Water Water issues in the world A highly debated problem Fears for - - PowerPoint PPT Presentation

Natural resources economics M1

Water

CHAPTER ONE PART II

Water issues in the world A highly debated problem

Fears for water shortage with climate change 'Sustainable' use of freshwater is at stakes Bad quality of water provision in poor countries Financial needs : the public/private management debate From water provision to public services and politics

Water issues A dramatic consumption increase

A 6 fold multiplication between 1900-2000 (330km3 → 2100 km3)

(1900) 5% of accessible run-off (2000) 15% (2050) 23% ? (expected)

'Water stressed' areas:

(2000) 1,7% of the world population in water stressed regions (2025) 8,6% (2050) 17,8%

Methodogical care : withdrawals and consumption

Water use trends 1900-2000

Fig 10 : W ater withdrawals in the world from 1900 up to 2000

Methodological problems : 'scarcity tables'

Type of countries Water availability Water 'rich' > 1700 m3 per year per capita Periodic water scarcity 1000 m3/y/p – 1700 m3/y/p Chronic water scarcity 500 m3/y/p-1000 m3/y/p Absolute water scarcity < 500 m3/y/p Grille des richesses et pauvretés en eau en m3/habt/an (pluie -évaporation + entrée par les

rivières)

Abondance >20000 m3/hab/an Islande Finlande Suède 630 000 22 600 21 800 Pays très riches > 10000 m3/hab/an Irlande Luxembourg Autriche 14 000 12 500 12 000 Pays riches > 5000 m3/hab/an Pays-Bas et Portugal∗ Grèce 6 100 5 900 Situation correcte > 2500 m3/hab/an France Italie Espagne 3 600 3 300 2 900 Pays pauvres < 1500 m3/hab/an Royaume -Uni Allemagne Belgique 2 200 2 000 1 900

Water issues Water provision

>1 billion people without enough water access 2,5 billion people without sanitation service

Irrigation

250 millions ha irrigated ( 5 fold the 1900 level) The main consumer : 1435 km3 (> 66% of total consumption)

Financial issues

180 billion $/year are needed but only 80 b$/y are spent 20 b$/y for population needs but only 10 b$/y spent (50% Daid)

Private funding : the regulation debate (Bolivia and Argentina)

Water as a resource A mix of a renewable and exhaustible ressource

River flows = renewable ressources Aquifers, lakes = renewable ressources with delay Groundwater = 'water mine' = exhaustible resource at human scale

Renewal rate of some main world groundwater aquifers

Average annual renewal rate Renewal delay (years) Big artesian basin (Australia) 5.10-5 20 000 Sedimentary basin of Saoudia Arabia 3.10-5 33 000 Northern Sahara basin (Algeria, Tunisia). 1,4.10-5 70 000 Nubian Aquifer (Egypt, Libya) 1,7.10-4 6 000 Parisian water basin (France) 5.10-5 20 000 Ogallala Aquifer of Texas High Plains (USA) 5.10-4 2 000 Arizonian Aquifers (USA) 2,5.10-4 4 000 Maranhao Basin Aquifer (Brazil) 13.10-4 800 In : Jean Margat : Les gisements d'eau souterraine, La recherche N° 221 Mai 1990.

Water sharing between competing uses

The net surplus of residents The net surplus of farmers Optimal allocation equates the net marginal surplus functions of the users.

S RqR

S aqA

Fig 11 : The optimal allocation of water to competing uses

Marginal net surplus of residents S'R(qR) Marginal net surplus of farmers S'A(qA) qR qA pW Q

Optimal allocation of water

Optimization program: The corresponding Lagrangian: The optimality conditions: Lambda : marginal opportunity cost of the limited flow of water Under surplus functions concavity : is a decreasing function of the available flow: Max S RqRS AqA s.t qRqAQ L=S RqRS AqAQ−qR−qA sRqR=sAqA= Q Q=qRqA=sR

−1sA −1≡Q

Environmental quality of water The 'damage function' approach

Environmental cost suffered from water diversion or pollution Environmental damages are expected to increase with human pressure over the water resource

The 'environmental benefit' approach

Welfare is increased by good environmental conditions

Use values : lower pollution costs Non market values : recreative activities and natural amenities Non use values : existence values, option values, bequest values

Equivalent in principle but...

A 'damage function' model

The optimization problem: The optimality conditions: First equality : equalize weighted marginal surpluses Second equality : equalize marginal benefit of increased pressure

• ver the environment and marginal environmental damages

Note that :

More social weight for residents→less marginal surplus (the residents total surplus increases with social weight )

MaxRS RqRAS AqA−E DqRqA RsRqR=AsAqA=E d D dqR =E dD dqE RAs RqRs AqA

An 'environmental benefit' approach A seemingly formulation:

The water constraint is now explicitely taken into account.

The first order conditions:

The first equality is the same: weighted marginal surpluses of the users must be equalized The second also: The marginal social cost of more environmental quality must be equal to the environmental marginal benefit The third equalize surpluses and environmental benefits to the

• pportunity cost of the water flow constraint

MaxRS rqRAS AqAE BqE s.t. qRqAqEQ RsRqR=AsAqA=E dBqE dqE =

Comparing the two approaches: Tempting :

« The marginal opportunity cost of water scarcity is the marginal environmental benefit » Appears in the economists water group working on 'cost recovery' in a benefit-cost perspective for the European Water Framework (DCE, 2000). The idea is to try to recover the scarcity value of water (the

• pportunity cost) from an environmental benefit evaluation study based

upon amenity values.

But confusing because:

The opportunity cost comes from the water scarcity level for ALL uses, and not only for the environmental use. The drawback of the damage approach is to impute all environmental degradations to adverse human decisions Nature can suffer from water scarcity even without human presence

'Abundance' and 'scarcity'

Assume there exists such that : Remember : costs are included in the net surplus function These consumption levels maximize the social surpluses of the users (unconstrained optimum)  qR ,  qA s R  qR=s A  qA

Fig 12 : a case of abundance of water

 qR  q A sR(qR) sA(qA) Q

Scarcity and abundance

The constraint is no more binding : The marginal opportunity cost is zero (null scarcity value) The water resource is called abundant in this case It is scarce in the opposite case An economic definition of a 'scarcity index' and not a physical one:

Takes care of social welfare and living standards (huge variety) Incorporates water quality (not only volume based) Takes delivery costs into account Variety of use is explicitely accounted for.

The marginal opportunity cost = the marginal scarcity rent of water Same as in the case of Land resources  qR  qAQ

Water scarcity rents

A government wants to concede an exclusive exploitation right

• ver a water flow (a river)

The monopoly firm can charge freely the water and is assumed able to extract all the surplus from the users The firm should hence maximize social surplus Assume perfect substituability of water Total surplus at period t Marginal surplus at time t The surplus maximizing consumption level at time t Water availability constraint for the period t S t qt st qt qtQt



qt st   qt=0

Wtaer scarcity rents What is the maximal price for this concession ?

Consider the scarcity rents flow

Fig 13 : An example of a path of the net marginal surplus

t Scarce water Scarce water Abundant water Abundant water

Water scarcity rents

The total value of the flow is the present value of the total net surpluses stream up to T periods This is the maximal amount the monopoly would pay for the concession This is also the total rent of the water flow of the 'river value'. Extension of the concept of land rent to water resources Rent is a consequence of scarcity and not of the fixed size of the natural asset (land or water) M =∑

t=0 T

 1 1it St min { 

qt ,Qt}

Sharing a river (a spatial analysis) A simple 'spatial' model

Surplus and marginal surplus : There exists wich maximizes the net surplus Water comes from upstream : and from incoming flows (rainfalls) : Spatial flow dynamics:

X x Users consume Q(x)



Q x v x ,  Q x=0 V x ,Q x v x ,Q x z x,  z  x z x=−min Q x,  Q x xz x1

A pure cake eating problem Assume no extra water incoming (pure canal problem)

In this case the water flow spatial dynamics is simply:

Upstream users consume « before » downstream users

A specific norm over minimum flow :

Necessary and sufficient condition:

The social optimum problem: Assume that water is essential in the following sense; z x−z x1=−Q x z x  z z 0  z Max ∑

x=0 X

V x ,Q x s.t. z x=−Q xz x1,Q x0, z 0  z

lim

Q 0v x ,Q=∞

A pure cake eating problem.

Transform the spatial dynamics problem into a static one: Form the Lagrangian The optimality conditions: Find back a familiar result, lambda is the marginal opportunity cost of the limited flow constraint. Lambda=0 if water is abundant If not, the optimality condition implicitely defines : Define the aggregate consumption : z 0=−∑

x=0 X

Q x  z   z L= ∑

x=0 X

V x ,Q x[  z− ∑

x=0 X

Q x] v x ,Q x=

∀ x∈{0,1 ,... , X }

Q x , Q = ∑

x=0 X

Q x ,

Pure cake eating problem

Properties of Properties of The aggregate consumption is also a decreasing function of The equation has only one solution This solution determines the optimal water allocation to the users.

The dependance of downstream users with respect to upstream users plays no role in the optimal allocation solution

Q x ,

∂v x ,Q x ∂Q x

d Q x=d  

∂Q x , ∂ =

1

∂ v x ,Q x/∂Q x 0

Q 

lim

 0Q  

z−  z ,

lim

  ∞Q =0

 Q =  z −  z 

¿

Egoistic behaviour of the upstream users

Let us assume that there exist a subset of upstream users such that: The set of users should consume The downstream users could not consume anything The downstream users marginal surpluses go to infinity There appears trade opportunities between upstream users (with a zero marginal opportunity cost) and downstream users. If water transfers are impossible, severe suboptimal allocation With water trade, optimal allocation is restored (without transaction costs)

∀ x∈X U ,

∑

x∈X U

Q x  z−  z



Q x

Water trade

Optimality ex post has effects on income:

Upstream users increase their income, they benefit from their location along the river Downstream users must pay to get access to the water, their income is lowered. They lose from their location.

A consequence of such a 'prior appropriation doctrine'

Here the 'first arrived, first serve' principle benefits to the upstream users (the 'first served')

Water doctrines The prior appropriation doctrine

Has ex post effect upon income with ex post water transfers

The riparian doctrine

Gives access rights to people located near the river banks

The common property doctrine

The river is a common property of all users. May lead to a social optimum under supervision

The State appropriation doctrine

Water property is given to a public body Delegation to the private sector is possible Price covering cost plus the marginal opportunity cost (water rent)

Sharing a river Taking inflows into account

The spatial dynamics is now: Developping the recurrence equation: The flow norm constraint applies to any location Form the Lagrangian: Simpilify notations : z x=−Q x xz x1 z x=−∑

t =x X

Q t∑

x=t X

 t   z  z L= ∑

x=0 X

V x ,Q x ∑

x=0 X

 x[  z∑

t =x X

 t −∑

t=x X

Q t −  z ]  x=∑

t=x X

 t 

Sharing a river

Rearrange summations: First order conditions: The net marginal surpluses increase in the upstream direction The net marfinal surpluses are no longer equal. A constraint relaxation upstream has more impact than downstream. Solving when all constraints are binding:

L=∑

x=0 X

V x ,Qx∑

x=0 X

x[ zx− z]−∑

x=0 X

[Qx∑

t=0 x

t]

v x ,Q x=∑

t=0 x

 t  v x1,Q x1=v x ,Q xx1 x≡∑

t=0 x

t  , Q x≡Q x , x ,

∑

t=x X

Q t , t =  z  x−  z

Sharing a river Resolution algorithm

Start from x=X: get from the flow constraint : Solve backwards from x=X down to x=0: get At x=0, we get : Since by construction: Solve forward from x=0 to x=X: get Solve for x=0 to X:

The marginal opportunity costs at each location are interdependent (jointly determined by the recurrence system) More easily solved using dynamic programming techniques  X  ,Q X =Q X , X 

{0, 1 ,... , X }

0=0 x1=X x1

{ 0, 1,... , X }

Q x=Q x , x