke price does not change an optimal allocation as long as the choke price exceeds the equilibrium price. In our model, the Kuhn-Tucker optimality conditions are unaffected by any change to a choke price that leaves the optimal quantity from backstop supplies at zero. For instance, if groundwater is the alternative source and if it is too costly relative to the marginal surface supply source, then it does not matter if groundwater is slightly more, or much more, expensive than the marginal supply source. In both cases, groundwater is unused. As another sensitivity analysis, all choke prices are alternately increased and decreased by 50% from base case levels. All resulting choke prices still exceed base case equilibrium prices. From Table 7, net benefits shrink (increase) when choke prices shrink (increase). Absolute gains do not change because the optima stay the same; percentage welfare gains thus move inversely to choke prices. However, percentage gains depend upon the choke prices assumed; for instance, moving from Scenario 1 to Scenario 3 yields percentage gains of 5–9%, depending upon choke prices. Potential gains from improving water use efficiency will likely be largest when water is in scarce supply or when increased demand leads to greater scarcity. These circumstances are explored next. Simulating aggregate water supply variations requires focusing on soil moisture, river flow volumes, and allowable diversions. Soil moisture consists of spring soil moisture augmented by effective precipitation. In the base case, a 50th percentile (cumulative probability) effective precipitation level is used. Alternative hydrologic events are defined by varying the level of effective precipitation and then allowing for alternative irrigation demands. A drought flow is defined by using a 25% effective precipitation level, while a surplus flow is defined by using a 75% effective precipitation level. The farm sub-model is then used to derive the corresponding aggregate water demands. Whereas the base case incorporates long-term mean natural river flows, the drought flow and surplus flow events incorporate river flows one standard deviation lower or higher than long-term mean flows. Finally, in the drought flow and surplus flow events, we assume that there is regulatory intervention reducing or increasing the allowable licensed diversions by 27.5% from base case values, reflecting short-run resource management as would be practiced under an historical command-and-control (priority-based allocation) regime. With a drought event, the increase in net benefits associated with a shift from Scenario 1 to Scenario 3 is approximately 14.8%, or nearly $85 million per season; see Table 7. Gains achievable through both intra- and inter-regional water trade are more than double those of the base case. By contrast, the surplus flow outcomes for a shift from Scenario 1 to Scenario 3 yield a 2.6% gain, less than half the 6.3% gain achievable in the base case.

46

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

Increases in urban populations and rural areas under irrigation may lead to even greater relative water scarcity. To examine prospective future scarcity and the potential benefits from adopting market mechanisms, we consider a case based on the year 2010, in which economic agents face circumstances similar to 1995, but both demands and licensed diversion volumes are larger.7 Irrigators in 2010 operate a larger stock of capital equipment, but with no technological advances over 1995. Under demand conditions projected for 2010, with water supplies at long-term mean flows, Scenario 1 net benefits are about 25% larger than in 1995, yet percentage gains from Scenario 1 to Scenarios 2 and 3 change little from the base case (Table 7).

7. The results in perspective Our results are generally consistent with those of other studies that model marketbased improvements in water allocation. For example, Booker and Young [5,6] found that intra-regional transfers from low value uses (e.g. irrigation) to high value uses (e.g. municipal water districts) yield substantial benefits. They also found that because observed differences between marginal economic values of consumptive uses are relatively modest among uses in different regions, the added benefit of inter-regional trade is minimal based on consumptive use values alone. However, if non-consumptive use values (e.g. reduction of salinity concentrations) are also considered, economic benefits of interregional trade rise. Booker and Young [6] and Marin and Smith [3] conclude that substantial gains accrue when inter-basin trade is allowed, and emphasize that the allocation mechanism (e.g., market exchange versus a central authority) determines the distribution of gains. There are other published results for the South Saskatchewan River basin, but they rest on a different optimization model utilizing different assumptions [7,32]. Lo [7], for example, reports much higher dollar values for net benefits and relative gains from intra- and inter-regional water trade than we find. However, the many differences in the two modeling approaches prevent explicit comparison or reconciliation of the estimated potential benefits from improved allocations.8 7

For the year 2010, projected urban demands are determined as follows. The 1995 per capita consumption level for each of the four major urban centers is calculated. Then, the 2010 population for each center is estimated by projecting a compound annual growth rate on 1995 populations. The 2010 population estimate is multiplied by the 1995 per capita consumption to yield 2010 reference quantities. To estimate 2010 industrial consumption, 1995-to-2010 gross consumption growth factors for the urban centers are applied. Projected irrigation demands are derived by multiplying total assessed acres for each irrigation region by the gross consumption-per-hectare ratio calculated from 1995 data. 8 Differences between our model and that of Lo [7] and Horbulyk and Lo [32] are as follows. Lo’s base case involves reliable or drought flows; ours uses long-term mean flows. Lo models historical allocations by constraining net consumption quantities (based on licensed volumes); ours imposes limits on diversion quantities, which in some cases are less than licensed volumes. Lo employs demand functions for untreated water; we employ demand functions for treated water and incorporate processes which transform untreated water into treated water incurring costs for diversion, upgrading, conveyance, effluent treatment and water losses occurring in these processes. Lo utilizes linear net demand functions; we utilize constant-elasticity demand functions to represent urban, industrial and irrigation demands. Lo utilizes (implicit) choke prices which are the vertical intercepts of her linear demand functions; we adopt

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

47

8. Concluding remarks Unique for analyzing surface water uses in southern Alberta, our model has several noteworthy characteristics: a static orientation (one growing season); a network representing flows in four river sub-basins; in urban locations, conversion of untreated water into treated potable water and conversion of waste water to untreated surface water; nonlinear (constant price elasticity) water demands and exogenous choke prices; a cropping sub-model to estimate irrigation demands; and the ability to represent different hydrologic years or events. All of these features appear important for properly measuring the social welfare of water supply and consumption. Short-run percentage gains from inter-regional water trade in the South Saskatchewan River basin are relatively small for a year of surplus flows or for a year of mean flows (from under 3% to a bit more than 6%, respectively). However, relative to a base of some $600 million per season, the potential gains in an average year exceed $38 million per season. In a drought situation, the gains appear substantial (about 15%, or $85 million per season). The general pattern of gains appears quite robust to a range of alternative assumptions and parameter values. One noteworthy finding is that choke pricesFused with our constant-price-elasticity demand functionsFcan significantly influence the measurement of relative potential gains: reducing choke prices by half from the base case raises the relative gains to more than 9%, while raising choke prices by half lowers them to 5%. This dependence arises because choke prices are conjectural: there is no historical experience with them. None of these gains subtracts the various (one-time or recurrent) costs of instituting improved allocation mechanisms, nor do the gains include the costs or cost savings associated with historical command-and-control allocation mechanisms. Aggregate benefits, estimated for the entire river basin, do not highlight the pattern of gains and losses to individual classes of users or to specific sub-basins. This pattern can easily be extracted from our model solution. Moreover, model aggregation may hide differences (and larger benefits) that might appear if focus were placed on individual semi-arid regions exhibiting much stress on water resources. On balance, our findings tend to support the Government of Alberta’s present cautious approach to modifying the mechanisms for surface water allocation in Southern Alberta. Efficiency improvements to surface water use through market pricing are likely to be relatively large at least part of the timeFduring drought yearsFand small part of the timeFsuch as during surplus-flow years. The costs of moving to market pricing may include up-front administrative and compliance investments and recurrent costs borne in all years. Such institutional and environmental costs, associated with a change of water allocation policy, are not included in our model. Nevertheless, our basin-wide optimization approach allows us to explore such issues as desired. For example, we might envision a phased introduction of intra- or inter-regional water trade, targeting first the markets where the model identifies the greatest potential gains. As well, we might explore scenarios in which price ceilings are placed on irrigation water during some specified transition period to ease the distributional impacts of introducing market pricing and

( footnote continued ) explicit assumptions about choke prices. Other differences are in: demand and supply data, factor input and product prices and assumed cropping patterns. Lo’s model allows a larger geographical scope for inter-regional water trades. We also use a cropping sub-model; Lo does not.

48

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

perhaps reduce political opposition to market-based reforms in surface water allocation (see Mahan [8]). Numerous advantages accrue from examining water allocation issues using an optimization approach. For example, where the model makes explicit the historical sources of water leakage and process or conversion losses, the relevant constraint shadow prices can provide valuable insight as to which investments in loss prevention (and demand management, more generally) yield the best social return. Similarly, where groundwater and surface water management are to be combined (as in conjunctive water management), model solutions can be used to target efficient groundwater use and development. Acknowledgements Jim Booker provided us with the GAMS files used in research reported in [6] and we learned a lot by examining his files. Thanks to Jim for his GAMS files and to Wendy Mahan for her assistance in preparing the figures and tables. We also extend thanks to Jim, Dianne Draper, Lynda Lo, the referees and the editor for helpful comments on this work. Any errors and all opinions are ours alone.

References [1] Flinn JC, Guise JWB. An application of spatial equilibrium analysis to water resource allocation. Water Resources Research 1970;6:398–409. [2] Vaux Jr. H, Howitt R. Managing water scarcity: an evaluation of interregional transfers. Water Resources Research 1984;20:785–92. [3] Marin C, Smith M. Water resources assessment: a spatial equilibrium approach. Water Resources Research 1988;24:793–801. [4] Enright C, Lund JR. Alternative water-district organization: screening-level analysis. Journal of Water Resources Planning and Management 1991;117:86–107. [5] Booker JF, Young RA. Economic impacts of alternative water allocations in the Colorado River Basin. Water Resources Research Institute, Colorado State University, Fort Collins, 1991. [6] Booker JF, Young RA. Modeling intrastate and interstate markets for Colorado River water resources. Journal of Environmental Economics and Management 1994;26:66–87. [7] Lo L. Water scarcity and the potential gains from water trading in Southern Alberta. Unpublished M.A. thesis, Department of Economics, University of Calgary, 1995. [8] Mahan RC. Efficient Allocation of Surface Water Resources in Southern Alberta. Unpublished M.A. thesis, Department of Economics, University of Calgary, 1997. [9] Brooke A, Kendrick D, Meeraus A. GAMS: A User’s Guide, Release 2.25. South San Francisco: The Scientific Press, 1992. [10] Hartwick JM, Olewiler ND. The economics of natural resource use, 2nd ed. New York: Addison-Wesley, 1998. [11] Kulshreshtha S, Tewari D. Irrigation water demand in Saskatchewan: a linear programming approach. Technical report submitted to Saskatchewan Water Corporation. Department of Agricultural Economics, University of Saskatchewan, Saskatoon, 1987. [12] Kulshreshtha S, Tewari D. Value of water in irrigated crop production using derived demand functions: a case study of South Saskatchewan River Irrigation District. Water Resources Bulletin (American Water Resources Association) 1991;27:227–36.

R.C. Mahan et al. / Socio-Economic Planning Sciences 36 (2002) 25–49

49

[13] Alberta Environment. Hydrology Branch, South Saskatchewan River Basin Historical Natural Flows: 1912 to 1978. Government of Alberta, Edmonton, 1982. [14] Alberta Environmental Protection. Alberta’s State of the Environment: Comprehensive Report. Government of Alberta, Edmonton, 1994. [15] Alberta Environmental Protection. Report on Instream Flow Needs: Investigation of the Bow River. Fish and Wildlife Division, Government of Alberta, Edmonton, 1994. [16] Alberta Agriculture. Fertilizing irrigated grain and oilseed crops. Government of Alberta, Edmonton, 1993. [17] Alberta Environment. Planning Services Branch, Alberta Industrial Water Use Survey 1981. Government of Alberta, Edmonton, 1983. [18] Bow River Irrigation District. 1995 Financial Statement and Annual Report, Alberta. [19] Eastern Irrigation District. 1995 Annual Report, Alberta. [20] Lethbridge Northern Irrigation District. 1994 Financial Statement and Annual Report, Alberta. [21] St. Mary Irrigation District. 1989 Financial Statement and Annual Report, Alberta. [22] Western Irrigation District. 1995 Annual Report, Alberta. [23] City of Calgary. 1991 Annual Report. Engineering and Environmental Service Department, Calgary, Alberta. [24] City of Calgary. 1995 Financial Report, Calgary, Alberta. [25] City of Lethbridge. 1995 Annual Report, Lethbridge, Alberta. [26] City of Medicine Hat. 1994 Financial Report, Medicine Hat, Alberta. [27] City of Red Deer. 1995 Financial Statement, Red Deer, Alberta. [28] McNeill R, Tate D. Guidelines for municipal water pricing. Social Science Series No. 25, Inland Water Directorate, Water Planning and Management Branch, Environment Canada, Ottawa, 1991. [29] Tate D, Renzetti S, Shaw H. Economic instruments for water management: The case for industrial water pricing. Social Science Series No. 26, Ecosystem Sciences and Evaluation Directorate, Economics and Conservation Branch, Environment Canada, Ottawa, 1992. [30] Young R. Why are there so few transactions among water users? American Journal of Agricultural Economics 1986;68:1142–51. [31] Horbulyk TM. Canada. In: Dinar A, Subramanian A., editors. Water pricing experiences: An International Perspective, World Bank Technical Paper No. 386. The World Bank: Washington, 1997. p. 37–45. [32] Horbulyk TM, Lo, L. Welfare gains from potential water markets in Alberta, Canada. In: Easter KW, Rosegrant MW, Dinar A, editors. Markets for water: potential and performance. Boston: Kluwer Academic Press, 1998. p. 241–257.