Journal of Environmental Management 67 (2003) 291–301
www.elsevier.com/locate/jenvman
Water transfers, agriculture, and groundwater management: a dynamic
economic analysis
Keith C. Knappa,*, Marca Weinbergb, Richard Howittc, Judith F. Posnikoff d
a
Department of Environmental Sciences, University of California, Riverside, CA, USA
Economic Research Service, United States Department of Agriculture, Washington, DC, USA
c
Department of Agricultural and Resource Economics, University of California, Davis, CA, USA
d
Pacific Alternative Asset Management, Irvine, CA, USA
b
Received 8 September 2000; revised 10 December 2001; accepted 11 July 2002
Abstract
Water transfers from agricultural to urban and environmental uses will likely become increasingly common worldwide. Many agricultural
areas rely heavily on underlying groundwater aquifers. Out-of-basin surface water transfers will increase aquifer withdrawals while reducing
recharge, thereby altering the evolution of the agricultural production/groundwater aquifer system over time. An empirical analysis is
conducted for a representative region in California. Transfers via involuntary surface water cutbacks tilt the extraction schedule and lower
water table levels and net benefits over time. The effects are large for the water table but more modest for the other variables. Break-even
prices are calculated for voluntary quantity contract transfers at the district level. These prices differ considerably from what might be
calculated under a static analysis which ignores water table dynamics. Canal-lining implies that districts may gain in the short-run but lose
over time if all the reduction in conveyance losses is transferred outside the district. Water markets imply an evolving quantity of exported
flows over time and a reduction in basin net benefits under common property usage. Most aquifers underlying major agricultural regions are
currently unregulated. Out-of-basin surface water transfers increase stress on the aquifer and management benefits can increase substantially
in percentage terms but overall continue to remain small. Conversely, we find that economically efficient management can mitigate some of
the adverse consequences of transfers, but not in many circumstances or by much. Management significantly reduced the water table impacts
of cutbacks but not annual net benefit impacts. Neither the break-even prices nor the canal-lining impacts were altered by much. The most
significant difference is that regional water users gain from water markets under efficient management.
q 2003 Elsevier Science Ltd. All rights reserved.
Keywords: Agriculture; Groundwater; Transfers; Economics; Management; Markets; Dynamic programming
1. Introduction
Water transfers and the associated mechanisms for
achieving them are the subject of intense policy debate in
the western region of the US and other areas of the world.
This is due to water supplies that are frequently fully
allocated, growing water demand for urban and environmental uses, opposition to construction of new reservoir
systems, and existing institutional structures that often limit
transfers. Since agriculture is the predominant water user,
and since some existing uses within agriculture may have
relatively low valuations of water at the margin, it is likely
* Corresponding author. Tel.: þ 1-909-787-4195: fax: þ1-909-787-3993.
E-mail address: keith.knapp@ucr.edu (K.C. Knapp).
that a significant majority of transfers will involve
agriculture (National Research Council, 1992; Howitt,
1998). These transfers might be between alternate uses
within agriculture, or from agriculture to urban and
environmental uses. Knowledge of how water transfers
potentially affect agriculture and the environment is
fundamental to the policy process.
Many major agricultural areas overlie groundwater
basins. Significant groundwater pumping occurs in normal
years, and may increase substantially in dry years. At the
same time, return flows from agriculture and conveyance
losses also provide significant recharge to the underlying
aquifers. Institutionally, groundwater usage typically occurs
under common property conditions. This means that
withdrawals are essentially unregulated in that overlying
0301-4797/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0301-4797(02)00162-7
292
K.C. Knapp et al. / Journal of Environmental Management 67 (2003) 291–301
users are free to extract as much water as can be beneficially
used. In this setting the likely effect of surface water
transfers will be to both increase pumping and decrease
recharge. One set of questions in evaluating surface water
transfers is therefore the potential impact on agricultural
production and the groundwater resource under common
property conditions. This is a dynamic problem since
increased pumping and/or reduced recharge will lower the
water table over time. This increases future pumping costs
which in turn affect future extraction rates.
Water transfers also have potential implications for
groundwater management and vice versa. Common property usage is economically inefficient since groundwater
extractions by individual pumpers lower future water table
levels for everyone and there is insufficient incentive to
account for this in individual decision-making (Negri, 1989;
Provencher and Burt, 1993). Groundwater management is
defined here as regulation of the extraction rate to achieve
economically efficient use of the resource. If successful this
will yield a higher level of social net benefits than under
common property use. Water transfers will affect the
efficient level of withdrawals as well as the magnitude of
inefficiency under common property use and hence the
economic incentive to initiate management. A converse set
of issues is whether groundwater management can potentially alleviate adverse consequences of water transfers on
regions.
A number of economic studies evaluate surface water
transfers in general as well as potential effects on
agriculture and the environment. These include Vaux and
Howitt (1984), Howe et al. (1986), Saliba (1987),
Weinberg et al. (1993), Keplinger et al. (1998), Willis
and Whittlesey (1998) and McCarl et al. (1999) as just a
few examples among many. This literature generally
relies on annual models and does not consider evolution
of the groundwater resource over longer time horizons. A
moderate-sized literature has also developed on the
economics of groundwater use and management. These
studies explicitly account for groundwater dynamics over
time, and also address the common property versus
economically efficient usage issue. Classic studies include
Burt (1964), Brown and Deacon (1972) and Gisser and
Sanchez (1980), and there have been a number of
extensions and empirical applications since then. These
studies focus on overlying uses and do not address how
out-of-basin water transfers might affect in-basin groundwater use and management.
This paper evaluates the effect of surface water
transfers on agricultural production, groundwater management, and water pricing, explicitly taking into account
aquifer dynamics over time. Kern county in California is
used as a representative example. Four alternate transfer
mechanisms are considered: involuntary cutbacks, voluntary water sales for a contracted amount, transfers
associated with canal-lining schemes, and a spot market
for water. These mechanisms are analyzed under both
common property and economically efficient management. Outcome measures examined include dynamics of
the agricultural production/groundwater aquifer system,
equity effects on agriculture, and implications for
groundwater management.
2. Model and data
We consider that portion of Kern County which lies in
the Central Valley (Fig. 1). This region overlies the
major aquifer in the Valley and has approximately
364,225 ha of farmland. Kern county lies south of the
Delta but north of the Los Angeles metropolitan area.
The California State Water Project ships water south
from the Delta to Kern county and other major
agricultural areas in the Valley, as well as the heavily
urbanized areas of Southern California. The future is
likely to see increased competition for this water as
environmental needs restrict water conveyance through
the Delta under dry conditions and population grows in
Southern California.
Although inter-basin water transfers associated with
water markets in California are rare, two such projects
already exist or are being planned for Kern county.
These include one water storage and transfer project
currently in operation, the Kern Water Bank, and another
conjunctive surface water storage and transfer proposal,
the Arvin – Edison exchange project, under intensive
negotiation. Additional economic pressure for transfers
from Kern county will likely occur in the future due to
both the county’s location and the relatively high quality
of water being delivered to its contractors. Thus Kern
county is an excellent case study of water transfer effects
on a joint agricultural production/groundwater aquifer
system.
A mathematical model for analyzing water transfer
effects on the region is derived from the groundwater
economics literature. Social net benefits are defined as
returns to land and management in agricultural production
in the region plus the value of water transferred outside the
region. Social net benefits in year t are
pt ¼
ð wt
0
pðwÞdw 2 ps ðwst þ wet Þ 2 cðht ;wgt Þ þ
ðwet
pe ðwÞdw ð1Þ
0
where p is the irrigation water demand curve, p s is the price
of surface water, c is the groundwater pumping cost
function, and p e is the export demand curve. Variables
are wt is total irrigation water, wst is surface water use, wgt is
groundwater withdrawals, wet is water exports under spot
markets, and ht is the hydraulic head of the groundwater
aquifer.
The first term on the right-hand side of Eq. (1) gives net
returns to agriculture as a function of water use, the next two
terms are the cost of water supplied to the region and the last
K.C. Knapp et al. / Journal of Environmental Management 67 (2003) 291–301
293
Fig. 1. Map of California showing the Central Valley running in a generally North-South direction. The Delta drains the Sacramento valley to the north and the
San Joaquin valley to the south, with outflow through the San Francisco Bay. The southern 1/3 of the valley is a closed basin except in very wet years. The study
area is the portion of the valley lying within Kern county.
is benefits from external water sales. Regional net benefits
are the value of agricultural production in the region net of
all costs except land and management, plus revenue from
external water sales. These are (1) minus consumer surplus
accruing outside the region; that is, (1) with the last integral
replaced by revenue from water sales. Municipal and
industrial (M&I) water uses are not explicitly included here
in either social or regional net benefits. These uses are quite
small compared to agricultural withdrawals in the region
and demand is very inelastic. We therefore assume that only
agriculture will be subject to water transfers and/or
groundwater management and that M&I uses are constant
over time.
Parameter values are noted in the Appendix. A quadratic
demand curve for applied irrigation water is specified as
pðwÞ ¼ a0 þ a1 w þ a2 w2
ð2Þ
with the parameters estimated from data in KCWA (1998)
as well as Feinerman and Knapp (1983) and Knapp and
Olson (1995). As estimated, the demand curve has a vertical
intercept at approximately $11.84 ha21 cm21, water use at a
zero price is 65.4 £ 106 ha cm yr21, and the curve is convex
to the origin. Specification of the export demand curve is
described in a later section.
Groundwater pumping costs are defined as
cðh; wg Þ ¼ ðk þ esÞwg þ eðh 2 hÞwg þ
e ðwg Þ2
Asy 2
ð3Þ
where k is average cost per ha cm of groundwater
extractions related to equipment use, e denotes pumping
costs per unit of lift per unit of water, s is drawdown, and h
is height of the land surface. The first term captures costs
associated with maintaining and repairing capital (well and
pump) equipment resulting from use of the well and pumps
for withdrawals, plus the energy costs associated with drawdown below the water table surface as the pumps run.1 The
second term captures the energy costs of lifting water from
1
The water table level in the model is the height of the water table
relative to some datum (sea level in our case) with no pumping. As
groundwater is extracted, the water table in the immediate vicinity of the
wells is lowered, creating what is known as a cone of depression or
drawdown. This downward gradient is necessary for water to flow into the
well, and is ultimately due to the finite transmissivity of the aquifer. The
drawdown implies additional energy costs needed to lift water to the land
surface beyond those implied by the regional water table level, hence its
inclusion in the pumping cost formula.
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K.C. Knapp et al. / Journal of Environmental Management 67 (2003) 291–301
the existing water table surface to the land surface, and the
third term captures the effect that, as water is withdrawn
over the course of the irrigation season, the water table level
is declining. Well and pump related costs and drawdown
were estimated from data in Dixon (1988) adjusted for
inflation. Energy costs were estimated from data in Feinerman and Knapp (1983) and Dinar (1994) also adjusted for
inflation.
Applied irrigation water is defined as
wt ¼
wst
þ
wgt
ð4Þ
or just the sum of applied surface and ground water. Surface
water usage is constrained by
wst # ð1 2 gÞðs 2 wet Þ
ð5Þ
where g is the fraction of surface flows lost to deep
percolation during conveyance through the water district
and s is average annual surface water availability to the
district which is assumed to be constant over time. Current
California law specifies that groundwater can generally be
used only on overlying land. This formulation restricts
water exports to only surface water. This also implies that
water transfers are occurring before the water reaches the
regional boundary, thus reducing the amount of conveyance
losses to the aquifer.2
Surface water for this region comes from three major
sources: the California State Water Project, the federal
Central Valley Project, and the Kern River. Annual average
surface flows are 24.3 £ 106 ha cm yr21. Of this amount,
70% is assumed available for irrigation and the remainder
recharges to the aquifer as conveyance losses. Deep
percolation flows from agricultural production are assumed
to be 20% of the amount applied. These parameters, along
with the aquifer parameters, are from Feinerman and Knapp
(1983). Initial hydraulic head was estimated from data in
KCWA (1998).
The equation of motion for the groundwater aquifer is
given by
htþ1 ¼ ht þ
½gðs 2 wet Þ þ bwt þ v 2 wgt Asy
ð6Þ
where v is net natural recharge to the aquifer, b is the
fraction of irrigation water that percolates through the
rootzone to the groundwater aquifer, A is the aquifer area,
and s y is the specific yield of the aquifer. Net natural
recharge includes recharge from natural sources and lateral
flows, as well as possible leakage through the bottom of the
aquifer. Natural recharge is quite small in the empirical
2
Stochastic surface flows are not considered here. The intent of the paper
is to analyze the effects of transfer programs on the expected values of
various hydrologic and economic variables. Previous work suggests that the
groundwater problem is close enough to certainty-equivalence that the first
moments will not be impacted significantly by the introduction of
uncertainty. Future work could extend this study by also considering the
impacts of transfer programs on second and higher moments of the
hydrologic and economic variables.
model in comparison to other sources of recharge and is
assumed here to be a constant. The reference point for
computing hydraulic heads is mean sea level (MSL).
Hydraulic head is bounded by h # ht # h where h and h
are the lower and upper bounds respectively as determined
by the aquifer geometry.
3. Surface water cutbacks and quantity contract exports
Most of the groundwater basins underlying the major
agricultural regions in California are currently unregulated
with regard to withdrawal volumes (Hauge, 1998). This is
true for our study area as well as many other parts of the
American West and other areas outside the US (Hauge,
1998). Thus it is appropriate to first analyze common
property groundwater usage and then consider transfer
effects under that regime.
The basic concepts of groundwater use under common
property conditions are well-known and set out in Gisser
and Sanchez (1980), Negri (1989), Provencher and Burt
(1993) and Gardener et al. (1997) among others. Under
common property usage there is no regulation of the
resource system; individual growers are assumed to make
decisions that are strictly in their own best interest and
ignore effects on others. With many users, each of whom
is small compared to the resource, the effect of an
individual’s current decisions on future levels of the
regional groundwater stock is perceived to be negligible.
Therefore decisions are made in each period to maximize
net benefits Eq. (1) in that period without regard to the
future level of the groundwater stock. This maximization
is subject to the constraint that groundwater extractions
are limited to the available supply, and the water
constraints (4) and (5). Numerical simulations of this
system were carried out using GAMS (Brooke et al.,
1992).
The results are shown in Fig. 2 and Table 1 for an
initial hydraulic head of 51.2 m above MSL and a 50year time horizon. With no transfers, hydraulic head
declines over this interval by some 7.6 m or 15%. As the
hydraulic head declines, groundwater becomes more
expensive and so withdrawals are somewhat reduced as
well. Annual net benefits decline by approximately
$12.36 ha21 (3%) during this period as a consequence
of increased pumping costs and reduced withdrawals.
Since these declines are relatively small over the time
interval, the results suggest that—absent regulation—the
system is probably not far from a steady-state. Of course
these are only yearly expected averages; the analysis
neglects the inevitable year-to-year variability in surface
water supplies which translates into fluctuating withdrawals and water table levels over time.
Involuntary cutbacks in surface flows to basins have been
imposed in the CVPIA for several areas in California
(dependent on flow conditions) to meet environmental goals
K.C. Knapp et al. / Journal of Environmental Management 67 (2003) 291–301
Fig. 2. Effects of involuntary surface water cutbacks under common
property usage for the Kern county agricultural production/groundwater
aquifer system.
(Loomis, 1994; Weinberg, 1997a).3 To analyze this, we
suppose that a specified cutback in surface water deliveries
to the basin begins in the first year of the 50-year simulation
and continues for every year thereafter. We also assume that
with these cutbacks, growers will no longer have to pay for
this water. Also to be noted is that the cutback is in total
surface water availability (s); the water export variable wet is
set equal to zero. Since some surface deliveries s are lost
during conveyance, the cutback translates into a smaller
cutback in actual surface water available for irrigation,
although recharge to the aquifer is also adversely affected.
Fig. 2 and Table 1 illustrate the results for cutbacks of 10
and 20% from the original supply of 24.3 £ 106 ha cm yr21.
With reduced surface water availability, growers rely more
3
The CVPIA of 1992 mandates that some 14.8 £ 106 ha cm of water
annually must be re-allocated to environmental uses. Under average water
supply conditions, this requirement implies that approximately 20% of
current CVP deliveries would be transferred from agricultural water users
to the environment (Loomis, 1994; Weinberg, 1997a). However, it should
be noted that this reallocation is only from federal water supplies; it does
not include reallocations from state or local supplies. Also, some of this
water may be met in other ways, such as use of so-called ‘surplus’ water
resulting from improved operating procedures (Loomis, 1994). Thus the
actual percentage reduction in total surface water diversions to agriculture
for environmental uses could be significantly lower.
295
heavily on groundwater, thus further lowering the water
table. For example, the 10% cutback lowers the water table
by 5.5 m after 20 years and by 10.1 m after 50 years in
comparison to the base run, with comparable effects for the
20% cutback about double these amounts. The effect on
withdrawals is more complicated. In particular reduced
surface water availability tends to ‘tilt’ the withdrawal
schedule. In the early years withdrawals are greater with
larger cutbacks as would be expected. However, at some
point later in the horizon, the extra pumping lift makes
groundwater sufficiently expensive that withdrawals eventually become less than withdrawals with no cutbacks. Also,
recharge is reduced.
The bottom panel in Fig. 2 shows what happens to annual
regional net benefits in the basin with cutbacks. For the 10%
cutback, annual regional net benefits are reduced by
$15 ha21 yr21 after 20 years and $22 ha21 yr21 after 50
years. Comparable effects for the 20% cutback are again
approximately double these amounts. An overall conclusion
about the effects of surface water cutbacks on groundwater
usage in the unregulated case thus depends on the
persepective. If one considers the 10% cutback and a
short-horizon, then the impacts are modest. If one considers
the larger cutback and/or a long horizon, then the effects are
more substantial.
Hydrologically analogous to involuntary cutbacks is a
voluntary water transfer program on an extended quantity
contract basis with compensation. Water transfer volumes
analyzed here are identical to the pure cutback case. In
particular we consider wet equal to 10 or 20% of available
surface water in every period over the horizon. Growers
continue to pay the surface water price ps ¼ $3 ha21 cm21
whether it is used or transferred. In this instance withdrawals and hydraulic head stay the same as in the
analogous cutback case (Table 1). The only change is the
fiscal impact on farmers which depends on the price
received for the water.
In an actual situation the price received for water by the
region p e will depend on a variety of factors including
negotiating and bargaining strengths. Here we focus on a
break-even water price calculated as the cost of water to
growers ($3 ha21 cm21) plus an amount sufficient to cover
the losses identified in the pure cutback case. These breakeven prices are calculated to leave the district equally well
off in present value terms over the 50-year horizon as it
would be without the transfers. Such prices are of value to
districts trying to decide how much to accept for future
water sales.
One way to calculate such break-even prices is to
determine a price in each period that equalizes the loss
in annual net benefits in that period from the transfer.
We refer to this as a sequential pricing strategy.
Continuing with common property usage, break-even
prices are $3.64 ha21 cm21 for water transferred in year
1, $5.17 ha21 cm21 for water transferred in year 20, and
$6.34 ha21 cm21 for water transferred in year 50. Another
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K.C. Knapp et al. / Journal of Environmental Management 67 (2003) 291–301
Table 1
Water transfer effects on the Kern county agricultural production/groundwater aquifer system
Policy
Common property
Efficiency
wg50
h50
pa
wg50
h50
pa
14.8
43.6
374.31
12.3
67.7
380.34
6.03
14.4
14.1
33.5
23.2
361.56
347.77
12.1
12.0
57.6
47.2
367.88
354.46
6.33
6.70
Extended quantity contract
10%
14.4
20%
14.1
Canal-lining
12.2
Water markets
15.4
33.5
23.2
33.2
23.2
374.31
374.31
368.72
360.84
12.1
12.0
10.4
13.2
57.6
47.2
53.6
49.7
380.34
380.34
373.54
388.24
6.03
6.03
4.82
8.10
No transfers
Involuntary cutbacks
10%
20%
Annualized GWM benefits
wg50 , groundwater withdrawals in year 50 (106 ha cm yr21), h50, hydraulic head in year 50 (meters above MSL). pa, annualized regional net benefits over the
50 year horizon per-hectare of farmland ($ ha21 yr21). Annualized GWM benefits, benefits to groundwater management computed as the difference in
annualized social net benefits under economic efficiency and common property ($ ha21 yr21).
approach is to calculate a single (uniform) break-even
price to be paid annually. This is referred to here as a
uniform pricing strategy. Using the present-value losses
noted previously, we calculate this break-even price as
$4.95 ha21 cm21. These are the minimum annual prices
that the region should accept for a uniform level of annual
water transfers over the 50-year period in order to achieve
at least the same present value of net benefits.4
The results show that the dynamic groundwater effects
and the time horizon are critical in determining the breakeven price for water transfers, and that a static analysis
ignoring these effects could seriously underestimate these
prices. With sequential pricing, the year 50 break-even price
is 74% larger than the year 1 break-even price, while the
uniform break-even price is 36% greater than the year 1
break-even price. These differences arise because prices
implied by short time horizon calculations (e.g. the first
period) do not account for the longer-term impacts of the
transfer on the quantity of groundwater available or the
costs of using it. Thus a static analysis relying on year 1
results could seriously underestimate appropriate prices to
charge for water.5
4. Canal-lining
We next consider the effects of canal-lining in the
unregulated aquifer with a subsequent transfer of ‘saved’
4
These prices only apply for relatively small transfers-for larger transfers
the break-even price could rise given non-linearities in the net benefit
function. Also, these prices still leave the district worse off after year 50,
although this effect will be small in present value terms evaluated at the
beginning of the horizon.
5
Break-even prices were also calculated under economic efficiency.
Under the sequenced approach, break-even prices are $3.81 ha21 cm21 in
year 1, $5.03 ha21 cm21 in year 20, and $6.40 ha21 cm21 in year 50. The
uniform (annualized) break-even price is $4.86 ha21 cm21. Thus these
break-even prices are very comparable to those calculated under common
property.
supplies out of the basin. The idea is that an outside
entity invests in canal lining which reduces percolation
of surface flows to the water table. The amount of saved
water is then transferred to the outside entity. This is
analogous to the proposed transfer between the Imperial
Water District and other Southern California water
agencies (Wahl, 1994). Nominally at least the outside
entity presumably gains from this transaction while the
agricultural producing region is at least not worse off. It
will be seen that in actuality the situation is somewhat
more complicated.
It can be shown that this scheme results in a gain in
surface water available for irrigation to the district, although
this gain is not likely to be large in most instances. Although
surface flows to the district are reduced, this reduction is
more than made up for by the reduced conveyance losses for
what remains. However, the reduction in deep percolation
flows affects hydraulic head and hence groundwater
extractions. Theoretical analysis (available from the
authors) establishes that steady-state hydraulic heads and
groundwater extractions are reduced in this scheme under
both common property and efficient usage in comparison to
the base case. This is true at least for small changes in canallining if not all changes. Thus there are somewhat opposing
effects on the agricultural region and empirical analysis is
needed to determine the net outcome.
For the empirical analysis, we consider the canal-lining
transfer scheme with a change in the surface water
infiltration coefficient equal to 0.1 and water transfers
equal to 2.43 £ 106 ha cm yr21. Thus the new coefficient
value is g ¼ 0:2 and surface water flows to the district are
s ¼ 21:87 £ 106 ha cm yr21 : Consistent with theoretical
analysis, this canal-lining project results in a hydraulic
head at year 50 some 10.4 m lower than that in the base case,
and groundwater withdrawals some 2.59 £ 106 ha cm less
than base levels in year 50 (Table 1). Annualized net
benefits in the region are reduced by $5.58 ha21 of farmland
per year.
K.C. Knapp et al. / Journal of Environmental Management 67 (2003) 291–301
As noted, there are two somewhat counteracting effects
of this scheme on the region: First, there is an increase in
available surface water for irrigation in each year. This
shows up in terms of reduced groundwater extractions and
in fact net benefits in the region are higher than without the
canal-lining scheme in the early years. However, there is
also a negative impact on the region in terms of reduced
flows to the water table from percolation below the canal.
This latter effect eventually comes to dominate and after
some point annual net benefits are below the base level as
pumping costs increase due to an increased lift and this in
turn reduces withdrawals. Although the program might
nominally appear reasonable at first glance since saved
water from the canal-lining is being transferred, in actuality
the region is somewhat worse off, so either less than the
saved water should be transferred or the region needs to be
financially compensated in some way.
5. Water markets
We now consider water markets as a mechanism of
intersectoral transfers and allocation, again for the unregulated aquifer. Here we assume the basin receives its full
allotment of surface water, but farmers are allowed to sell
water to the urban sector on an individual basis. We suppose
a competitive market with many buyers and sellers in the
external market. Each is relatively small compared to the
market and takes price as a given. Since competitive
markets are economically efficient under the First Welfare
Theorem (Varian, 1992), optimizing Eq. (1) simulates a
competitive market with respect to exports. This market is
restricted efficient in that for a given year with a given
hydraulic head it would not be possible to achieve a higher
level of social net benefits in that year.
The export demand curve in (1) gives marginal benefits
from water exported to urban areas outside the region under
consideration. It is net of transport costs and thus reflects
prices at the region’s border. The export demand curve is
specified as
pe ðwÞ ¼
3
X
bi w i
ð7Þ
i¼0
and was estimated from Vaux and Howitt (1984). They
divide the California urban sector into two regions with
estimated supply and demand curves for each. Each of these
were aggregated, then horizontally subtracted to determine
an aggregate net import demand curve for this sector. This
curve was then adjusted for inflation, transport costs, and
Kern county’s surface supply as a fraction of California
agriculture’s surface supply, to determine the export
demand curve for Kern county. This curve is fairly inelastic
reflecting residential and industrial users greater degree of
ability to pay for water. Other definitions, equations and
constraints are as before.
297
Selected results are in Table 1. Over the 50-year horizon,
water exports from Kern county begin at 5.00 £
106 ha cm yr21 and decline to 4.88 £ 106 ha cm yr21. This
decline is due to the fact that as the water table falls, the
shadow value of surface flows rises and hence less is offered
for sale on the market. Previous studies of water transfers
are generally static. Quantitatively, these results demonstrate that the structure and flow of transfers could evolve
over time as the aquifer responds. Quantitatively, this effect
is quite small and is due to the inelastic export demand curve
noted earlier. This level of water exports under common
property is roughly 20% of the available surface inflows to
Kern county. Thus the other hydrologic variables under
competitive water markets are approximately as shown in
Fig. 2 for the 20% cutback.
In year 1, social net benefits are $138 million without
markets and $236 million with markets, for an increase
of 71%. In year 50, the comparable percentage increase
due to water markets is 61%. Thus competitive water
markets can result in substantial societal gains; they are
driven by the greater willingness-to-pay for water in the
urban sector and the consequent inelastic demand.
As noted earlier, regional net benefits are given by
Eq. (1) minus consumer surplus accruing to the urban
sector. In the first year, we find regional net benefits
essentially identical with and without water markets. In
the last year (year 50), regional net benefits with water
markets are actually 7.5% less than without markets. The
first result is explained by the fact that marginal pumping
costs are essentially flat at the equilibrium level; this
means that exports can be supplied with a very minimal
increase in water prices in the region. In other words, the
export supply curve is very flat so there is minimal
producer surplus from opening up markets; almost all the
gain in social net benefits is accruing to external water
consumers. For the second result, the surface water
exports imply larger groundwater extractions which
drives the water table level lower than it would otherwise
be. In this example, at least, the (static) gains from trade
to the region are outweighed by the increased pumping
cost and the region is worse off.
At first glance these results may seem at odds with
economic theory since water sales are voluntary; however,
this is not the case. In each period considered individually,
water sales leave the agricultural region at least as well off
as no water markets in that period given the existing
hydraulic head and other hydrologic conditions at the
beginning of the period. Furthermore, water sales are by
individuals in a competitive market, thus there is no market
power being exerted. The fact that they lose in the long term
compared to no markets cannot by overcome by individual
agents acting separately since, under common property
usage with many agents and no regional collusion, it would
not pay for individual agents to try and hold back on water
sales and their own groundwater usage in order to stem the
falling groundwater table. It is rational for them to operate
298
K.C. Knapp et al. / Journal of Environmental Management 67 (2003) 291–301
solely on a period-by-period basis without regard for the
future.
6. Economic efficiency and groundwater management
The analysis so far has only considered an unregulated
aquifer which is the current institution in the study area. It is
well known that common property usage is economically
inefficient (Negri, 1989; Provencher and Brut, 1993)
implying a potential role for management. This is due to
externalities where individuals ignore costs imposed on
others. Dixon (1988) provides extensive theoretical and
empirical evidence on this. As a consequence, common
property usage results in excessive withdrawals and lowered
future water table levels. There is also considerable interest
in the policy arena in groundwater management (Hauge,
1998), and in some circumstances California water law
prohibits water transfers unless a groundwater management
plan is in place (California Water Code, sections 1220 and
1745.10). Accordingly, we now consider economically
efficient use of the resource and in particular the
implications of water transfers for groundwater management and vice versa.
Burt (1964) initiated numerical analysis of economically
efficient groundwater management. For economic efficiency, the time path of groundwater extractions maximizes
the present value of social net benefits Eq. (1) over an
infinite horizon
1
X
ð1 þ rÞ2t pt
ð8Þ
t¼1
where r is the discount rate. This optimization is subject to
the equation of motion Eq. (6), the other constraints and
definitions (2) – (5), and various bounds and non-negativity
conditions. The problem is solved using dynamic programming methods written in the GAMS language (Brooke et al.,
1992), where successive approximations are used to
calculate the value function which is then used in forward
simulations to estimate time-series values over the 50-year
horizon. Selected results are in Table 1.
In contrast to common property usage, economic
efficiency results in an increasing hydraulic head over the
simulated time span for the original surface water
allocation. The difference is significant; after 50 years for
example, there is almost a 24.4 m difference in pumping lift.
Although the system does not reach steady-state during the
horizon considered, optimal management will eventually
result in a steady-state, and obviously the water table will be
at a substantially higher elevation than under common
property usage. Optimal withdrawals are significantly lower
than withdrawals under common property usage. This
results from the fact that the economically efficient solution
accounts for the effect of current withdrawals on future
pumping costs, whereas the common property solution does
not. Although not illustrated, social net benefits are reduced
in the early years under efficient use due to reduced
extractions and the consequent adjustments on the part of
growers. After some point, however, management results in
increased annual social net benefits relative to common
property usage due to reduced pumping costs and also
narrowing the gap in terms of extractions.
Benefits from groundwater management are the difference in present value of social net benefits under economic
efficiency and common property. Beginning with Gisser and
Sanchez (1980), a large number of studies have generally
found relatively small social benefits from managing
groundwater (Feinerman and Knapp, 1983; Nieswiadomy,
1985; Reichard, 1987; Kim et al., 1989; Brill and Burness,
1994; Provencher and Burt, 1994; Knapp and Olson 1995;
Burness and Brill, 2001). After annualizing, groundwater
management benefits are $6.03 ha21 yr21 for the basin
considered here over the 50-year horizon and with the
original surface allocation. Consistent with previous
economic studies of groundwater management, this figure
is fairly low. Note also that this is only the benefit from
management, it does not consider management costs
(contracting, monitoring and enforcement) which would
make the net benefits of groundwater management even
smaller.
Intuitively, water transfers from the basin make the
groundwater resource more valuable and so the gains from
management should increase as surface water availability
decreases. This is borne out by the results of our analysis
(Table 1). A 10% cutback in surface water deliveries
increases annualized management benefits by 5% compared
to the original surface water allocation, while the 20%
cutback results in an 11% increase over the no cutback case.
Thus, in relative terms the surface water reductions do imply
significant increases in the incentive to manage the resource.
Likewise, the other transfer policies may also increase the
benefits from management. Overall, however, benefits from
groundwater management appear to remain rather modest.
If these results and those of the previous literature are
correct, then groundwater management as a precondition for
water transfers would need to be justified on grounds other
than the pumping cost and stock externalities examined to
date in the groundwater economics literature.6
A converse question is to what extent management might
mitigate the adverse effects of water transfers on the
regional basin. Qualitatively, the effects of transfers under
economic efficiency are comparable to those under common
6
Note, however, that regional management benefits can be significantly
larger than the social management benefits. For example, regional
management benefits are $27.40 ha21 yr21 with water markets in
comparison to social management benefits of $8.10 ha21 yr21. This
implies a larger incentive for the region to adapt management than
indicated by the social benefit calculation. It also implies possible equity
effects from management: with water markets, external water consumers
lose from initiating efficient groundwater management while the region
gains.
K.C. Knapp et al. / Journal of Environmental Management 67 (2003) 291–301
property: they lower the water table over what it otherwise
would be, tilt the extraction schedule, and may lower annual
net benefits from agricultural water use depending on the
type of transfer. With the 20% cutback for example, the
effect is strong enough that the optimal water table declines
over time instead of increasing as with no transfers or the
10% cutback under efficiency. Quantitatively, the 20%
cutback after 50 years lowers the water table by 47% under
common property (compared to the original allocation), but
only 30% under efficiency. Comparable figures for annual
net benefits are 13% for common property and 12% for
efficiency. As another example, annualized regional net
benefits under the canal-lining scheme are still reduced
under economic efficiency compared to the original
allocation. Thus optimal management may mitigate only
some (if any) of the adverse effects of transfers on the
aquifer.
Under common property usage we found that competitive water markets can reduce regional net benefits when the
dynamic effects on groundwater are accounted for. An
interesting question is whether this still holds under
economically efficient management. Under economic efficiency, water exports from the region are a constant (over
time) 4.81 £ 106 ha cm yr21. This is somewhat less than
exports under common property usage, the reason being that
with optimal management the user cost of groundwater
extractions is now accounted for. This means that growers
are somewhat less willing to substitute current extractions
for reduced surface flows, hence somewhat less surface
flows are exported. Social net benefits as defined by Eq. (1)
are almost constant over the horizon and the gain in social
net benefits for the combined agricultural/urban system
from opening up markets is again quite substantial (67%).
Annualized regional net benefits over the 50-year
horizon are $388 and $380 ha21 yr21 with and without
water markets respectively under efficiency. Thus opening
up water markets in conjunction with optimal groundwater
management implies a gain of $8 ha21 yr21 for agricultural
producers who are the water sellers in this problem, or a gain
of approximately 2%. Note that this assumes that the gains
from groundwater management are internalized in the
region. This could occur through quantity restrictions on
groundwater withdrawals, in which case users capture the
benefits of management, or through a pumping charge
which is rebated back to users in a lump-sum fashion so as
not to distort the incentive effects of the charge.
transfers of 5– 15% away from agriculture might not be
unreasonable over the next 20 – 30 years in California.7 The
consequences of alternate transfer programs on agriculture
are evaluated here for Kern county, California.
Water transfers lower water table levels as expected;
however, the effect on groundwater withdrawals is more
complicated. Initially withdrawals increase with surface
water transfers as expected, but eventually they decline.
This can be attributed to both the reduced conveyance
losses and deep percolation flows from surface flows as
well as the increased pumping costs. Quantitatively the
effects of transfers may well be moderate at most, at
least for the level of transfers analyzed here. For
example, we find that a 20% transfer level results in a
31% increase in pumping lift and a 13% reduction in
annual regional net benefits from agricultural production
after 50 years in comparison to the no-transfer case.
A major concern with water transfers is the equity effects
on the regions supplying the water. Certainly regions with
involuntary cutbacks will lose, but, as noted, the effects are
not necessarily large when one considers the range of
possible adjustments. The canal-lining scheme, although
nominally fair and initially beneficial to the region, may also
result in net losses to the region over time due to the reduced
conveyance losses which help recharge the aquifer. Likewise, we also found that competitive water markets and no
groundwater management can result in regional losses from
transfers. Although agricultural water sellers are gaining on
a year-by-year basis given water table levels in each year,
the extra withdrawals-generated by farmers substituting
groundwater for the surface water they transfer-imply
reduced water table levels over time which in turn generate
increased pumping costs and lower withdrawals. Thus some
of the fears of water-exporting regions about water markets
have a legitimate grounding and it may therefore be
necessary to take extra steps for everyone to share in the
net benefits of establishing water markets beyond just
setting up a textbook water market.
Accounting for dynamic effects is also important for
districts contemplating water sales. For example, if the
district prices water according to the initial conditions, then
the break-even price would be $3.65 ha21 cm21; however,
the break-even price would be $6.32 ha21 cm21 in year 50
under a sequenced approach or $4.86 ha21 cm21 in the
annualized approach. Thus prices charged by the district for
7
7. Conclusions
Water transfers from agriculture to environmental and
residential/industrial uses are likely to become increasingly
common over the next few decades in California and other
parts of the western US and world. It is difficult to estimate
the magnitude of these transfers, but a review of existing
studies as well as the results here suggests that, on average,
299
Vaux and Howitt (1984) found water transfers from agricultural to
urban uses ranging from 6.3% of total agricultural supplies in 1980 to
11.5% of total agricultural supplies in 2020. In a more recent analysis of
Central Valley agriculture, USBR (1998) estimated that the vast majority of
all water transfers would be from Tulare Basin agriculture (including Kern
County) to Southern California urban users, and that four percent of the
surface water in that region would be transferred, or a total of
1.2 £ 106 ha cm. Weinberg (1997b) calculated that water transfers from
CVP water users under the CVPIA would be four percent of federal water
use when voluntary water transfers were the only provision considered.
Environmental re-allocations are discussed in footnote 3.
300
K.C. Knapp et al. / Journal of Environmental Management 67 (2003) 291–301
its water can only be accurately calculated by accounting for
grower response to surface water reductions and the
associated changes in the water table level.
We found that in some instances economically efficient
management will mitigate adverse impacts of surface water
transfers, but not in many circumstances or by much.
Management had little impact on the canal-lining losses and
break-even price calculations. Management did reduce the
water table impacts under cutbacks by a significant amount
but not the annual net benefit impact. Perhaps the most
striking effect of management occurs with water markets.
Here we did find that the region was better off under water
markets although the gain was not large. Whether this is a
general result or just holds for the particular study area here
is an open question.
A somewhat surprising result in the groundwater
economics literature is the relatively low level of benefits
from initiating management, so it is natural to ask whether
water transfers will alter this finding. Reductions in surface
water availability due to transfers increase stress on the
aquifer and social benefits from groundwater management
increase as might be expected. In percentage terms the
increase can be substantial; however, the overall level of
social management benefits remains rather small. There can
be equity effects, however, and in some instances benefits to
the region from initiating management can substantially
exceed social management benefits.
In some locales in California, water cannot be transferred
out of basins without a groundwater management plan and
there is often a presumption in the general policy literature
that groundwater management should be initiated as a
precondition to transfers. The results here suggest that
groundwater management is neither a necessary nor a
sufficient condition for everyone to share in the benefits of
reducing the barriers to transfers and the associated water
reallocations. This holds under the pumping cost externality
analyzed here. Other phenomena such as land subsidence,
water quality, seawater intrusion, natural habitats, or equity
considerations could imply a role for management beyond
that considered here.
Acknowledgements
The authors thank Don Erman for suggesting the research
topic, Dan Sumner for editorial comments, and Phyllis Nash
for assistance with the graphics. Two reviewers and the
Journal editorial staff provided numerous helpful suggestions leading to a substantially improved exposition.
Appendix A
See Table A1.
Table A1
Parameter values for the Kern county agricultural production/groundwater
aquifer system
Parameter
Description
Value
r
a0
a1
Interest rate
Water demand intercept
Water demand slope
a2
Water demand quadratic
k
e
s
ps
s
g
b
A
h
h
sy
v
h1
b0
b1
Well/pump O&M costs
Energy cost
Drawdown
Surface water price
Annual surface inflows
Surface water
infiltration coefficient
Deep percolation coefficient
Aquifer area
Land height
Aquifer bottom
Specific yield
Natural recharge
Initial hydraulic head
Export demand intercept
Export demand slope
4%
$11.88 ha21 cm21
2$0.29713
[106 ha cm]21 (ha cm)21
$1.76 £ 1023
[106 ha cm]22 (ha cm)21
$0.50 (ha cm)21
$0.039 (ha cm)21 m21
18.3 m
$3.00 (ha cm)21
24.30 £ 106 ha cm yr21
0.3
b2
Export demand quadratic
b3
Export demand cubic
0.2
0.52 million ha
117 m above MSL
71 m below MSL
0.13
0.641 £ 106 ha cm yr21
51 m above MSL
$41.30 ha21 cm21
2$8.82348
(106 ha cm)21 (ha cm)21
$1.235
(106 ha cm)22 (ha cm)21
2$0.1938
(106 ha cm)23 (ha cm)21
Monetary values are 1992 dollars. Data sources are described in the
text.
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