Copyright 1998 by Peter Berck 1

A Water Primer

© 1998 by Peter Berck

P. Berck 2

Water Economics

Rain property rights

Reservoirs, Canals, and Treatment Efficient Pricing Border Prices Subsidies for Whom?

P. Berck 3

Property Rights

Limited as to extent right to use: consumptive use v. total use transport: use only here or can transport hydraulic mine: damaging uses

prohibitedWater flow is Stochastic

some years a lot, others a little

P. Berck 4

The Uncertainty Paradigm

Distinct states of nature (SON) rains a little. Say 0 - 10”, 1000 ac ft available medium amount, say 11 - 20”, 2000 ac ft rains a high amount, say 20” +, 4000 ac ft.

Probability of each SON PL + Pm + Ph =1

Rights give rules by SON

P. Berck 5

Two Types of Theoretical Rights

Sharing x% of flow in each

state of nature. IBM& Barley same

cutback in low flow Disk Plant would want

to buy water from Barley farm in 0-10” state.

Not efficient if can’t buy

Contingent Claims Market for water by

state of nature e.g. 1000 ac ft

when rainfall is 0-10” this year

Arrow Debreu show that CE w.r.t. contingent claims is PO

P. Berck 6

Real Types of Rights

Appropriative First in use, first in

right. Must use. May transport. Is quantified

Riparian Live next to river and

can use it to flood land. Use not req.

Not strictly quantified

Contractual Classes of users priority among classes sharing within classes

Reserved High prority, no need

to use

Open Access Take what you want.

P. Berck 7

In California (See Map)

Individual Appropriators

Quasi Gov appropriators

RipariansExchange

ContractorsWater Districts and

their customers

State and Fed Project

Delta-MendotaFriant dam and S.ShastaSan Luis UnitKesterson and

Drain

P. Berck 8

EBMUD

Junior to Woodbridge

Mokelumne is more than 100% appropriated

Dam for 1000/ ac ft?

Fear of Adjudication

Could buy water and have less.

(Fish would get more)

P. Berck 9

Rights Issues

Transferability Within Basin? Between Basins Security of transferred rights Damage to non-participants

Security Use it or lose it.

Availability every two weeks? Little bits daily?

P. Berck 10

Claims about Appropriative Rights

Transferable, Divisible, Appropriative rights are equivalent to contingent claims. By Arrow-Debreu, they are efficient. (Berck and Lipow)

Every utility maximizer prefers senior to junior appropriative rights. (Burness and Quirk)

P. Berck 11

State Contingent Claim

Expand notion of goods to include things like Umbrella when it rains Umbrella when it doesn’t rain

Every state of nature has different goods

CE w.r.t. contingent goods is PO

P. Berck 12

Contingent Claims

Right to water in ONLY one SON is a contingent claim.

Treat each contingent claim as a separate good.

Means can buy and sell “water if there are between 0 and 10” of rainfall”

First Welfare Theorem says a Competitive Equilibrium is a Pareto Optima.

P. Berck 13

Contingent Claim example

1 has purchased 3 different claims 1000 if there is 1000 ac ft available 1500 if there is 2000 ac ft available 1500 if there is 4000 ac ft available

2 has purchased 2 different claims 500 if there is 2000 ac ft available 2500 if there is 4000 ac ft available

Supply = Demand for water in all SON

P. Berck 14

Appropriative Rights

W is water flow and is random 1000, 2000 or 4000 ac

ft

Aj is water right of jth individual 1st: 1500 ac ft 2nd: 2500 ac ft

i < k Ai is water rights of individuals prior to k. A1 = 0

A2 = 1500

(A3, if he existed, = 4000.

P. Berck 15

Appropriative (con’t)

k gets min(ak,Ak) 1 gets: 1000, 1500,

1500 2 gets: 0, 500, 2500 (3 would get 0,0,0)

get the minimum of what’s left or your rights.

ak =

Max(0, W - i < k Ai) a1 = 1000, 2000,

4000 depending on how

much there is. a2 = 0, 500, 2500

is water left over for individuals k when the flow is W

P. Berck 16

Stochastic Dominance 1st degree

Consider rights of equal quantity (e.g. 1500 each)

In every SON the Senior rights holder (1) gets no less than the Junior rights holder 2.

It does not matter what the probabilities of the states are.

Every water-lover would prefer to be senior to being junior.

P. Berck 17

Senior is better

F(W) is CDF of Water Availabilityak= Max(0, W - i < k Ai)

water available to k and junior

Gk(a) = F(i < k Ai +a) for a 0; else 0. CDF of water available to k and junior

Claim: Gk FSD Gk+n

P. Berck 20

Efficiency of ‘Appropriative’

Wi is water in state of nature in states of natureneed n appropriators Ak = Wk- Wk-1

so that all water is claimedBuy kth right and get water in state of

nature k or moreSell k+1th right and get water ONLY in

state k! State Contingent Claim

P. Berck 21

Reality Check

Real systems don’t turn off IBM and grow barley, even if IBM is “junior”

Class I II and III water on the Fed. Project are attempts to capture state contingent nature

Israeli base allocation with high price over base is another method

P. Berck 22

Marginal Revenue Product

MRPw =P (F(K,W+1) - F(K,W)) k is another input, capital or fertilizer w is water P is the price of the ag. output, cotton.

Use an input until its price r, r = MRPw

This is a rule for profit max. Can you prove it?

P. Berck 23

Economic Efficiency

Price = MRP Price is the (marginal) value of what is

produced with the waterWhat price? Border Pricing Rule

Value of tradable is it’s price in trade Gifts from government don’t count in

price Non-tradable goods used to make

tradables can also be priced this way

P. Berck 24

Water Delivery

Rain, Reservoirs, Canals, and Treatment

Should charge Value of Raw Water + Marginal Cost of Storage+ Marginal Cost of Transfer + Marginal Cost of Treatment

P. Berck 25

Price: An Example

Cotton is marginal crop Acreage adjusts to economic conditions. Assume Average Yield 70 cents per lb for cotton 12 c is value of cotton from additional m3

of water.Dinar and Ariel; Calif. ‘91UC Coop Ext cost data only 8 c /m3

Kislev, Israel Av. 1980-88. 8.7 c/m3

P. Berck 26

MC of Transport

Israel/Jordan/West Bank MC is between 2 and 50 c/m3

2 near the Jordan 50 in the Negev (Bank, 1990)

Efficiency: On average, grow less cotton in Negev Grow more crops near Jordan River

P. Berck 27

California Cotton

Power is priced too low. (Border Price) Capital costs are intentionally subsidized

(not MC) Operating costs are misstated on low side

(is MC) Cotton is subsidized (Border Price)

Efficiency? Less field crops in dry times in Westlands

P. Berck 28

P MC

In agriculture, Water often can not pay its transport cost, much less storage or treatment

Underlying value of water (value of rain) is taken as zero.

Underlying value of water needs to be found

P. Berck 29

Value of Water Rights

markets give best evidence of value of underlying rights

CA has limited markets for water rights

markets also lead to efficiency in water allocation

there are many caveats

P. Berck 30

Water Sales are Difficult

Rights weren’t (and in Mid-east aren’t) saleable

Ag. and Urban not same waterDownstream users objectMultiple agencies all end up with veto

suppose every time you tried to buy a candy bar you had to notify your dentist?

P. Berck 31

Water is Scarce?

When the price is set at zeroIn Drought CA bought water at $125/ac-ftCouldn’t sell at $250 and had to dump itCa and Israel: 75%+ of water goes to Ag.

Some of this water actually makes GDP lower A great deal of it is at value less than $125/ac-ft

which is low for industry and drinking

P. Berck 32

Price Water by Wetness

Water when it is a wet year isn’t scarceWater when it is a dry year is scarceNeither Israeli nor Ca. Systems change

price enough when supply changesPossible in both cases to shut down

Semi-conductors and grow wheatDams make wet-year water into dry

year water

P. Berck 33

Water Storage Projects

Build when P of output made with project water greater than Cost, or B/C > 1

Use border prices for region’s marginal output, like cotton for potential imported intermediates,

like alfalfa pellets for energy to pump the water

P. Berck 34

Water Markets in Mid East

Underlying rights need to be dependent upon water availability

Rights must be freely tradableWater markets would reallocate water

to high value usesSubsidies to water industry would endPeace is necessary for Water markets