Irrigation Economics

Transcription

1 Irrigation Econoics The Hydrologic Cycle Rain Evaporation Irrigation Run-on Agricultural Production Run-off Deep Percolation to Groundwater The use of irrigation water depends on: Econoics (prices and costs) Crop Selection Land Quality and Environental Conditions Irrigation Technology Water Manageent Choices depend on: Type of Crops Irrigation Technology Level of Water Availability

2 Soe Stylized Facts About Irrigation: Irrigation water is easured in "acre-feet," AF, which is the aount of water needed to cover one acre of land to a one foot depth (before water is lost to percolation). Irrigation Efficiency easures the percentage of water that is actually consued by the crop. Typical Water Use of Coon Crops: Heavy water users: Rice; Alfalfa: 5-7 AF/year Mediu water users: Fruits: AF/year Cotton: AF/year Vegetables:2-3.5 AF/year Low water users: Wheat: AF/year Irrigation efficiencies of several irrigation technologies: Gravitational: Furrow.65 Border.65 Sprinkler: Manual ove.8 Center pivot.8 With field crops Low volue: Drip.95 Not used with alfalfa, wheat LEPA.9 Used in field crops Mini-sprinkler.9 Used with trees Currently, the price of water is set adinistratively and is not the result of the axiizing behavior of econoic agents.

3 How The Choice of Irrigation Technology Affects Output: Water is applied to the surface, percolates through the soil and is taken up by the root syste. If the soil is dry and a bucket of water is poured on it, ost of it will fail to pereate the soil, but will instead exit the land in the for of runoff. If the soil is first oistened, then it uch ore readily absorbs water drip irrigation: applies water slowly so that the crop can absorb it better Most of the water applied is absorbed by the plant. drip irrigation systes are very expensive to set up. sprinkler irrigation: distributes water unevenly (through space and tie) Less of the water applied is utilized by crops; greater evaporation and runoff sprinkler systes are relatively inexpensive to set up. gravitational systes such as flood or furrow: pool water on a portion of land. less water efficient than sprinkler or drip (greater evaporation and surface runoff).

4 A siple odel of irrigation technology choice: Ag. production is a function of the effective water taken up by the crop. (called Effective Irrigation Water) Effective water is the product of two coponents: applied irrigation water (the quantity of water applied) irrigation efficiency ( fraction of applied water taken up by the crop) per-acre production function for an ag. product: y = f(e) y = agricultural output per acre e = effective irrigation water per acre -- fe > 0 and fee < 0 Effective water equation: ei = a*h(i,q,c) a = applied water per acre h(i, q, c) = irrigation efficiency i = irrigation technology, where we assue two possible irrigation technologies, labeled with an index variable i: Traditional technology: i=1 Modern technology: i=2 (dh/di) > 0: higher i results in higher irrigation efficiency q = land quality: water-holding capacity, soil quality and topographical conditions such as slope. hq > 0, thus, an increase in land or water quality increases irrigation efficiency. c = cliate variables (teperature, huidity, etc.) hc is abiguous

5 Model of irrigation technology choice (cont) The farer s per-acre profit-axiization proble can be expressed as the following discrete/continuous choice proble: ( ) ( ) ax Π = Pf e w + z a k i, a ( ) ( i) ax Π = Pf ah( i, q, c) w + z a k i, a Π = profit; P = output price zi = cost of water puping and pressurization ki = fixed cost of technology i; w = price of water Assuptions: h(i=1) > h(i=0) efficiency is higher with odern technologies. k1 > k0 Modern technology requires higher fixed cost. z1 > z0 Puping cost is higher with odern technology. For a given i, optial water use is deterined by the F.O.C.: d Π = Pf e ( w + z) = e a i Pf eh ( i, q, c ) ( w + zi) = 0 da where fe and ea are the appropriate partial derivatives. i i i Rearranging: w + z h( i, q, c) i = Pf e MC of effective water = MVP of effective water.

6 The Technology Adoption Decision At soe level of land quality, all else being equal, switching technologies will axiize profits. This level of land quality is called the switch point. it is never profitable to far land of quality < q(i=1) high-quality land: either technology is profitable, although the traditional technology is ore profitable. oderate quality (between q(i=1) and qs): odern technology akes profitable land that was previously not worth faring The switch point is based on a coparison of Profit(i=0) with Profit(i=1).

7 Crop selection Crop selection depends on the levels of econoic paraeters such as land quality and water prices. In general, farers siultaneously choose crop type, irrigation technology and applied water use levels to axiize profits, based on the levels of econoic paraeters such as land quality. Modern technologies are ore likely to be adopted with: Moderate to low quality land; high value crops Low quality water; high price water. What are soe of the effects of technology adoption? Recall that profit axiization requires: w + z i = Pf e h(i) assue for siplicity that z0 = z1, (puping costs are the sae) and recall fro page 2 that fe > 0 => h(i=0) < h(i=1) ==> fe(i=0) > fe(i=1) ==> e0 < e1 odern technology increases the optial level of effective water use. (does not iply higher applied water use) In ost cases, odern technology REDUCES the optial level of applied water use, and is therefore water-saving. If e 0 < e 1, then q 0 < q 1. Thus, odern technology increases crop output.

8 Crop Selection (cont) If Land quality is high, water quality is high and weather is ild: h(i=1) and h(i=0) are not very different the adoption of odern irrigation technology does not change the optial levels of crop output or applied water use by uch. If land quality is low, water quality is low, or weather is hot: adoption of odern irrigation technology ay affect optial crop output and applied water use significantly. When land quality is low and teperature is high, the effect of adopting new technology depends on water price: Increase In Decrease In Water Price Crop Output Applied Water Use Low ($15/AF) Minial (0-5%) High (30-40%) Med ($15-$80/AF) Mediu (5-15%)Mediu (15-20%) High ($80+/AF) High (25-50%) Low or neg. (<5%)

9 An Exaple of Technology Choice Under Markets: an individual farer is growing a crop, Y Crop Production Function: Y = 30e - 0.2e 2 The price of y is: P = $80/ton The price of water is: V = $400 / A-F π = PY - Va - F --a = the input applied water, and F = fixed costs two technologies: Sprinkler Irrigation is 50% efficient and costs $10,000 to install Drip Irrigation is 75% efficient and costs $20,000 to install calculate profits under each syste, then copare: Under Sprinkler Irrigation: S 2 Max. π = $80( 30e 0. 2e ) 400a $10, 000 a { } subject to: e = 05. a substituting in the constraint S 2 Max. π = 800a 4a $10, 000 a { } Foc: S dπ = a = 0 da which yields: a* = 100 AF. Substituting the value a* into the profit expression we get: π S = $800(100) - 4(100) 2-10,000 = $30,000

10 Exaple (cont) Under Drip Irrigation: D 2 { π = } Max. $80( e. e ) a $20, a subject to: e = 0. 75a substituting in the constraint: D 2 { π = } Max., a a $20, a Foc: d π D = 1, a = 0 da which yields: a* = A-F. Substituting the value a* into the profit expression we get: π D = $800(77.78) - 4(77.78) 2-20,000 = $34,444 Since π D > π S, the farer is better off investing in a drip irrigation syste Drip Irrigation Uses Less Applied Water: (77.78 < 100) Drip Irrigation Uses More Effective Water: 0.75(77.78) = > 50 =0.5(100) Output Per Acre is Higher Using Drip Irrigation: Y D > Y S

11 Irrigation Under Water Markets and Queuing Systes Total water available for all acreage in a watershed is A Total acreage of productive ag. land in the region is L The production function is: y = f(e) e = ahi e = effective water per acre; a = applied water per acre y = f(e)= axiu output per acre e= e, effective water associated with axiu yield Under a queuing syste Senior rights owners use water until the VMP of water = 0, which is the level that will axiize yields. e - applied water use is a = per acre h0 - Junior rights owners use whatever water is left. Under a queuing syste of water rights: water price = 0 per acre fee for water use = µ Total acres under a water rights syste: Total output = Ah 0 y Output price = P Producer surplus = P Ah y e e u Ah. e 0 0 A a Ah0 = < L e

12 Irrigation Under Water Markets and Queuing Systes (cont) Is the queuing syste efficient? Junior rights owners do not get enough water if scarcity exists. A unit of water would provide positive MVP to junior owners The last unit of water on a senior owners land provides MVP =0. => The Queuing Syste is Inefficient. MVP J + MVP S The queuing syste leads to under-utilization and over-irrigation of land. Under a Market Syste efficient solution involves applying water uniforly across all land to equate the MVP. water per acre = A L yield per acre = yi = f ki A L price of water = VMP of applied water = Pf e h l k 1 = the fixed cost of ipleenting the technology ( k 1 > k 0 ) The producers' annual profits per acre are: π 1 = Py i A L Pf e h i k i µ t so that: π 1 = Py 1 A L Pf e h 1 k 1 µ t π 0 = Py 0 A L Pf e h 0 k 0 µ t ( π 1 π 0 ) = P( y 1 y 0 ) A L Pf h e ( h 1 0 ) ( k 1 k 0 )

13 Irrigation Under Water Markets and Queuing Systes (cont) Technology 1 is selected if: (π 1 - π 0 ) > 0 Both technologies require the sae water per acre, because water is evenly distributed across all acres as a result of equating the MVP. When the arket price of water is taken as a constant in the proble, the choice of technology can be expressed as: Select technology 1 when: P(y 1 - y 0 ) > k 1 - k 0 Both technologies result in the sae water use per acre, but the odern technology increases the yield by raising the aount of effective water received by the crop. If the arket value of the increase in yield is greater than the extra capital costs involved with investing in the new technology, the farer should invest.

14 Coparing Market and Queuing Outcoes Assue that, under arket conditions, technology i is optial and adopted by all farers. Under a arket syste all arable land is utilized. The transition to arket will increase irrigated land fro A e h 0 to L. Lf h A Ah > 0 i L e o Output will increase by: Y = f ( e ) as water is shifted fro low MP land to the high MP lands of junior rights holders. Output per acre of senior rights owners will decrease fro f(e) to f (A/ L e i ). water per acre of all users will decrease fro e h 0 to A/L. A In the transition to the arket, e h i L A h 0 e units of water which were used to produce the output associated with area B in the figure are allocated to irrigate new lands.

15 Coparing Market and Queuing Outcoes (cont) If the senior rights owners have to buy water under arkets, they are losing fro the transition. Under water arkets, they now have lower yields, they now have to pay for water, and they also ust pay to adopt the new technology, since doing so is now optial. Their loss per acre is: Pf e Pf h A ( Pf h A L L k u ) i + e i + i +. But if the senior rights are given the property rights to the water, they ay win. They still have lower output than under queuing, but the gain fro selling excess water ay overcoe this output loss. Their incoe per acre will be: Pf h A e h A L L Pf h A L t k i + i e i i If the transaction costs are high, there is no incentive to switch to a syste of water arkets. Naely, if: P Y + ki L k 0 A / ( h0 e ) t > L When transaction costs per acre exceed the per acre change in output plus the cost of adopting the optial odern technology less the cost savings of senior owners not adopting the conventional technology, water arkets ay be inefficient. Because arkets for final products have negatively sloped deand, the transition fro queuing to arkets will also reduce the arket price of agricultural coodities. Senior rights owners ay thus lose, even if they sell water because of the price decline of their outpur. Producers as a whole ay actually lose, but consuer surplus will increase.

16 Nuerical Exaple of Market vs. Queuing Land Base (103 acres) Deand Elasticity Queuing Outcoes Output (106 lbs.) Output Price ($/lb.) Irrigated Land (103 acres) Producer Profits (106 dollars) Market Outcoes: Adjustent Costs = $5/acre Output (106 lbs.) Output Price ($/lb.) Water Price ($/AF) Irrigated Land (103 acres) Technologies 2 2, Snr. Rights Net Profits ($106) Snr. Rights Gross Profits ($106) Percent Gain in Social Welfare 5.4% 16.3% 5.4% 23.8% Market Outcoes: Adjustent Costs = $50/acre Output (106 lbs) Output Price ($/lb.) Water Price ($/AF) Irrigated Land (103 acres) Technologies 2 2, Snr. Rights Net Profits ($106) Snr. Rights Gross Profits ($106) Percent Gain in Social Welfare - 0.5% 4.6% - 0.5% 10.3%

17 Deand for Water 250 D2 P = MVP of Water in 150 Agriculture ($/AF) P = 0.75 D1 Non-Ag Water Deand ($/AF) Water Available for Agriculture (illion AF) The deand functions for water can be derived according to the price of output and the available technology. The deand function has several steps and each is associated with a different technology. when urban deand is sall (D1), gains fro arkets are not spectacular, and traditional technology is optial since the MVP of water in alternate uses is sall. when water deand is high (D2), arkets lead to adoption of odern technologies and reduce ag. water use substantially. In general, there will be less objection to arkets aong users of scarce resources if existing users of the resource (senior rights holders or polluters) are given the right to sell perits.

18 Queuing Vs. Markets: A Nuerical Exaple the far production function is: y = 8e 2e 2 There are two technologies available: The traditional technology has a 50% water efficiency: h 0 =0.5 The odern technology has a 60% water efficiency: h 1 =0.6 Suppose for two technologies: P = 125, µ = 100, t = 50. Total water stock is, A = 6000 AF, Total land stock, L = Queuing Outcoe: Technology 0 is chosen. Senior rights holders ax. yield: Max{ y = 8e 2e 2 } the FOC: y e = 8 4e = 0 => e y e = 2, = 8, Water applied per acre is: a = e h0 2 = 0. = 4. 5 Acreage utilized siply depends on how far the water flows: AQ = 6, 000 = Aggregate output: Y Q = y (A Q ) = 8(1,500) = 12,000. Incoe per acre: π Q = 8(125) = $900. Total Far Incoe= (1,500 acres)($900/acre) = $1,375,000.

19 Queuing Vs. Markets: A Nuerical Exaple (cont) Market Outcoe: the case when only the traditional technology is available. Declining MVP of water and hoogeneous land quality iplies it is optial to distribute water evenly across all land 6000 => applied water per acre: a = = Effective water: e* = 3(0.5) = 1.5 Output per acre: y* = 8(1.5) - 2(1.5) 2 = 7.5 Aggregate Output: Y M = = Total incoe = 2000[ ] = py µ t Water price = VMP = p f e h 0 = 125 ( ).5 =125. Senior rights owners are given the right to sell surplus water: Senior rights owner owns 4 AF of water, uses 3 AF under a syste of water arkets and sells the reaining AF for $125: π * = $125( 7. 5) ($125) = $ Junior rights owners' profit per acre is: π * = $125( 7. 5) ($125) = $

20 Queuing Vs. Markets: A Nuerical Exaple (cont) the case when the odern technology is available e e * Effective water: a = 3 = e* = 18. h Output per acre: y* = 8( 18. ) 2( 18. ) = Aggregate output under arket: Y* = (2,000)(7.92) = 15,840 Total incoe = Water price = p f e h ( ) = py µ t c =125[ 8 4(1.8) ].6 = = 60. Assuing, as before, that Senior rights owners are allowed to sell their surplus water: Senior rights owners' incoe = Junior rights owners' incoe = ( 7. 92) = $ = 630.

21 Queuing Vs. Markets: A Nuerical Exaple (cont) Iplications: Establishing water arkets is welfare iproving. adoption of odern technology is in the best interest of society. total far incoe is higher when farers adopt new technology. Adopting odern technology is in the interest of junior rights holders Adopting odern technology is not in the interest of senior rights holders senior rights owners profit fro a arket syste, but only when odern technology is not adopted. Now Say the Governent Appropriates the Water Rights If the governent is given the water rights, then both senior and junior rights holders ust purchase water. The water price is still P = VMP in either case. Profit per acre is now the sae for the both senior and junior rights holders, which is what we already calculated for junior rights holders above. Therefore, it is now in the best interest of senior rights holders to invest in the new technology. the allocation of property rights achieves the sae result in ters of allocative efficiency: P = MVP = arginal profit per acre Different incentives are created for technology investent