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 Title Page
 Introduction
 Model
 A case of productivity differe...
 Conclusion
 Reference
 Appendix






Group Title: Working paper - International Agricultural Trade and Policy Center. University of Florida ; WPTC 04-05
Title: Explaining participation in spot and options markets for water
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Title: Explaining participation in spot and options markets for water
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Table of Contents
    Front Cover
        Page i
    Center information
        Page ii
    Title Page
        Page 1
    Introduction
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
    Model
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
    A case of productivity differential
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
    Conclusion
        Page 21
        Page 22
        Page 23
    Reference
        Page 24
    Appendix
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
Full Text

WPTC 04-05


i -ional Agricultural Trade and Policy Center



EXPLAINING PARTICIPATION IN SPOT AND OPTIONS
MARKETS FOR WATER
By
Ram Ranjan, Noel Gollehon, & Marcel Aillery

WPTC 04-05 December 2004


WORKING PAPER SERIES


i~fr


UNIVERSITY OF
FLORIDA


Institute of Food and Agricultural Sciences


"j_









INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER


THE INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER
(IATPC)

The International Agricultural Trade and Policy Center (IATPC) was established in 1990
in the Institute of Food and Agriculture Sciences (IFAS) at the University of Florida
(UF). The mission of the Center is to conduct a multi-disciplinary research, education and
outreach program with a major focus on issues that influence competitiveness of specialty
crop agriculture in support of consumers, industry, resource owners and policy makers.
The Center facilitates collaborative research, education and outreach programs across
colleges of the university, with other universities and with state, national and
international organizations. The Center's objectives are to:

* Serve as the University-wide focal point for research on international trade,
domestic and foreign legal and policy issues influencing specialty crop agriculture.
* Support initiatives that enable a better understanding of state, U.S. and international
policy issues impacting the competitiveness of specialty crops locally, nationally,
and internationally.
* Serve as a nation-wide resource for research on public policy issues concerning
specialty crops.
* Disseminate research results to, and interact with, policymakers; research, business,
industry, and resource groups; and state, federal, and international agencies to
facilitate the policy debate on specialty crop issues.











Explaining Participation in Spot and Options Markets for Water1





Ram Ranjan
Postdoctoral Associate
International Agricultural Trade & Policy Center
Food and Resource Economics Department
University of Florida
Ph: 352 392 1881 -326
Fax: 352 3929898
Email: rranjan(aifas.ufl.edu

Noel Gollehon
RED/PMT, USDA-ERS
lS,\11 [, Washington DC
Ph: (202) 694 5539
Fax: (202) 694-5775
Email: GOLLEHON( ers.usda.gov

&

Marcel Aillery
RED/PMT, USDA-ERS
1, 11 \[, Washington DC
Ph: (202) 694 5511
Fax: (202) 694-5775
Email: MAILLERY(ers.usda.gov



Presented at the WAEA Conference in Hawaii, July 1st, 2004.






December 2004



Preliminary Draft. Not for Citation or Quotation.

1 Views expressed in this paper are of the authors' alone and do not necessarily reflect the views of the
organizations to which they belong.









Introduction

Currently, agriculture accounts for the major share of water use in the U.S.

However, demand for water outside agriculture has been steadily rising over time.

Demanders include, agricultural transfers within agriculture, municipal, industrial, and

environmental users. Despite a higher value of water to the outside users, there have

been few transactions of water from the agriculture to the outsider users, thus creating a

water shortage to the later (Gaffney 1997, Michelsen 2000, etc.).

Water transfers through markets have been advocated as a means of mitigating

water-supply shortages to the outside users. However, various factors have limited the

development of operational markets for water in the past. These include physical,

financial, institutional limitations2. Young (1986) describes four basic ingredients of an

institution that would make water markets viable- security, flexibility, certainty, and

consideration of third party impacts. Even where the physical conditions have been

optimal, significant institutional bottlenecks exist in the form of transaction costs and

risks. Lund (1993) shows that the risk associated with the actual delivery of water, to the

water buyer, matters and can be a significant factor in determining the success of water

markets. Such risks of failure generally arise from court challenges posed by third parties

who might be affected by such transfers. To the sellers of water, the fear of adverse

consequences from trade may form the most significant hindrance to market

participation3. Adverse impacts on the farmers from federally induced markets may have

political fallouts too.


2 See Ranjan et al. (i" 1'4) for a detailed review of the water market related literature for the US.
3 Most studies, however, have found little impact on the agricultural sector from water transfers. Howe et
al. (1990) examine the impact from water transfers on the area of origin for a seven-county reach of the
Arkansas River in southeastern Colorado. Their analysis involves an input-output based approach that









Market based approaches such as the 'options' and the 'spot' markets have been

identified as the preferred instruments to facilitate this transaction as they offer various

degrees of risk mitigation to the buyers and sellers of water.

Much of the water transfers currently occurs through spot markets. In the context

of water, spot markets refer to ad hoc leasing of temporary water use rights in response to

a water-supply restriction underway. Spot markets typically involve agricultural sellers

and other irrigators, or other parties representing municipal or environmental interests.

Some studies have emphasized the role of spot markets in facilitating water transactions

as they allow more flexibility and generally do not cause severe third-party impacts.

Saleth et al. (1991) assess how spot markets would be restricted to few participants in

presence of third party impacts caused by the flow pattern of water. For example, if a

water transaction between two parties infringes upon the original water rights of

downstream users, the scope of water transactions may be limited. In presence of such

thin spot markets, transactions may be characterized by bargaining, the outcome of which

would be affected by such factors as the size of the bargaining units, the nature of water

rights (equal sharing versus priority sharing), the nature of the bargaining mechanism,

and the availability of information on the participants payoffs.

Of the two types, the spot market and the contingent market, the latter has been

advocated to be of particular interest in various regards. Howitt (1998) makes the case



incorporates both backward and forward linkages of the agriculture sector. They find that total losses to the
agriculture sector from irrigation reductions are insignificant and easily accounted for by the gains to urban
areas from increased water transfers.
On the other hand, Moore and Dinar (1995) come up with opposite conclusions. They design
various models of input use involving two inputs- surface water and land- to test whether such factors
might be treated as fixed by the farmers. Empirical models are estimated using data from western San
Joaquin Valley of California. The model results indicate that farmers treat surface water as fixed input
rather than a variable one, with significant implications for federal water policy, the Central Valley Project
Improvement (CVP) Act.









for options markets by arguing that spot markets and the permanent-rights markets

constitute two polar cases wherein risk is shifted from one party to the other. In case of

spot markets, most of the risk is borne by the buyer due to the thin market characteristics

of such transactions. In the case of permanent rights market, the seller of the rights needs

to evaluate the value of his rights given current and expected future demands. The risk of

selling the rights at a lower price than what may occur at sometime in the future is always

there, especially if the seller is risk averse. These risks and uncertainties introduce

significant transaction costs. He argues that options markets can help lower the risks

arising from both supply and price uncertainties to both parties. Michelson and Young

(1993) examine the role of water-supply options contracts in facilitating water markets.

Under this kind of contract, owners of the water (farmers) do not give up rights to water

and typically lose access to water only in the dry periods. A number of conditions must

be satisfied in order for the option markets to work. Chief amongst them are reliability of

water supplies (to ensure sufficient water during dry years and plenty during normal

years), well defined property rights, ability of the seller of the water rights to temporarily

suspend his operations, availability and knowledge of risks of drought, and attractiveness

of option contract costs as compared to alternative costs of attaining water in dry years.

The authors further cite features of the water market that distinguish it from other kind of

options contracts. These include the temporary nature of the contract (transferring use Vs

ownership rights), potential exercise of the option multiple times over the contract period,

and exercise of option being supply- dependent rather than price dependent. They define

the option value of water as the difference in the cost of the options contract and the next

best alternative source of water.









In sum the spot and options markets serve the needs of both the buyers and sellers

in terms of risk sharing and smoothing uncertainties in water demand and supply.

However, despite such advantages offered by these markets, their development has been

slow in the US so far. In certain cases, the success has been partial with one of the

markets failing to materialize, thus posing significant challenges to participants in terms

of risk sharing and supply insurance.

While options and spot markets have been promoted as a means to alleviate the

water shortages faced by buyers, there are substantial risks to the farmers participating in

these markets. These risks are a cause of significant concern to the federal agencies that

are responsible for disaster mitigation for farmers. Federal promotion of such markets

implicitly places the burden of adverse impacts of markets on such agencies. Such

adverse consequences may primarily be dictated by the relative composition of

participants between the spot and options markets. Spot markets offer higher rewards to

the water sellers but also carry higher risks in terms of price fluctuations with them.

Option markets help hedge against water price fluctuations but may severely affect the

agricultural sector due to long term water commitments. Losses include forgone

agricultural output from long term committed sale of water to the farmers, loss of

employment and agricultural productivity and forward linkage effects that include the

buyers of agricultural outputs4.




4 Some impacts of long term water transfers include loss of soil fertility due to prolonged periods

of no-cultivation, invasion of fallow lands by alien species that might be costly to eradicate, increased

waste water treatment costs, and reduced agricultural productive capacity (Howe 1997).









It is pertinent to understand the forces determining the relative success of the spot

and options markets in order to access the burden to the federal agencies from adversely

impacted farmers. A proper understanding of the underlying forces will also help predict

the cases when one or both the markets fail to take off. While concerns to the farmers are

justified, the value of water to buyers is much higher and successful functioning of

options markets is an important concern for them. Early identification of option market

failure may pave the way for alternate means to mitigating water shortages in certain

areas.

In order to understand the relative participation between the spot and the options

markets we need to account for the factors that affect decision making for the market

participants. The risks arising from sale of water to the farmers constitute a significant

element in their decisions to trade water. Such risks are affected by several factors that

include the demand and supply side uncertainties, uncertain opportunity costs of water,

etc. Profits are also affected by the size of the market that in turn is determined by the

number of participants in the market, the elasticities of demand, etc. An individual

farmer's choice between the spot and the option market is affected by his profitability

considerations in the two markets. Market participation in such cases may involve

incorporation of forward looking general equilibrium impacts into individual decisions.

Such feedback calculations may determine and explain the relative success of one market

over the other.

This paper addresses the dynamics between spot market transactions and option

markets, where conditions permit market transactions for water. The paper develops two

models (one for multiple farmer case and the other involving its application to two









farmers case) that are used to examine producer participation choice between spot or

option markets, under dynamic price and resource-supply conditions. The first model

considers a collective of farmers of similar productivity. The second model extends the

first model to a specific case of two farmers with differential productivity and strategic

behavior. Simulations are defined to assess the effect of key variables on market

participation, including agricultural water demand, the price of water, land supply, price

elasticity of demand for agricultural output, and the productivity of agriculture. Factors

resulting in the failure of markets, where incentives are insufficient to promote

participation, are also evaluated. Policy implications and conclusions follow.




Model

In this model we explore the interaction between a large urban buyer and a group

of homogenous farmers, a typical situation characterizing water exchange in such

markets, in a general equilibrium framework involving two time periods. In the first

period, the buyer offers an option and exercise price for water purchase in the options

market. Farmers decide between entering the option market and waiting for the spot

market. In the second period water supply is known and the spot market evolves to meet

the buyer's residual demand. However, the decision to enter one or the other market

needs to be taken at the beginning of period one based upon the expected profits in the

two markets.

Benefits from spot or options market sale of water are affected by the collective

choice of the farming community. For instance, if farmers expect the future spot prices

to be high, they would hold back their water and not enter the options market. This in









turn would lead to a glut of water in the spot marker thus lowering its price. Similarly,

the relative composition of farmers between the spot market and the options market

would determine the total supply of agricultural output. If the demand for agricultural

output is price elastic, profitability in the agricultural market would depend upon the

distribution of farmers between the spot and options market. Farmers who sell their

water in the options market would have less or no flexibility to use it for agricultural

purposes in a dry year, while farmers in the spot market could decide the optimal

allocation between the spot market sales and agricultural use water based on the marginal

revenue criterion. Profitability from spot and options market participation would depend

upon the expectation of future water supply, which would determine the availability of

water for agricultural uses both in the spot and options market. A dry year would raise

the spot market benefits whereas a wet year would raise the options market profitability

relative to the spot market. Therefore, in a competitive equilibrium, the expected benefits

in the two markets would be equalized. This is the framework adopted for the model

below.

Let there be N farmers, each farmer with one unit of surface water right (w)

and L units of land. Farmers have a choice of selecting between the spot market and the

options market. If they decide to enter the options market they must deliver the water to

the urban buyer at the predetermined options and exercise prices. There is, however,

some uncertainty over the supply of surface water. This uncertainty is denoted by a

probability density function f(s), with 1 > s > 0 where s is the 'realized' sale of water to

the urban buyer in wake of a drought. The idea is that, though the farmer receives an

option price for the sale of his entire 1 unit of water, the actual amount of water that is









sold is determined by availability of water in a dry year. For example, if the farmer

receives only half of his annual supply of water, he can deliver only that much to the

buyer. Also, the farmer has groundwater supply in a wet year equal to G units, which too

is affected by the drought conditions. Thus, if in a dry year the surface water supply to

the farmer is s, then his groundwater supply is Gs5. Let the production function for the

agricultural commodity x for the farmer be denoted by:


(1) x = Aw'L1

where y is the share of water in the total output. Let h be the option price offered by the

urban buyer, k the exercise price and let the urban demand for water be:

(2) Q = p or, p = lQ

where P is the price of water in the water market and a the elasticity of demand. Let u

be the price of water paid by the farmers for the use of surface water. Let n be the

number of farmers who decide to enter the options market. The expected supply of water

in the options market would be:

1
(3) E(SS(options)) = n sf (s)ds
0

Therefore, the expected supply of water in the spot market would be:

1
(4) E(SS(spot)) = (N- n) sf (s)ds
0

The residual urban demand for water in the spot market would be:

1
(5) Q = p- n sf(s)ds
0


5 Groundwater may be affected disproportionally, however this assumption does not lead to any loss of
generality.









Demand for water for agricultural uses in the spot market would be given by the equality

between marginal productivity of water and the price of water:


(6) MVPW =AyL1 (w +Gsf(s)ds) -z = p w = Gsf (s)ds
0 0

where z is the price of the agricultural output and the w is the demand for surface water.

Note that the expected marginal product should include the expected output from use of

groundwater too. Therefore, the total expected demand for water in the spot market is

given by:


1 1 1
E(DD(spot)) = (zA 1- Gsf(s)ds + p- nsf(s)ds
SzAy 0


Water market would clear when expected demand equals expected supply:

(8)


E(SS(spot)) = (N- n) sf (s)ds =
0

1 1 1
DD(spot) = (N n)((zA -- )- Gsf (s)ds) + p- n sf(s)ds


The above equation would lead to the solution of price of water P in terms of all other

variables as:

(9) p* = p(A, N, n, a, z, y, L, f(s), s, G)

Expected agricultural output in the spot market would be given by:


(10)


x(spot)=(N-n)AL1- ((z P )1)
zA 5y


Total expected agricultural output in the spot market and the options market combined

would be:









*1
(11) x(option) = (N- n)AL Y(( P( ,-) ')+ nAL' ((f (s)ds)


Agriculture market clears when demand equals supply. Let the demand for agricultural

output be equal to:

(12) z-

where 8 is the price elasticity of agricultural demand. Therefore, the price of agricultural

produce would be solved by equating the demand and the supply as:


(13) (N n)AL ( ( P(-)Y )+nAL1 (f(Gs) f(s)ds)'= z
zA Wy/J

This gives the price of the agricultural commodity as:

(14) z*= Z(A,L,N,n,a,,/, y,f(s),G)

Profits from spot market participation would be sum of expected agricultural profits and

the profits from spot market sale of water to the urban buyer:

(14)

P* Y i
(spot) =(N- n)AL z( ) -(N-n)rL-(N-n) (u + d G)sf(s)ds +
) zAyL +

(N-n)p*( f(s)ds -((z ) Gsf(s)ds))
0 zslf-' 0

where r is the rent on agricultural land

Now let's get back to the options market. The expected profits in the options market is

the sum of the option and the exercise price and the net benefits from the agricultural

output:

1 1 1
(15) h+ ksf(s)ds+zL' ( Gs)yA-rl- (u+d*G)s)f(s)ds
0 0 0









Farmers would weigh the profits from the options market to the profits from the spot

market in deciding between the two. Therefore, under equilibrium the two would be

equal:

(16)

S1 1 1
(spot) = AL 'zA( rL usf (s)ds + p (f f (s)ds (( ) Gsf (s)ds))=

1 1 1
h+zL' ( Gs)'A -rl- (u+d *G)s)f(s)ds+ ksf(s)ds
0 0 0


Solving (16) would lead to n, the number of farmers who decide to enter the options

market, and (N-n), the number of farmers who decide to enter the spot market.

The above approach assumes that the in an equilibrium, both the markets

will have some participants in them. However, in reality, it may happen that one of the

two (or both) markets fail to attract any participants. This will lead to a concentration of

all farmers into one (or none) of the markets. This would happen when the profits to a

single farmer in one of the markets, when all the participants decide to enter it, exceed

those from the other when he is the only entrant in that market. Intuitively, if the

expected supply of future water is low and the productivity in agriculture is high with a

low elasticity of demand (such as for an export good), farmers would stay away from the

options market as it would reduce the water available to them in a dry year. This same

condition would also lead to a spot market failure if the marginal revenue product of

water is higher than the existing price of water in the spot market. In Appendix A-i we

derive these conditions for the failure of either of the markets.

The above equations are analytically intractable due to the exponential

terms in the equations and we need to put more structure on the model in order to









perform numerical simulations. We assume that the production function for the

agricultural commodity is Cobb-Douglas and the uncertainty associated with water

supply has a uniform distribution. Accordingly expected profits in the options market are

(solving (15)) given by:


(17) (h+ zAL' (G /2) -rL + K /2)
2

Expected supply of water in the options market is given by solving (3):

(18) E(supply in the options market) -
2

Expected residual demand in the spot market is given by solving (5):


(19) Q=p --
2

Expected supply of water in the spot market is given by solving (4):

N-n
(20)
2

Spot market demand for water to be used in the Ag sector is given by solving (6). Market

in water clears when demand for water equals the supply of water:

(21)

N-n
E(SS(spot)) =N
2


DD(spot) =(N- n)((- )Y -G/ 2)+ p- n
zA yL 2

Equation (21) would give P* the market clearing price of water. Solving (13) we get the

market clearing condition in the agricultural output sector:










(22) (N-n)AL1 ( ( Pz )y)+nAL1 (G/2)'= zP
zA y

Finally, the market clearing condition between the spot and options market is given by:

(23)


r(spot)=ALl z( zP rL d*G/2+
zAyL 2
1 1
p*( ( )y- +G/2)=(h+zAL y(G/2)Y -rL --d*G/2+K/2)
2 zAyL1' 2

Solution of (21)-(23) simultaneously would yield the prices and the distribution of

farmers between the two markets. Next, we solve the above equations using MATLAB

to derive the expected constitution of farmers between the two markets. We also perform

numerical simulations by means of parameter variations to understand the impact of key

parameters on deciding market composition. Model parameters are presented in

Appendix A-2.

Results

The results of the simulations are depicted through figures below. Figure 1 shows

the effect of market size on prices of water and agricultural output in the base case.

Predictably, the prices fall with an increase in the number of farmers (INSERT FIGURE

HERE). However, the distribution of agricultural output in the two markets goes in

opposite directions with an increase in the market size. More output is produced in the

option market as compared to the spot market as the number of farmers increase. This is

due to the fact that an increase in the number of farmers raises the expected supply of

agricultural commodity lowering its expected price relative to the price of water in the

option market. Whereas, when the number of farmers is lower than the base case (10









farmers), the output in the spot market is higher than the option market due to the high

returns from sale of agricultural commodity. This is primarily due to the fact that more

farmers prefer to enter the spot market and use water in agriculture rather than lose it in

the option market. This is depicted in figure 2 below (INSERT FIGURE HERE). As the

number of farmers increases, the concentration of farmers in the option market rises

whereas it falls in the spot market. Figure 3 shows water transaction in the spot market

(INSERT FIGURE HERE). Note that both the spot market sale and use of water are high

when the number of farmers is low. Less number of farmers means a lower supply of

water in the urban market and a lower output of agricultural commodity. As a

consequence prices are high in both the markets. Figure 4 looks at the effect of varying

the share of water (gamma) in the production function of farmers (INSERT FIGURE

HERE). Increasing the share of water also has the adverse consequences of decreasing

the share of land in the production function. If land is available in plenty (relatively) then

the total output may go down. This is what happens in the example chosen above. As

gamma is increased, more and more people opt for the spot market where they could

purchase water for agricultural uses. As a consequence of reduced output in agriculture

and increased demand for water prices go up for both water and agricultural produce.

The sustainable equilibrium thus leads to increasing concentration in the spot market with

rise in gamma. These effects are depicted in figures 4 and 5 (INSERT FIGURE HERE).

Figure 6 depicts the impact of demand elasticity of agricultural output on the distribution

of farmers and the agricultural outputs in the two markets6 (INSERT FIGURE HERE).

An increase in the elasticity of demand raises the concentration in the spot market as

6 The parameter beta is the inverse of the agricultural elasticity of demand; therefore higher beta would
imply lower elasticity.









more output could be sold without lowering the price, thus leading to higher revenues.

As a consequence, output rises in the spot market and falls in the options market.

Farmers would enter the spot market with the hope of buying more water and making

large profits. The consequential effects on expected water and agricultural prices are

depicted in figure 7 (INSERT FIGURE HERE). Note that both water and agricultural

prices rise as the elasticity of demand increases. Increase in water demand raises water

prices for the urban users. Figure 8 looks at the impact of increased land availability on

the distribution of farmers (INSERT FIGURE HERE). The impact on the distribution is

felt through the decrease in price of agricultural commodity due to increased output from

more land availability. Thus, option market becomes more attractive compared to the

spot market. Price effects and the distribution of water between agricultural and urban

uses is depicted in figure 9. Similar effects are felt by increasing the overall productivity

of the farmer through the parameter (A) and are depicted in 10 and 11 (INSERT

FIGURES HERE).

A Case of Productivity Differential

Let's next consider the case of productivity differential across farmers. Assume

that farmers differ in their productivity (without putting any further structure on their

distribution). Whether the highly productive farmers would decide to enter the spot or

the options market would depend upon several factors. To simplify this further let's

assume that there are only two farmers, one with high productivity and the other with low

productivity7. This setting will allow us to explore the conditions under which it is

optimal for a typical farmer to prefer one market to another. It will also allow us to

7 One could also assume a uniform distribution of productivity; however, the analysis would be blurred in
such a case. For instance, a few farmers with large productivity may have similar implications for the
market as a large number of farmers with lower productivity.









derive conditions under which one (both) of the markets may fail. Since we have only

two farmers, we need to allow for strategic behavior. We model this problem in a game

theoretic setting where both the farmers decide simultaneously between the spot and the

options market. Let the production function for the farmer with low productivity (farmer

1) be:

(24) x = A1L1YW

and the production function for the high productivity (farmer 2) be:

(25) x = A2L1 W

There are four possible payoffs to each of the farmers depending upon what the other

does. Let these be represented as:

Matrix of Payoffs: Farmer 2 (options market) Farmer 2 (spot market)



Farmer 1(options market) (z ( .( )

Farmer 1 (spot market) (,_ .) ( TI2)



where the first one is the payoff to the farmers when both of them decide to enter the spot

market and so on. Next we derive the payoffs. When both the farmers decide to enter the

spot market, there would be no water sold in the options market. The demand for water

for water in the spot market would consist of the agricultural demand plus the urban

demand. The agricultural demand is given by:

p 1 1
(26) (( zAp-Y -r1 jGsf(s)ds) for farmer 1 and ((zA2 1 y- Gsf(s)ds)

for farmer 2.
for farmer 2.









Total demand including the agricultural demand is given by:


(27) ( P )r-1
ZA yL12


2 Gsf (s)ds) +( +P-"
0 zA 2 7L


Water market clearing condition:


(28) ( P )rY
zA yL1r


1 I
2fGsf(s)ds)+( 1 p- +P-
0 zA2 7yL


This would lead to price of water p". The agricultural market clearing condition is given

by:


(29) A,( l) )y-1 -
zAl yr


+A2( P2 )-
zA2 1yy


This would yield the price of agricultural commodity. The profits for the two farmers can

then be derived as:

(30)


rL (u + d G)sf(s)ds + p *((sf(s)ds- Gsf(s)ds)
0 0 zA 7 0
1 1 1 1
+ d G)sf(s)ds + p *(( sf(s)ds SS p 1) + Gsf(s)ds)
0 z A2L 0


When both the farmers decide to enter the option market, their payoffs could be derived

as:

(31)


h+ (zoo(L -1(Gs)A, -rl-(u+d*G)s)f(s)ds+ ksf(s)ds ,
S0
( loI 2o) =2 1 1
h + (z (L-(Gs) YA 2-rl (u+d G)s)f (s)ds + ksf (s)ds
0 0


2 sf (s)ds


( ** -l
("l, s- ) = A1 7 0--L -r


S21 z 2 I -









When the high productivity farmer decides to enter the spot market and the low

productivity farmer the option market, the residual demand for water in the spot market

can be derived as:

(32)


(- )-1 Gsf (s)ds) +P sf (s)ds = sf (s)ds
zA21L 0 0 0

This would lead to a price of water as ps. The price of agricultural output zs0 could be

similarly derived as:

1
(33) A, ( )r- L'- + A2L1-7 (f Gsf(s)ds)Y = z-


The payoffs to the two farmers are:

(34) ( ',,)=


A,( so -, yL -rL- (u+d*G)sf(s)ds+pso(( sf(s)ds-( + Gsf(s)ds))
{ 0i 0ZSAl1 1 }


h + A2L1 ( Gsf(s)ds) z- rL- (u+d G)sf(s)ds +k sf(s)ds
0 0 0J


Similarly, the payoffs when farmer 1 enters the options market are given by:

(35) ( lo, I as)=



h + A 1gL) ( Gsf(s)ds) z0S rL (u + d G)sf(s)ds + k sf(s)ds ,
L 0 0 0 J
( 1 1
A21 (-)/-' L rL f (u + d G)sf(s)ds+p' ( sf(s)ds( ) + Gsf(s)ds))
z A2 yL 0 0 zOS AyL1 0











Using parameter values in table 2 in appendix A-2, we perform simulations to look at

cases for successful and failed markets8.

Results for the Two Farmers Case

The Base case as shown in the Table 1 (INSERT TABLE 1 HERE), leads to a

spot market failure. The parameters are chosen such that it is a dominant strategy for

both the farmers to enter the option market. This condition is made feasible by a high

option value and exercise price combined with demand for water in the urban market.

Also observe that the high productivity farmer makes higher profits and is less adversely

affected in all four of the scenarios in the payoff matrix. Table 2 (INSERT TABLE 2

HERE) gives an example where the option market fails. This is made possible by

selecting a higher water demand curve (through parameter PO). The influence of

productivity differential is more clearly brought out by Table 3 (INSERT TABLE 3

HERE), which depicts a case of low option value and exercise price. In such as case

neither of the markets are dominated by the other. There are two equilibriums involving

both farmers going into the spot market or the option market. However, none of them

could be ruled out over the other. Option market for both yields higher payoffs than spot

market; however, there is no way to avoid the inferior outcome of both settling for the

spot market without pre-decision communication. This may explain, why it is possible

for options market to fail even under favorable circumstances when the strategic behavior

amongst farmers is taken into consideration. Finally, Table 4 looks at the impact of a

much higher productivity differential on the market participation outcomes (INSERT



8 Formal derivations of the conditions for market failure for the two farmer case are available upon request.









TABLE 1 HERE). Contrary to intuition, farmer one who has low productivity gains

more from spot market participation than option market participation. One would expect

that when water has lower yields in agriculture, entering the options market would be

more beneficial. However, when the effects of the other participant on water and

agricultural prices are incorporated, this may not hold. Farmer two, who has a

comparatively higher agricultural yield from water, has options market as his dominant

strategy. This is so as agricultural prices are highly susceptible to agricultural output, and

therefore farmer two being the larger producer of it is able to contribute more towards its

fall. Farmer one on the other hand benefits from option market participation of farmer

two by opting out of it and waiting for the spot market where he sells his water to the

urban buyer. Note that being not able to produce much from water inhibits his ability to

benefit from high agricultural prices and therefore he prefers to stay in the spot market

even though both farmers entering the option market raises agricultural prices

significantly. As a result, spot market is the dominant strategy for him.



Conclusion

This paper models the issue of relative success of spot and option markets for

water. The issue is important and timely as the relative excess of water in the agricultural

sector compared to outside needs makes it imperative that all available market

mechanisms be exercised. The analysis performed in this paper is relevant due to several

reasons. First, it highlights situations under which one or both the markets may fail. An

understanding of such situations may prepare the policy makers in advance for ensuing

water shortages. Second, it may provide a framework to assess the success or failure of









water market introductions in the past. Third, the prediction of relative participation may

help in guiding public policies that are aimed at mitigating the consequences of water

markets to the farmers. For instance, if contingent markets may have long-term impacts

such as loss in productivity and employment, etc., a relative composition of farmers

between the two markets would help decide the nature of other policies such as subsidies

and taxes in order to induce the right participation that optimizes the social welfare.

The approach adopted in this paper provides deeper insights into the observed

behavior of farmers, which may not be easily obvious. The N farmer case model

provides numerous valuable insights into the equilibrium outcome market composition

under uncertainty and forward-looking behavior. For instance, if the agricultural demand

is high and expected future supply of water low, farmers would like to hold off their

water from the options market and use it in agricultural production or sell it in the spot

market. However, when the simultaneous impacts of homogenous farmers faced with

similar situations are concerned, the response may not be so. This is due to the fact that

as the number of farmers who plan to enter the spot market rises, the profits in agriculture

may fall depending upon the price elasticity of demand. Profits in the option market

would rise, on the other hand, with fewer participants remaining in that sector. The

equilibrium distribution of participants would be achieved when the profits to the

marginal farmer in the two markets are equalized. Conditions are also derived for

complete failure of either of the markets. The analysis is further, extended to consider

the impact of heterogeneity amongst the sellers on their distribution between the spot and

the options markets. The analytical findings are further enriched through numerical

simulations. The strategic behavior amongst farmers plays a much more significant role









when the number of participants is low. This is apparent from the two-farmer case where

Nash equilibrium may involve both superior and inferior outcomes. In such a case there

is no way to predict the outcome unless public policies induce collaboration for greater

common good.

The analysis of the model must not be taken at its face value as ground conditions

may vary. Unfortunately there is not much empirical evidence to test our model. It is

hoped that the insights from this study would provide reasonable predictions of the

relative participation in the two markets, (including the cases when either of the markets

may fail entirely) based upon the key variables such as water supply uncertainty, market

size and strategic behavior, thereby aiding policy makers with valuable information to

provide adequate institutional settings and supplementary policies aimed at mitigating the

adverse consequences of water trade to the farmers and the environment.









References


1. Gaffney, M. "What Price Water Marketing?: California's New Frontier",
American Journal of Economics and Sociology, 56(4) 1997.

2. Howe, C.W., J.K. Lazo and K. R. Weber, "The Economics Impacts of
Agriculture-to-Urban Water Transfers on the Area of Origin: A Case Study of the
Arkansas River Valley in Colorado", American Journal of Agricultural
Economics, 72(5), 1200-1204, 1990.

3. Howe, C.W., "Increasing Efficiency in Water Markets: Examples from the
Western United States", in 'Water Marketing-The Next Generation' edited by
T.L. Anderson, and P.J. Hill, 1997.

4. Howitt, R.E., "Spot Prices, Option Prices and Water Markets", in Easter, K.W.,
M.W. Rosegrant and A. Dinar eds. Markets for Water: Potential and
Performance, Kluwer Academic Publishers, 1998.

5. Lund, J.R., "Transaction Risk versus Transaction Costs in Water Transfers",
Water Resources Research, 29(9):3103-3107, 1993.

6. Michelsen, A.M., J. F. Booker and P. Person, "Expectations in Water-Right
Prices", Water Resources Development, Vol. 16, No. 2, 209-219, 2000.

7. Michelsen, A.M., and R.A. young, "Optioning Agricultural Water Rights for
urban Water Supplies during Drought", American Journal of Agricultural
Economics, Vol. 75, 1010-1030, 1993.

8. Moore, M. R., and A. Dinar, "Water and Land as Quantity-Rationed Inputs in
California Agriculture: Empirical Tests and Water Policy Implications", Land
Use, 71(4), 445-61, 1995.

9. Saleth, R. M., J. B. Braden, and J. W. Eheart, "Bargaining Rules for a Thin Spot
Market", Land Economics, 67 (3): 326:39, 1991.

10. Young, R. A., "Why Are There So Few Transactions among Water Users?"
American Journal ofAgricultural Economics, 1143-1151, 1986.


11. Ranjan, R. N. Gollehon, and M. Aillery, "Getting the Farmers' Feet Wet (Dry?) in
the Water Market: Why isn't the Invisible Hand Working?", Internal Draft,
USDA-Economic Research Services, 2004.









Appendix A-i

Let's first look at the conditions for the spot market failure. Let's assume that (N-l)

farmers have already indicated to enter the options market. The spot market would fail if the

profits from entering the options market to the last farmer, who is yet to decide, are higher than

the expected profits from entering the spot market. The price in the options market would be:

r 1 1/
(A) z = NAL1Y ( Gsf (s)ds)Y
0

Therefore, his expected profits in the options market are:


(B) NALl ( Gsf(s)ds)'l ALl (I Gsf(s)ds)' rL-(u+d*G) sf(s)ds+klf(s)ds
0 0 0 0

Now, let's look at the picture in the spot market. He would be the only entrant in the spot

market. Therefore, the water market would clear when his demand for agricultural use

plus the urban demand equal the total expected supply of water. That is:

1 1 1 1
(C) ( P -- )-1 Gsf(s) + p- -(N-1 sf(s)ds = sf (s)ds


This would lead to a price of water pPo '"lrein terms of the price of agricultural

commodity zp"""a're and other parameters. The agricultural market would clear when:


(D) AL1- ( P ) -1) +(N-1)JAL-r (Gs)Y f(s)ds= z
zA^l1

Solving which we can get z"pt""" Next we derive the profits in the spot market to this

farmer as:









spotrfaiure )
z(spot) = Al-z(z sp-glre )-Y r -rL- (u + d G)sf(s)ds +
(E) spotfalure 1 1
ppora'e ( f (s)ds p(P )-1 + Gsf (s)ds)
o 0 o

If we are interested in the parameters such as elasticities of demand for water and the

agricultural commodity, we could derive a relationship between the two that would

divide farmer's decision space into two regions; on one side of which spot market

becomes attractive and on the other the options market. This would be given by:


(F) NAL- ( Gsf(s)ds) AL' (I Gsf(s)ds) rL -(u + d G) f(s)ds +k f (s)ds



('(F)0t)= AL1 ALz( L
0 0 0 0



spotfalure 1
Z(spot) = AL1-z( )r1 _- rL (u +d *G)sf(s)ds +

spotfailure 1 1
spo'ure (I f (s)ds ( rA P- ) + Gsf(s)ds)




Similarly spot market failure conditions could be derived as follows:

Demand for water in the spot market would be:


(G) (N -1)(( ~- ) -Gsf(s)ds)) + p sf (s)ds (N -1)sf (s)ds
zA0 0 o

The agricultural market would clear when:


(H) (N-1)AL1 P* -- -)+AL1 (Gs)Y f(s)ds= z -
zAL

Next we derive the profits in the spot market to this farmer as:










optionfailure 1
zr(spot) = z p -l )Y rL f(u + d G)sf(s)ds +
z optionfadlure A 7-L-'

(I 1 optionfalure 1 1
otonfalure( f(s)ds -(zopt nfilure + Gsf(s)ds)


His expected profits in the options market are:

1 1 1
(J) "optionfailure AL Gsf(s)ds)' rL u f(s)ds + k f(s)ds
0 0 0

The condition for option market failure, then, is :

(K)


optionfaiure
i (spot) = AL1 z(op~,iA yL1 1 -

1 p optionfailure
p opo i( f( oponfsu)ds -( Opt A ly )
0 z A L


rL- (u+d*G)sf(s)ds +
0
v-1 1
+ Gsf (s)ds) > z"PtonfaI"e AL1
0


1 1
rL (u + d G)J f(s)ds + k f(s)ds
0 0

Appendix A-2


Model Parameters for the N Farmers Case


Model Parameters for the Two Farmers Case


Gsf(s)
(f Gsf (s) ds)
0


N Y a P L G A PO zO u d k r h


10 .5 .5 .5 2 .1 .5 3 3 1.1 1.2 1.5 .1 .05


N Y a P L G Al A2 PO z0 u d k r h


2 .5 .5 .5 2 .5 .4 .6 .3 .9 1.1 1.2 1.5 .1 .05













Figure 1: Base Case--prices


35





25

-- price of water
2 price of ag-commodity


~1 5 -- ag-output-spot market
ag-output-option market



05



7125 725 8 10 13 20
N (total numner of farmers)



Figure 2: Base Case--n (farmers in the option market)
25



20 n (farmers in the option market)
20 n=N/2



15



10



5




7125 725 8 10 13 20
N (total numbers of farmers)












Figure 3: Base Case--Water Transaction in the Spot Market


ag use of spot water
ag sale of spot water
ag sale of spot water


2.00


1.50


1.00


0.50


0.00


-0.50


-1.00


-1.50


N


Figure 4: Effect of Share of Water in Ag Production (gamma) on n

12

Sn
10 ----ag output in spot market

ag output in the option market
8


Gamma


7.125











Figure 5: Effect of water share (gamma) in Ag Commodity
Production


- -wa
--ag
ag


07 ag


ter price
-commodity price
use of spot water
sale of spot water


gamma


Figure 6: Effect of Elasticity of Ag-Commodity Demand (beta) on


--.-- n


-ag output in the spot market
ag output in the option market


beta


04












Figure 7: Effect of Elasticity of Ag Demand (beta) on Spot Market


-*-water price
-U-ag-commodity price
3- ag use of spot water
-*-ag sale of spot water








0.05 0.5 0.8


beta



Figure 8: Effect of Land Availability on n


n

ag output in the spot market
ag output in the option market


2 05 2
Land use












Figure 9: Effect of Land (L) on Spot Market


-*-water price
ag price
Swater-demand in spot for ag use
water supply in the spot market by ag











0.2 0.5 2


L (land)





Figure 10: Effect of Ag Productivity Paramter (A) on n


--ag output in the spot market
-ag output in the option market
ag output in the option market


A (productivity paramter)












Figure 11: Effect of Ag Productivity Paramter A on spot Market



-*-water price
S-ag price
ag-use of spot water
ag sale of spot water









02 05











Results for the Two Farmer Model

Tablel: Case of Spot Market Failure

Base Case S (Farmer 2) O (Farmer 2)

S (Farmer 1) (-.59, -.57) (-.55, .44)

O (Farmer 1) (.21,-.32) (.21, .44)




Table 2: Case of Option Market Failure

P0=3 S (Farmer 2) O (Farmer 2)

S (Farmer 1) (3.33, 5) (4, .44)

O (Farmer 1) (.21, 4.14) (.21, .44)



Table 3: Possibility of Inferior Outcomes

k=.05, h=.005 S (Farmer 2) O (Farmer 2)


S (Farmer 1) -0.5941 -0.5686 -0.5667 -0.6015

O (Farmer 1) -0.8011 -0.4813 -0.5618 -0.3327


Table 4: Higher Productivity Differential Impact (One Equilibrium)

k=.05, h=.005, Al=.1, A2=.6 S (Farmer 2) O (Farmer 2)


S (Farmer 1) -0.619 -0.4891 -0.7062 0.1678

O (Farmer 1) -0.9401 -0.218 -0.7862 0.3827




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