Water-supply - California ; Supply and demand

Ronald H. Schmidt

English

Research Papers in Economics

FRBSF WEEKLY LETTER
,,"~umber 92=43, December 4, 1992
Diamonds and Water:
A Paradox Revisited
On October 30, President Bush signed legislation
into law that makes it possible for recipients of
water from California's Central Valley Project to
resell that water. This legislation is controversial,
because it is expected to plant the seeds for the
development of a water market in California,
Among the most frequently cited objections to
using markets to allocate water are concerns that
the results would be unfair and disruptive: In par-
ticular, opponents argue that a move to market
prices would mean a large shift in water from
farms to cities. This change in water allocation,
they argue, would lead to reduced agricultural
income and production, lower income in agri-
culturally dependent communities, and higher
food prices. In the extreme, this stylized scenario
predicts a world with fountains in Beverly Hills
and desolation in California's central valley farm-
ing region.
This vision of the distributional consequences of
a market system for water results, in part, from
putting together two statements about price de-
termination and drawing the wrong conclusion.
These statements are that (a) water is extremely
valuable, and (b) that the value of a commodity is
reflected in its price. Thus, the conclusion drawn
by some is that water prices would be high in a
marketsystem and that low income and agri-
cultural consumers would be severely limited
in their abilities to purchase water.
This conclusion does not necessarily follow,
however. In fact, a similar debate took place in
the economics literature in the eighteenth and
nineteenth centuries before being put to rest by
Alfred Marshall. Known as the "Diamond-Water
paradox:' the issue sought to explain how the
observed price of water could be below that of
other commodities, such as diamonds, given
water's high value in sustaining life. Marshall's
solution to the paradox was to recognize that
prices reflect the value ofthe last, or marginal,
unit, not the value of all units consumed. He
demonstrated that a commodity that has high
value to society could have a low price if it
were available in sufficient supply.
As discussed in this Weekly Letter, this insight is
relevant to the current debate. The evidence sug~
gests that water markets would not lead to a high
price for water, because while urban users now
pay a significantly higher price than agricultural
users, that reflects differences invalues ofthe last
unit consumed by the two groups given artificial
restrictions on trading. In fact, the eyidence sug-
gests that water use patterns would not be affected
significantly, implying that the effects on agricur-
ture and agricultural communities would not be
large.
The paradox
The diamond-water paradox was puzzled over
for nearly a hundred years in the economics lit-
erature. Adam Smith considered the issue in the
late eighteenth century, and David Ricardo spent
considerable effort trying to understand this
seemingly logical inconsistency with relative
price determination. Why would water, which
is essential to life, carry a price that is below that
of diamonds, whose use is far less critical?
Ricardo, the father of the labor theory of value,
tried to apply that theory to this case. He argued
that the cost of a commodity reflected the em-
bedded labor needed to bring that product to
market. Thus, he argued that water was relatively
cheap because it required less labor effort to
acquire than did diamonds.
While seeming to solve the dilemma, it was left
to Marshall to develop the correct answer to the
paradox. Marshall's answer can be seen in the
figure. Supply and demand curves for diamonds
(good 1) and water (good 2) are shown in the
two panels of the figure. As shown in the figure,
prices are determined where supply and demand
intersect in each market (points B and G), and
given the low quantity of diamonds, the equi-
librium price of diamonds exceeds that ofwater.
The important factor to note is that this is a mar-
ginal condition. Prices measure the value of the
final unit consumed. The total value derived from
use is measured by the area under the demandFigure 1
Comparing Supply and Demand in Two Markets
FRBSF
Price
A
Price
Good 1
Good 2
Quantity
as evidence that markets would allow those con-
sumers to bid up the price paid by farmers to a
high level. Given these prices, it is argued that
selling water would be more profitable than
growing crops, which would lead to il sharp
curtailment of agriculture.
In fact, these fears are overstated. High water
prices are observed in urban areas, but those
prices are not indicative of a market price for a
farmer's water. Urban prices are higher than agri-
cultural prices for two basic reasons. First, urban
prices are higher because the water has to be
pumped further and treated to meet higher qual-
ity standards. In California, for example, these
costs can exceed $100 per acre foot in many
urban areas. Those charges would continue to
be applied, which would result in a significantly
higher urban price even with a market price at
the wholesale leveL Thus, a high urban price
does not necessarily imply a high price for water
at the farm level.
F
H Quantity
curve up to the last unit, areas ABCD and FGHI,
for diamonds and water, respectively. Clearly,
even though the value of the last unit of dia-
monds is higher than that ofthe last unit of water,
the cumulative value of water far exceeds that of
diamonds.
The solution to the paradox, therefore, differenti-
ates between marginal value (prices) and total
value. It is not necessary for the price of water to
be high to guarantee that it be used beneficially,
nor does a low price necessarily reflect an in-
appropriately low total value for the resource.
Instead, the price serves to ration water to users
by applying the criterion that the value to those
using water has to be at least as high as the price
on the last unit, while those that do not receive
water must value it at less than that price.
California water prices
Misunderstanding of this paradox underlies some
ofthe fears about water markets expressed by ag-
ricultural and political groups. Concern is high in
the agricultural regions that iffarmers could sell
their water, they would do so. The high prices
currently paid by urban users for water are used .
More importantly, current high urban prices re-
flect artificial limits on urban access to water.
While those prices reflect urban users'willing-
ness to pay given a fixed supply, their willingness
to pay is likely to fall off sharply as more water is
made available.
To see this point, return to the two figures. Let
the figures reflect the supply and demand for wa-
ter for two consumers, one urban (good 1), and
one agricultural (good 2). Because water is not
freely traded, the price for urban users is higher
than that for agricultural users given the limited
supply available to urban users. Consider a small
transfer to urban users, however, as indicated by
the shifting supply curves in each market. In that
case, a small increase in the supply of urban
water would cause a sharp drop in urban prices
(from B to E), while causing a small increase in
agricultural prices (from G to J). This asymmetric
effect on the prices of the two user groups is the
direct result of differences in the slopes of the
demand curves of the different groups.
As with the Diamond-Water paradox, price dif-
ferentials between agricultural users' willingness
to pay and urban users' willingness to pay reflect
differences in the marginal value of water given
available supplies. If supplies were allowed to
move between the two user groups, an equilib-
rium price (differing only by transportation and
processing charges) would emerge that shifts a
minimal quantity ofwater to urban users. Thus,
the fact that urban users are currently willing to
pay a. higher price at the margin does not mean
that they would pay that price for a large quantity
of water offered by farmers.Evidence
Some recent evidence is suggestive of the poten-
tial effect. Vaux and Howitt (1984) estimate that
price effects on agriculture and the magnitude
of water transferred in California would be rela-
tively small under a market system. Using up-
dated figures in 1991 dollars from that article,
Schmidt and Cannon (1991) found that average
agricultural water prices might increase as little
as $2.60 per acre foot-from $54.61 to $57.23-
while urban prices would fall significantly. The
model also suggests that urban consumption
would increase by less than a million acre feet
per year. (Agriculture in California consumed
approximately 28.5 of the total 34 million acre
feet in 1985, which was the last "normal" year
of water deliveries.)
These asymmetric effects on urban and agri-
cultuial piices reflect the features of the diagram.
Urban prices are high because quantities are
very limited. However, if supplies increase, the
prices urban users are willing to pay would
drop off sharply because their demands are very
inelastic. In contrast, agricultural consumers'
demands are more elastic at current levels of
consumption. Consequently, agricultural users
would be willing to sell some water even with
relatively small increases in water prices. (Recent
studies by agricultural economists suggest that a
10 percent increase in prices would free up 4 to
7 percent of agriculture's water which would
translate to 20 to 40 percent more for nonagri-
cultural users. Moreover, these estimates are for
short run responses. Over the longer run,re-
sponses are likely to be much larger as farmers
install new technologies that save water.)
The important implication from these studies is
that the disruption caused by moving to a water
market would be small. Most fundamentally, all
users of water have downward sloping demand
curves for water. Farmers derive greater value
from the first unit of water they use than from the
last unit, and while the last unit may carry a low
value, the cumulative value oftheir water use is
large. Thus, it is unreasonable to think that a
slight increase in the market price of water
would cause a farmer to stop all consumption-
he would simply move back along his demand
curve and use less.
Given the limited amount of additional water that
would be consumed by nonagricultural sources if
trading were allowed, price effects on the farms
cannot be large, at least on average. Small cut-
backs by individual farmers would be sufficient
to generate enough water to clear the market
with minimal agricultural price increases. More-
over, by engaging in those transactions, the
farmer would have the financiai resources to
invest in water-saving technologies.
Conclusions
Opponents ofwater markets fear the disruptive
effects of large increases in water prices that
might emerge from water reform legislation such
as that involving the Central Valley Project. How-
ever, studies estimating the magnitude ofthe
potential price increase find only small increases,
suggesting that the impact on water use will be
minimal.
This deviation between evidence and perception
recalls the struggle to resolve the "diamond-
water paradox" posed over 200 years ago and
its solution, which was a step forward in under-
standing price determination. Currently observed
price differences between urban and agricultural
markets reflect differences in the value of water
at the margin to those users given artificial lim-
itations on exchanges. Ifwater is traded between
the two parties, urban users quickly move down
their demand curves, suggesting that their will-
ingness to pay for the marginal unit-the price-
will fall rapidly. Conversely, faced with a market
decision, farmers would be encouraged to sell
some-notall-oftheir water, which would
cause agricultural prices to rise slightly, since
they are at a comparatively flat portion of their
demand curves. Because ofthese differences in
the shapes ofdemand curves, small increases
in agricultural water prices could free up enough
water to make urban water prices fall consider-
ably more-and have little real impact on the
farm community.
Ronald H. Schmidt
Senior Economist
References
Schmidt, R.H., and F. Cannon. 1991.Using Water
Better: A Market-Based Approach to California's
Water Crisis. Bay Area Economic Forum.
Vaux, H.J., Jr., and R.E. Howitt. 1984. "Managing
Water Scarcity: An Evaluation of Interregional
Transfers:' Water Resources Research Ouly)
pp. 785-792.
Opinions expressed in this newsletter do not necessarily reflect the views of the management of the Federal Reserve Bank of
San Francisco, or of the Board of Governors of the Federal Reserve System.
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Index to Recent Issues of FRBSF Weekly Letter
DATE NUMBER TITLE AUTHOR
5/15
5/22
5/29
6/5
6/19
7/3
7/17
7/24
8/7
8/21
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9/25
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11 /6
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92-20
92-21
92-22
92-23
92-24
92-25
92-26
92-27
92-28
92-29
92-30
92-31
92-32
92-33
92-34
92-35
92-36
92-37
92-38
92-39
92-40
92-41
92-42
Agricultural Production's Share of the Western Economy
Can Paradise Be Affordable?
The Silicon Valley Economy
EMU and the ECB
Perspective on California
Commercial Aerospace: Risks and Prospects
Low Inflation and Central Bank Independence
First Quarter Results: Good News, Bad News
Are Big U.S. Banks Big Enough?
What's Happening to Southern California?
Money, Credit, and M2
Pegging, Floating, and Price Stability: Lessons from Taiwan
Budget Rules and Monetary Union in Europe
The Slow Recovery
Ejido Reform and the NAFTA
The Dollar: Short-Run Volatility and Long-Run Adjustment
The European Currency Crisis
Southern California Banking Blues
Would a New Monetary Aggregate improve Policy?
Interest Rate Risk and Bank Capital Standards
NAFTA and U.S. Banking
A Note ofCaution on Early Bank Closure
Where's the Recovery?
SchmidtlDean
Cromwell/Schmidt
Sherwood-Call
Walsh
Sherwood-Call
Cromwell
Parry
Trenholme/Neuberger
Furlong
Sherwood-Call
Judd/Trehan
Moreno
Glick/Hutchison
Throop
Schmidt/Gruben
Throop
Glick/Hutchison
Zimmerman
Motley
Neuberger
Laderman/Moreno
Levonian
Cromwell/Trenholme
The FRBSF Weekly Letter appears on an abbreviated schedule in June, July, August, and December.

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Managing Water Scarcity: An Evaluation of Interregional Transfers:' Water Resources Research Ouly

Water Better: A Market-Based Approach to California's Water Crisis. Bay Area Economic Forum.

Diamonds and water: a paradox revisited

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Diamonds and water: a paradox revisited

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