Economic analysis of water allocation policies regarding Nile River water in Egypt

Agricultural Water Management 52 (2002) 155±175

Economic analysis of water allocation policies regarding Nile River water in Egypt Dennis Wichelns* Department of Environmental and Natural Resource Economics, University of Rhode Island, Kingston, RI 02881, USA Accepted 9 April 2001

Abstract The Government of Egypt is currently implementing projects that expand irrigated area on the Sinai Peninsula and in the southern desert. Those projects will reduce the supply of Nile River water available to farmers in the Nile Delta, which is a heavily populated and highly productive agricultural region. The southern desert project will obtain water directly from Lake Nasser, while a mixture of Nile River water and drainage water will be delivered to the Sinai. The true costs of the projects include the opportunity costs of water and capital that could be used alternatively in the Nile Valley and Delta, or in other productive endeavors. Economic analysis generates optimizing criteria that describe the role of scarcity values (opportunity costs) in determining the allocation of Nile River water that will maximize net social bene®ts. Policy implications are derived by comparing those criteria with the criterion that farmers implement when maximizing pro®ts from crop production. A small-scale simulation model demonstrates the potential impact of water allocation policies on regional net revenues. Results are discussed within the context of a broader view of national goals that include promoting economic growth, achieving food security, and enhancing the quality of life for Egyptians. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Egypt; Water allocation; Water policy; Economics; Food security

1. Introduction The demand for Nile River water is increasing in Egypt, where the population and economy are expanding at about 2 and 5% per year, respectively (EIU, 2000). The supply of Nile River water is limited by an agreement with Sudan, which provides Egypt with 55.5 billion m3 of water each year from Lake Nasser. When deep and shallow groundwater, drainage water, and treated sewage are added to that volume, the total *

Tel.: ‡1-401-874-4565; fax: ‡1-401-782-4766. E-mail address: [email protected] (D. Wichelns). 0378-3774/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 7 7 4 ( 0 1 ) 0 0 1 3 2 - 9

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annual supply becomes 63.7 billion m3, while annual water use is an estimated 61.7 billion m3 (Simonovic et al., 1997). Hence, water is not yet a limiting resource at the national level in Egypt, although some portions of the country experience water shortages in some years due to inadequate local supplies or capacity constraints in the delivery system (Radwan, 1997; Hopkins, 1999). As a result, Egypt has not yet developed and implemented national policies that reflect scarcity conditions for use in pricing or allocating irrigation and drainage water (Hamdy et al., 1995; Nassar et al., 1996; Attia, 1997). The Ministry of Public Works and Water Resources operates and maintains the national irrigation system that includes Aswan Dam, main and branch canals, barrages, pump stations, and an extensive drainage system in the Nile Delta (Elarabawy et al., 2000). The Ministry collects and recycles drainage water in the Delta to extend its water supply and to remove salts from the system. Currently, the Ministry recycles about 5 billion m3 of drainage water officially and its goal is to increase that volume to 7 billion m3 (Abu-Zeid, 1992; Abu-Zeid and Hefny, 1992; Willardson et al., 1997; Kotb et al., 2000). The re-use of drainage water increases the volume of blended irrigation water available to farmers located at the tail ends of secondary and tertiary canals, but sustained use of that water increases the salinity of agricultural soils. The Government of Egypt is currently implementing two projects that will expand irrigated area on the Sinai Peninsula and in the southern desert (Fig. 1). The Northern Sinai Agricultural Development Project is designed to reclaim up to 250,000 ha in the eastern Nile Delta and on the northern portion of the Sinai Peninsula (Elarabawy and Tosswell, 1998; Kotb et al., 2000). The El-Salam Canal, which originates in the Delta and siphons under the Suez Canal, will carry a blend of Nile River water (50%) and drainage water from the Bahr Hadous and Lower Serw drains in the Delta (Elarabawy and Tosswell, 1998; Bishay, 1993). The estimated annual water requirement for the 90,000 ha that will be reclaimed on the Sinai Peninsula is 1.7 billion m3 (Bishay, 1993). The goals of the Southern Valley Development Project, also known as the Toshka Project and the New Valley Project, include reclaiming up to 336,000 ha of desert land and establishing new communities that will relieve population pressure in the Nile Valley and Delta (Elarabawy and Tosswell, 1998). Private investors are expected to establish large farming operations that will specialize in horticultural crops for export to European markets (Wahish, 1998). The Toshka Project, which will obtain water from a new canal originating at Lake Nasser, will increase the demand for Nile River water substantially when all of the canals and pump stations have been completed. The estimated water requirement for the first stage of the project, which will involve reclamation of 210,000 ha, is 5 billion m3 per year (Elarabawy and Tosswell, 1998). Allocation of water to the Northern Sinai and Toshka Projects will reduce the supply of Nile River water available to farmers in the Nile Delta. Pertinent policy questions include whether such a re-allocation program will increase or decrease the net social benefits generated with Nile River water. The Nile Delta is a heavily populated, highly productive agricultural region, while the Sinai Peninsula and the southern desert are sparsely populated and the soils are not as inherently productive as those in the Delta. The Government of Egypt is hoping to ease population pressure in the Delta by moving people to the southern desert as the demand for labor there increases with new

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Fig. 1. A map of Egypt showing the Nile Valley and Delta, the El-Salam Project in the Northern Sinai, and the New Valley Project in the southern desert. Reprinted with permission from Kotb et al., 2000.

agricultural production and processing activities. However, it is not yet clear that the benefits of such a relocation program will exceed the costs. Allan (1994) suggests that the cost of providing the agricultural and social infrastructure required to induce farmers to live in remote reclamation schemes is more than US$ 25,000/ha. Elarabawy and Tosswell (1998) state that an estimated US$ 60 billion to US$ 90 billion will be required for investments in agriculture, urbanization, industry, and tourism in support of the Southern Valley Development Project during the next 20±30 years. This paper presents an economic model for use in evaluating the inevitable trade-offs involved when allocating Nile River water among competing regions and projects in Egypt. The goal of the model is to maximize the net social benefits generated with limited water resources. Optimizing criteria describe the role of scarcity values in determining the socially optimal allocation of water and in designing public policies to sustain that allocation. The criteria generated by the social optimization model are compared with the

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criterion that farmers implement when maximizing profits from crop production. That effort generates policy implications regarding efforts to encourage farmers to consider scarcity values when choosing crops and irrigation strategies. A small-scale simulation model demonstrates the potential impact of water allocation policies on regional net revenues. Results are discussed within the context of a broader view of national goals that include promoting economic growth, achieving food security, and enhancing the quality of life for Egyptians. 2. Maximizing net social benefits The national goal of maximizing the net social benefits generated with Nile River water can be described in a highly aggregated and stylized model that includes just four production regions or projects and the municipal and industrial sector. The regions include the Nile Valley, the Nile Delta, the Toshka Project, and the Northern Sinai Project. The goal is to depict the trade-offs that must be considered in discrete allocation decisions involving large regions or projects. The economic criteria generated by such a model apply equally well to allocation decisions involving smaller regions, as could be shown by using a more detailed, less aggregated version of the model. The national objective function is described as maximizing the net social benefits in any year, subject to a constraint on Nile River water supply and a constraint describing the volume of drainage water generated in the Nile Delta. The choice variables are the volumes of Nile River water and drainage water allocated to each of the four regions and to municipal and industrial use. The formal model is the following: Maximize NSB ˆ PT YT …WT ; ECT † ‡ PV YV …WV ; ECV † ‡ PD YD ‰WD ; DD ; ECD …WD ; DD †Š ‡ PS YS ‰WS ; DS ; ECS …WS ; DS †Š ‡ B…WM † C…WM † CS …WS ; DS † subject to :

CT …WT †

WT ‡ WV ‡ WD ‡ WS ‡ WM ˆ W;

CV …WV †

CD …WD ; DD † (1)

DD ‡ DS ˆ aWD

where NSB represents net social bene®ts. The total volume of Nile River water available each year is denoted by W, while the volume allocated to each of the regions is denoted by Wi, where i ˆ T (Toshka), V (Nile Valley), D (Nile Delta), S (Northern Sinai), and M (municipal and industrial uses). The volumes of drainage water delivered each year are denoted by DD for the Nile Delta and DS for the Northern Sinai. The proportion of Nile River water delivered in the Delta that becomes drainage water available for re-use in the Delta or in the northern Sinai is denoted by a. Agricultural benefits are described using a representative crop price, Pi and crop production function, Yi(
), for each of the four regions. Clearly, a more detailed model with many crop activities is needed to evaluate actual policy choices and obtain useful quantitative results. However, the optimizing criteria derived using this simplified framework are conceptually the same as those that would be derived using a more detailed model.

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The salinity of water deliveries, ECi, is included in each of the four crop production functions to denote the role of salinity in allocation decisions. Soil and water salinity are important issues in large areas of the Nile Delta where farmers have been using drainage water for a portion of their water supply for many years. Soil and water salinity are also pertinent issues in the northern Sinai and southern desert, where substantial soil reclamation is required before the land will generate sustainable crop yields. Water quality in the Nile Valley is generally very good, as the volume of return flows is small in comparison with the volume of water flowing in the Nile River. However, soil salinity is a problem in some portions of the Nile Valley where over-irrigation or the lack of an adequate drainage system has created a saline high water table (Kotb et al., 2000). The benefits and costs of providing Nile River water for municipal and industrial uses are described by B(WM) and C(WM), respectively. The cost functions for the four agricultural regions are given by Ci(
). The costs include operation and maintenance costs for the water delivery system from Aswan Dam to farm turnouts or pumping stations in all four regions and drainage system costs in the Nile Delta and the northern Sinai, where drainage water is collected and blended with water deliveries. There are nine first-order necessary conditions for this constrained optimization problem, seven of which pertain to the choice variables (WT, WV, WD, WS, WM, DD, and DS) and two that pertain to the water supply and drainage constraints, for which the Lagrange multipliers are lW and lD (Anthony and Biggs, 1996 pp. 254±256). The superscript (0 ) denotes a partial derivative with respect to the pertinent choice variable, unless otherwise noted. Choice variable

First-order necessary condition

WT WV WD WS WM DD

PT YT0 CT0 ˆ lW PV YV0 CV0 ˆ lW 0 PD ‰YD0 ‡ YEC EC0D Š CD0 ‡ alD ˆ lW 0 PS ‰YS0 ‡ YEC EC0S Š CS0 ˆ lW 0 0 B C ˆ lW 0 PD ‰YD0 ‡ YEC EC0D Š CD0 ˆ lD

DS

0 PS ‰YS0 ‡ YEC EC0S Š

lW lD

WT ‡ WV ‡ WD ‡ WS ‡ WM ˆ W DD ‡ DS ˆ aWD

CS0 ˆ lD

(2) (3) (4) (5) (6) (7) (8) (9) (10)

The first implication derived from the model is noted by observing that five of the firstorder necessary conditions, Eqs. (2) through (6), require that the sum of a set of terms on the left side of each equation is equal to lW. The left side of each equation describes the net value of an incremental unit of water in each of the regions and in municipal and industrial uses. For example, Eq. (2) requires that the incremental net value of water in the Toshka Project, PT YT0 CT0 , is equal to lW. A similar relationship appears in Eq. (3) regarding the incremental net value of water in the Nile Valley. Eqs. (4) and (5) have additional terms on the left side, due to the role of salts in water supplies in the Nile Delta and the northern Sinai, and due to the fact that a portion of

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water deliveries in the Nile Delta becomes drainage water available for recycling. The chain rule partial derivatives of crop yield with respect to the salinity of water deliveries, 0 YEC EC0i , in Eqs. (4) and (5) are likely positive, because the salinity of water deliveries in the Delta and the northern Sinai is reduced when a greater volume of Nile River water is included in those deliveries. Hence, the second half of the partial derivatives, EC0i , is 0 negative. The first half of the partial derivatives, YEC , is also negative because higher yields are obtained with lower salinity water. These additional terms in Eqs. (4) and (5) reflect the incremental water quality benefits of Nile River water in irrigation deliveries in the Nile Delta and the northern Sinai. The alD term in Eq. (4) reflects the incremental value of the portion of Nile River water deliveries in the Delta that becomes drainage water and is collected and blended with other water deliveries. When lD is positive, there will be an additional incremental benefit associated with the drainage water. The incremental net value of Nile River water allocated to municipal and industrial uses must also be equal to lW, to maximize net social benefits, as described by Eq. (6). Hence, at the optimal allocation, the incremental net value of water is the same in all four regions and in municipal and industrial uses, and that incremental net value is described by lW, which is also the partial derivative of net social benefits with respect to the Nile River water constraint, W. Hence, lW describes the rate at which net social benefits will increase if another unit of Nile River water becomes available. At the optimal allocation, that value must be the same in any of the competing uses. Two additional intuitive statements can be derived from these results. (1) If incremental net benefits are not the same in all regions, the sum of net social benefits can be increased by re-allocating water from uses of relatively low incremental net values to uses of relatively high incremental net values, and (2) any re-allocation of Nile River water from a use or region with a relatively high incremental net value to a use or region with a relatively low incremental net value will reduce the sum of net social benefits. Eqs. (7) and (8) are the first-order necessary conditions describing the optimal allocation of collected drainage water among the Nile Delta and the northern Sinai. In those equations, the chain rule partial derivatives of crop yield with respect to drainage 0 water volume, YEC EC0i , are likely negative, because the salinity of water deliveries in the Delta and the northern Sinai is increased when a greater volume of drainage water is included in those deliveries. Hence, the second half of the partial derivatives, EC0i , is 0 positive, while the first half of the partial derivatives, YEC , remains negative. In areas or in seasons in which the water volume effect of additional drainage water, described by Pi Yi0 in Eqs. (7) and (8), is smaller than the water quality effect described by 0 Pi YEC EC0i in those equations, the resulting incremental net value of drainage water, lD, will be negative. The optimal values of lW and lD are known in economics as shadow values or opportunity costs because they represent the incremental values of scarce resources in alternative uses. Those values must be considered when seeking the optimal allocation of scarce resources. In many countries irrigation water is delivered to farmers at prices that do not include the true incremental cost of delivery or the opportunity cost of water in alternative uses. As a result, the sum of net social benefits from water use in all regions and sectors is not maximized.

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3. Maximizing farm-level profits Farmers divert water from tertiary canals with the goal of maximizing net returns from crop production, subject to the timing and availability of the water supply. It is helpful to compare the farm-level optimizing criterion regarding water use with the first-order necessary conditions described in Eqs. (2) through (8). The profit maximization model for any one farmer can be described as follows: Maximize NRij ˆ Pij Yij …Vij ; ECij †

FC…Vij †

(11)

where NRij represents net revenue for any farmer, j, in one of the four regions, i, where i ˆ T, V, D, S, as described above. The only choice variable in this model is Vij, which is the volume of water diverted by the farmer for use in crop production. That volume will include only Nile River water in the Nile Valley and southern desert, while it will include a blend of Nile water and drainage water in the Delta and the northern Sinai. However, the farmer is not able to choose the proportion of drainage water in his or her water supply, as that proportion is determined by the Ministry of Public Works and Water Resources which operates the drainage water collection and recycling system. The farm-level cost of diverting water for use in crop production is described by the cost function FC(Vij), which may include the cost of lifting water from a below-grade tertiary canal in the Nile Delta or the cost of managing water delivery from one of the raised tertiary canals or underground pipelines that have been installed in recent years as part of the national Irrigation Improvement Program (World Bank, 1994; Depeweg and Bekheit, 1997; Hvidt, 1996, 1998). The single first-order necessary condition for the farm-level model pertains to the optimal choice of Vij and is described as follows: Pij Yij0

FC0ij ˆ 0

(12)

This condition suggests that a pro®t-maximizing farmer will choose the volume of water that equates the farm-level incremental value of water in crop production, Pij Yij0 , with the farm-level incremental cost of diverting the water, FC0ij . There are no additional terms, such as lW or lD, in Eq. (12) because individual farmers do not have the option of managing a de®ned supply of water for which they must consider alternative uses. 4. Policy implications Several policy implications can be described by comparing the first-order necessary conditions for the national level water allocation model with the single criterion describing farm-level profit maximization. The implications pertain generally to choices regarding the optimal allocation of Nile River water and to the public policies and expenditures that may be needed to achieve that allocation. In addition, results implied by the optimizing criteria can be compared with the current allocation of irrigation and drainage water to identify directions in which public policy might be shifted to enhance

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the sum of net social benefits generated by Nile River water, even if the optimal allocation is not yet achievable. 4.1. Allocation among regions As noted above, the first-order necessary conditions described by Eqs. (2) through (6) require that the incremental net benefit of water is the same in all regions, and in municipal and industrial uses. Achieving this criterion requires consideration of both the incremental benefits and costs of delivering water in the various regions and projects. At present, the incremental costs of delivering Nile River water to the Nile Delta and Valley are smaller than the costs of delivering water to the northern Sinai and the southern desert. The incremental benefits of water in the Sinai may be limited by soil quality and the proportion of drainage water included in water deliveries. In the southern desert, incremental values will be limited until the land has been reclaimed to support production of high-value export crops. Previous efforts to reclaim desert land in Egypt have been very expensive and results have not met expectations (Galal and Fawzy, 1993; Stoner, 1994; Meyer, 1998; Owen and Pamuk, 1998, p. 142). The optimal allocation of Nile River water among regions can be described in a graphic representation of the first-order necessary conditions. An example is provided in Fig. 2, where the incremental net benefits of water delivery in the Nile Delta are compared with incremental net benefits in the northern Sinai. It is assumed that water is more productive and the incremental costs of water delivery are lower in the Nile Delta than in the northern Sinai. Hence, the incremental net benefits curve for the Nile Delta, which

Fig. 2. Allocating a limited supply of water optimally among the Nile Delta and the Northern Sinai. Note: Water allocated to the Northern Sinai is measured from right to left on the horizontal axis.

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163

reflects all of the terms on the left side of Eq. (4), lies above the analogous curve for the northern Sinai, which reflects all of the terms on the left side of Eq. (5). The length of the horizontal axis in Fig. 2 denotes the limited supply of Nile River water. The optimal allocation of that supply among the two regions is found by equating the incremental net benefits with the shadow value of water, lW. The optimal volume for delivery in the Delta, WD , exceeds that for the northern Sinai, WS . 4.2. Allocation within regions Given the uncertainty regarding incremental net benefits of water supplies in the northern Sinai and southern desert, the sum of net social benefits might be enhanced by first improving the degree to which Nile River water is used efficiently in the Nile Valley and Delta, where crop production conditions are among the best in the world (Beshai, 1993; Ward, 1993). The incremental net value of water likely varies throughout the Nile Valley and Delta, as some farmers have more reliable access to water than others, and some soils have been degraded more severely than others, over time. Efforts to improve the distribution of Nile River water among Delta farmers, in particular, may enhance net social benefits substantially. As shown above, farmers equate the incremental value of water in crop production with the incremental cost of diverting water for irrigation. If farmers receive prices that do not reflect the true value of crops or if the incremental cost of water is less than the true incremental cost of delivery, the volume of water used by farmers will differ from the socially optimal volume. Incorrect price or cost signals can cause farmers at the head ends of secondary and tertiary canals to divert more water than they would otherwise choose to divert, thus reducing the volume of water available to farmers at the tail ends of delivery canals. Improving price and cost signals and implementing better control of water deliveries along canals will enhance the incremental net benefits of water within a region, such as the Nile Delta. 4.3. Farm-level incentives The optimizing criterion derived from the farm-level profit maximization model is quite different from the criteria derived from the national water allocation model. Farmers will equate the farm-level incremental cost of diverting water with the farm-level incremental benefit, but in the absence of policies that price or allocate water appropriately, they will have no incentive to consider opportunity costs or shadow values. As a result, the sum of water volumes demanded by farmers will exceed the socially optimal volume of water allocated to agriculture. The farm-level profit maximizing criterion for a representative farmer in the Nile Delta is compared with the socially optimal criterion in Fig. 3. If the farm-level cost of diverting water is FC0V , while the incremental cost of delivery to the farm turnout is CD0 and the shadow price is lW, the farm-level profit maximizing choice of water volume, WF, will exceed the socially optimal farm-level allocation, WF . Policies that might be implemented to raise the effective farm-level incremental cost of water to match the true social cost of water use, FC0V ‡ CD0 ‡ lW , include water pricing by volume or crop

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Fig. 3. Farm-level and socially optimal volumes of water use in the Nile Delta.

area, and a water allocation program that provides only the socially optimal volume of water to farmers. The analysis in Fig. 3 describes two components of the full incremental cost of water use that are not made evident to farmers when they choose irrigation strategies and water volumes. Those components are the incremental cost of delivering water to the farmer's turnout or pump, CD0 , and the opportunity cost of water in alternative uses, lW. In past years, the Government of Egypt collected revenue to operate and maintain the irrigation and drainage system indirectly by controlling the production and marketing of crops and retaining a substantial portion of the total revenue from crop sales (Moursi, 1993; Khedr et al., 1996; Harik, 1997, Chapter 4). The Government has ended its intervention in most crop production and marketing activities in recent years and it no longer collects revenues in that manner (Okonjo-lweala and Fuleihan, 1993; World Bank, 1993; Baffes and Gautam, 1996). As a result, the Government must consider alternative methods for raising revenue to operate and maintain the irrigation and drainage system. An effective program of water prices would enhance cost recovery efforts, while also motivating farmers to adjust their water demands in support of the national goal of maximizing net social benefits (Wichelns, 1998, 2000). 5. An empirical example The potential impacts of alternative water allocation policies on agricultural net revenues can be described using an empirical version of the conceptual model described above. The goal of this effort is to demonstrate the usefulness of economic criteria and the role of opportunity costs in policy analysis, rather than to derive accurate estimates of potential gains and losses. Hence, the empirical model developed for this task does not reflect the complex nature of agricultural production in Egypt, which involves many crops and

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production strategies. Constructing such a model would require substantial effort beyond the scope of this analysis. However, the results of this effort provide useful indications of the potential magnitude of net revenue impacts of alternative water allocation policies. 5.1. A small-scale simulation model A small-scale (10 ha) simulation model that includes three production regions (denoted as Delta, Toshka, and Sinai) and one crop (cotton) is used to compare the results of alternative water allocation policies when the total water supply is less than the sum of demands in the three regions. The 10 ha of land are divided in proportions that reflect the relative sizes of the irrigated area in the Nile Delta and the areas to be developed in the early stages of projects in the southern desert and on the Sinai Peninsula. There are about 1.5 million ha of irrigated land in the Delta (Ward, 1993), and current development plans call for reclaiming 210,000 ha in the southern desert and 90,000 ha on the Sinai Peninsula. Hence, the Nile Delta is represented by 8.3 ha in the model, while the Toshka and Sinai Projects are represented by 1.2 and 0.5 ha, respectively. A cotton production function that describes lint yield as a function of applied water (Grimes and El-Zik, 1990) is combined with a scalar that shifts the production function to depict cotton yield in each region: p Yi ˆ bi ‰ 3954 ‡ 1067 AWi 54:14 AWi Š (13) where Yi is cotton yield (kg/ha), AWi the depth of applied water (cm), and bi is a scalar that varies by region, such that bD ˆ 1:00, bT ˆ 0:85, bS ˆ 0:70. The subscript, i, includes the values of D (Delta), T (Toshka), and S (Sinai). This empirical production function was estimated by Grimes and El-Zik (1982) using data from California, rather than Egypt, but it reflects diminishing marginal returns to applied water and is appropriate for use in describing inherent trade-offs in water allocation decisions. Soil and water salinity variables are not included explicitly in the empirical production functions. However, the values of bi are chosen to reflect the lower levels of productivity expected in the southern desert and Sinai regions, relative to the Nile Delta, where soils are generally very productive. Water quality will be very good in the southern desert, but commingled drainage water will be used for irrigation on the Sinai Peninsula. Hence, the empirical production functions representing the Toshka and Sinai Projects are shifted below the function representing the Nile Delta, using scalar values for bT and bS of 0.85 and 0.70, respectively. The resulting production functions are shown in Fig. 4. The objective function in this empirical model is similar to the function described by Eq. (1), above, although it includes only agricultural costs and returns for three production regions. The goal is to maximize the sum of net revenue generated in the three regions, subject to the available water supply: Maximize SNR ˆ PAD YD …AWD † ‡ PAT YT …AWT † ‡ PAS YS …AWS † CD …WD ; ND † CT …WT ; NT † CS …WS ; NS † subject to :

‰WD ‡ WT ‡ WS Š ˆ W;

AD  8:3;

AT  1:2;

AS  0:5

(14)

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Fig. 4. Empirical production functions for cotton lint in the Delta, Toshka, and Sinai.

where SNR represents the sum of net revenues (US$ per year), P is the price of cotton (US$/kg), Ai the area planted in each region (ha), Yi the yield per hectare (kg/ha), AWi the depth of applied water (cm), Wi the volume of water applied (m3 per year), Ni represents non-water inputs, Ci the cost of production (US$ per year), and W is the total water supply (m3 per year). The production functions in this model differ from those that appear in Eq. (1), as they describe lint yield per hectare as a function of irrigation depth. Total yield is determined by multiplying yield per hectare by irrigated area. A single price of cotton is included for all regions (US$ 1.41/kg, as reported in the Financial Times on 23 December 2000). The estimated non-water costs of production are US$ 1084/ha and the farm-level cost of water is US$ 0.0089/m3 (World Bank, 1993). Irrigated areas (Ai) and irrigation depths (AWi) are the choice variables in this optimization model. The net revenue impacts of alternative water allocation policies will vary with the total volume of water available for irrigation in the three regions. That volume will likely decline in future, as municipal and industrial demands for water increase and as additional desert areas are reclaimed. Hence, the net revenue impacts are estimated for several levels of water supply. Two sets of scenarios are examined pertaining to two policy goals. 1. As the total water supply is reduced, the supply is allocated to maximize the sum of net revenues generated in the three regions. 2. As the water supply is reduced, irrigated area and the volume of applied water are held constant in Toshka and Sinai, while irrigated area and the average irrigation depth are reduced in the Delta.

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The first scenario is examined by solving the optimization model with only the constraints that describe the total water supply and the amounts of land available in each region. The second scenario is examined by adding constraints that require the irrigated areas to remain at 1.2 and 0.5 ha in Toshka and Sinai, respectively, and the irrigation depths to remain at the levels that maximize net revenue when the water supply is not limited. Results from both scenarios are compared with the optimal allocation of water when the available supply is greater than the sum of demands from the three regions. 5.2. Results 5.2.1. Allocating water to maximize the sum of regional net revenues The optimal irrigation depths when the water supply is not limiting are about 94 cm in each region, while the crop yields range from 911 kg/ha of lint in Sinai to 1302 kg/ha of lint in the Delta, given the production functions used in this analysis (Table 1). Net revenue ranges from US$ 160/ha in Sinai to US$ 711/ha in the Delta, with a sum of US$ 6500 per year from the 10 ha in the simulation model. The total volume of water applied on the 10 ha is 94,785 m3. The marginal value of water (lW) is zero in this scenario because water is not limiting. When the water supply is reduced, net revenue is maximized by reducing irrigation depths in all three regions and reducing irrigated area in Sinai, where the marginal productivity of water is smallest. For example, when the water supply is reduced by 5% to 90,045 m3, irrigation depths are reduced to 91 cm in the Delta, 90 cm in Toshka, and 88 cm in Sinai. Irrigated areas are maintained in the Delta and Toshka, while the irrigated area in Sinai is reduced by about 10% (Table 1). The marginal value of water in this scenario is US$ 0.018/m3 when the limited water supply is allocated optimally. Table 1 Optimal irrigation depths, crop yields, and net revenue when the policy objective is to maximize the sum of net revenues generated in three production regionsa Production region

Area in production (ha)

Water supply not limiting Delta 8.3 Toshka 1.2 Sinai 0.5 Sums

Crop yield (kg/ha)

Net revenue Per ha (US$/ha)

Total (US$ per year)

94.9 94.5 93.9

1302 1106 911

711 435 160

5898 522 80

10.0

Water supply reduced by 5% Delta 8.3 Toshka 1.2 Sinai 0.45 Sums

Applied water (cm)

9.95

6500 90.7 89.6 88.2

1297 1101 904

707 431 155

5868 517 70 6456

a Note: These results are generated using a 10 ha simulation model designed to demonstrate the trade-offs involved when choosing water allocation policies. The results do not describe truly optimal production areas or irrigation depths.

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Fig. 5. Areas in production when water is allocated to maximize the sum of net revenues.

Further reductions in water supply generate further reductions in irrigation depths and irrigated area. When the water supply is reduced by 10% from the original volume, it is no longer optimal to irrigate land in Sinai (Fig. 5). Irrigated area is reduced in Toshka when the water supply is reduced by 20% from the original volume. In the Delta, the optimal irrigated area remains at 8.3 ha until the water supply is reduced by 40%, although the optimal irrigation depth is reduced with each reduction in water supply. The marginal value of water (lW) rises as the water supply is reduced because the marginal productivity of water is higher at smaller irrigation depths. The marginal value becomes US$ 0.021/m3 when the water supply is reduced by 10%, and US$ 0.050/m3 when the supply is reduced by 20%. The estimated marginal value of water is the same in every region when water is allocated optimally, as required by the first-order necessary conditions described above. 5.2.2. Allocating water to maintain full production in Toshka and Sinai The net revenue impacts of a policy that seeks to maintain full production in Toshka and Sinai when the water supply is reduced are examined by imposing constraints requiring that irrigated areas and irrigation depths remain at 1.2 ha and 94.5 cm in Toshka and at 0.5 ha and 93.9 cm in Sinai. As a result, all reductions in irrigated area and irrigation depths occur in the Delta. The sum of net revenues is smaller for each reduction in water supply in this set of scenarios than in similar scenarios in which the limited water supply is allocated to maximize the sum of net revenues. The optimal irrigation depth in the Delta falls from 94.9 to 89.2 cm when the water supply is reduced by 5%, while full production is maintained in Toshka and Sinai

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Table 2 Optimal irrigation depths, crop yields, and net revenue when the policy objective is to maintain full production in the Toshka and Sinai regionsa Production region

Area in production (ha)

Water supply reduced by 5% Delta 8.3 Toshka 1.2 Sinai 0.5 Sums

Crop yield (kg/ha)

Net revenue Per ha (US$/ha)

Total (US$ per year)

89.2 94.5 93.9

1294 1107 911

704 435 160

5841 522 80

10.0

Water supply reduced by 20% Delta 7.7 Toshka 1.2 Sinai 0.5 Sums

Applied water (cm)

9.4

6444 77.4 94.5 93.9

1243 1107 911

642 435 160

4960 522 80 5562

a

Note: These results are generated using a 10 ha simulation model designed to demonstrate the trade-offs involved when choosing water allocation policies. The results do not describe truly optimal production areas or irrigation depths.

(Table 2). Crop yield in the Delta falls by just 8 kg/ha, as the reduction occurs in a relatively flat portion of the production function. Net revenue in the Delta falls by US$ 7/ ha, or about 1%. The sum of net revenues also falls by about 1%. A 20% reduction in water supply causes an 18% reduction in the optimal irrigation depth in the Delta and a 7% reduction in irrigated area when full production is maintained in Toshka and Sinai (Table 2). Net revenue in the Delta falls by 4.5% per ha, and by 16% throughout the region, contributing to a 14.5% reduction in the sum of net revenues generated in the three regions. Further reductions in water supply cause further reductions in irrigated area in the Delta (Fig. 6), while the optimal irrigation depth remains at 77.4 cm. For example, when the water supply is reduced by 30%, the optimal irrigated area declined by 22% to 6.5 ha, causing a reduction in Delta net revenue of 29%. The sum of net revenues declines by 26.5% in that scenario. The net revenue impact of a policy that maintains full production in Toshka and Sinai is reflected in differences in the marginal value of water, and in the way those values change with increasing scarcity. In particular, the marginal value of water increases in the Delta, while it remains at zero in Toshka and Sinai, where irrigation is maintained at depths that maximize net revenue when water is not limiting. Hence, when the water supply is reduced by 5%, the marginal value of water in the Delta is US$ 0.024/m3, while it is zero in Toshka and Sinai. Therefore, the sum of net revenues could be increased by reallocating water from Toshka and Sinai to the Delta. The marginal value of water in the Delta is one component of the opportunity cost of using water for irrigation in Toshka and Sinai when the Nile River supply is not sufficient to satisfy all competing demands. The net revenue from crop production in the Delta declines more sharply with reductions in water supply when the policy goal is to maintain full production in Toshka

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Fig. 6. Areas in production when water is allocated to maintain full production in Toshka and Sinai.

and Sinai (Fig. 7). The same is true regarding the sum of net revenues in the three regions (Fig. 8), as that sum is dominated by net revenue generated in the Delta. These reductions in net revenue represent one component of the loss in net social benefits caused by the policy of maintaining full production in Toshka and Sinai when the Nile River water supply is limiting. 5.3. Discussion Results obtained with the small-scale simulation model suggest that the net revenue impacts of reductions in agricultural water supply can be minimized by implementing policies that allocate water efficiently among competing regions or projects. Both the net revenue generated in the Nile Delta and the sum of net revenues generated in all three regions decline less sharply with water supply reductions when such a policy is implemented. That policy causes reductions in irrigated area in less productive regions, while maintaining production in regions with greater relative productivity. Several issues not addressed in the empirical model should be considered when evaluating water policy alternatives. For example, the diversion of Nile River water to the Sinai Peninsula likely will have a smaller incremental impact on Delta crop production and net revenues than diversions to the southern desert. The Sinai diversions will occur near the end of the Nile River irrigation system and will include commingled drainage water, while water for the southern desert will be taken directly from Lake Nasser. Hence, the southern desert diversions may reduce both the volume and quality of water available in the Nile Valley and Delta. The volume of water to be diverted there (5 billion m3)

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171

Fig. 7. Reductions in Delta net revenue when the total water supply is reduced, for two policy goals.

Fig. 8. Reductions in the sum of net revenues when the total water supply is reduced, for two policy goals.

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represents about 9% of the nation's Nile River supply, and that proportion will rise if diversions are maintained in years when the total supply falls below 55.5 billion m3. The empirical model lacks sufficient detail to describe actual farm-level responses to reductions in water supply, and those responses likely will reduce some of the losses in net revenue projected by the model. However, the model does assume that optimal irrigation depths are applied on all regions in both sets of policy scenarios. That assumption will cause an understatement of net revenue impacts if actual irrigation depths are not optimal. Actual farm-level responses and economic impacts will depend on the degree to which water supplies can be controlled and measured, and on the rules that govern water allocation and use. Renovations in both the physical and institutional components of the national irrigation system will enhance the ability of water managers and farmers to respond optimally to increasing demands on the limited water supply. 6. A broader view of policy goals Both the conceptual and empirical models described above include only a subset of variables that are pertinent when considering water allocation policies. Both models include costs and benefits of agricultural water use, and the conceptual model also addresses municipal and industrial uses. However, neither model addresses other dimensions of water values that are not captured in the net revenues from crop production or the net benefits of water use in cities and industry. When water is scarce, relative to competing demands, policy makers must also consider the role of water in promoting economic growth, achieving food security, and enhancing the quality of life in rural and urban areas. Some aspects of these additional considerations are not always reflected in the market prices of crops or in the current allocation of water among competing users. An expanded version of the national optimization model might address economic growth, food security, and the quality of life, while recognizing constraints regarding land, labor, capital, and water resources (Wichelns, 2001). The role of international trade in expanding opportunities for Egyptian producers and consumers can also be included in such a model. Egypt has a comparative advantage in the production of cotton, fruits, vegetables, and potatoes, but the production of horticultural crops is currently limited by constraints involving processing, transportation, and the size of export markets (World Bank, 1993; Greenaway et al., 1994). Efforts to expand the production and processing of fruits and vegetables and to develop new export markets, while emphasizing laborintensive enterprises, likely would enhance net social benefits. The land, labor, and water required to support such activities are presently available in the Nile Valley and Delta, while capital is relatively limited. Capital is required by large and small firms to invest in new production, processing, and marketing activities. The Government of Egypt must also invest in the infrastructure and institutions required to support the production, transportation, and marketing of higher-valued horticultural crops (El-Serafy, 1993). Capital, like water, must be allocated optimally among competing uses to maximize the net social benefits obtained from its investment. The opportunity cost of capital used to build irrigation canals and other infrastructure in the northern Sinai and

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southern desert includes the net social benefits that could be generated with similar investments in the Nile Valley and Delta (Elarabawy and Tosswell, 1998; Meyer, 1998). Efforts to develop new production areas, such as the northern Sinai and the southern desert must be evaluated within the context of competing demands for limited capital and water supplies, and in light of Egypt's pressing need to employ millions of new workers within the next 20 years (Assaad, 1997; Handoussa and Kheir-El-Din, 1998; IMF, 1998; World Bank, 1998). Public and private investments in new production and processing activities in the Nile Valley and Delta may generate net social benefits more quickly and in greater magnitude than projects in the northern Sinai and southern desert. Potential benefits include direct gains from employing larger numbers of rural residents without relocating them to southern Egypt and indirect gains in the form of higher incomes and enhanced food security in rural villages. In addition, investments in human capital will likely increase, following investments in new production and marketing enterprises, as private firms will benefit by providing education and training for rural residents. Investments in higher-valued production and marketing activities in the Nile Valley and Delta will enhance the value of incremental water supplies in those regions. If the costs of water delivery remain the same, then the net social benefits of water use will increase and the opportunity cost of removing water from the Nile Valley and Delta to support expansion of production other areas will also increase. In addition, as incomes improve in rural areas with investments in new production activities, residents and local governments will generate revenues that can be used to improve drinking water quality, reduce water pollution, and enhance other aspects of the quality of life for many Egyptians. 7. Summary and conclusions An economic model of water allocation among agricultural regions and the municipal and industrial sector illustrates the inevitable trade-offs that must be considered when seeking the optimal use of Egypt's limited water resources. The net social benefits generated with Nile River water will be maximized when the incremental net value of water is the same in all uses. That value, also called the scarcity value, is the opportunity cost of moving water from one region to another. Opportunity costs must be included when estimating the total cost of expanding agricultural production in new regions. Farmers seeking to maximize profits will not consider the opportunity costs or scarcity values of water in the absence of appropriate water pricing or allocation policies. For example, farmers in the Nile Delta have little incentive to consider the opportunity costs of water in municipal and industrial uses if their only expense for water is the cost of pumping it from a below-grade tertiary canal. Water pricing and allocation programs can modify farm-level incentives to reflect the national goal of maximizing net social benefits. Truly optimal decisions regarding water resources must acknowledge the role of water and other key inputs in promoting economic growth, achieving food security, and enhancing the quality of life. The availability of land, labor, and capital must be considered within a framework that includes a wide range of agricultural production, processing, and marketing activities. The optimal set of investments involving land and

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water resources will promote economic growth, reduce unemployment, and improve food security in rural towns and villages.

Acknowledgements I appreciate the helpful comments of Megumi Nakao and two anonymous reviewers. This paper is Rhode Island Agricultural Experiment Station Publication Number 3860.

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