Natural resources economics M1 CHAPTER ONE PART II Water
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 Islande 630 000 m3/hab/an Finlande 22 600 Suède 21 800 Pays très riches > 10000 Irlande 14 000 m3/hab/an Luxembourg 12 500 Autriche 12 000 Pays riches > 5000 Pays-Bas et Portugal ∗ 6 100 m3/hab/an 5 900 Grèce Situation correcte > 2500 France 3 600 m3/hab/an Italie 3 300 Espagne 2 900 Pays pauvres < 1500 Royaume -Uni 2 200 m3/hab/an Allemagne 2 000 Belgique 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 Fig 11 : The optimal allocation of water to competing uses S R q R The net surplus of farmers S a q A Marginal net Marginal net surplus of surplus of farmers residents Optimal allocation equates S' A (q A ) S' R (q R ) the net marginal surplus functions of the users. p W q R q A Q
Optimal allocation of water Optimization program: Max S R q R S A q A q R q A Q s.t The corresponding Lagrangian: L = S R q R S A q A Q − q R − q A The optimality conditions: s R q R = s A q A = Lambda : marginal opportunity cost of the limited flow of water Q Under surplus functions concavity : is a decreasing function of the available flow: − 1 s A − 1 ≡ Q Q = q R q A = s R
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: Max R S R q R A S A q A − E D q R q A The optimality conditions: d D dD R s R q R = A s A q A = E = E dq R dq E First equality : equalize weighted marginal surpluses Second equality : equalize marginal benefit of increased pressure over the environment and marginal environmental damages Note that : R A s R q R s A q A More social weight for residents→less marginal surplus (the residents total surplus increases with social weight )
An 'environmental benefit' approach A seemingly formulation: Max R S r q R A S A q A E B q E s.t. q R q A q E Q The water constraint is now explicitely taken into account. The first order conditions: dB q E R s R q R = A s A q A = E = dq E 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 opportunity cost of the water flow constraint
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 opportunity 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' s R q R = s A q A Assume there exists such that : q R , q A Remember : costs are included in the net surplus function These consumption levels maximize the social surpluses of the users (unconstrained optimum) Fig 12 : a case of abundance of water s A (q A ) s R (q R ) q R q A Q
Scarcity and abundance The constraint is no more binding : q R q A Q 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
Water scarcity rents A government wants to concede an exclusive exploitation right over 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 S t q t Total surplus at period t Marginal surplus at time t s t q t The surplus maximizing consumption level at time t q t s t q t = 0 Water availability constraint for the period t q t Q t
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 Abundant Scarce Scarce water Abundant t water water water
Water scarcity rents The total value of the flow is the present value of the total net surpluses stream up to T periods 1 T M = ∑ 1 i t S t min { q t ,Q t } t = 0 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)
Sharing a river (a spatial analysis) A simple 'spatial' model V x ,Q x v x ,Q x Surplus and marginal surplus : X x 0 Users consume Q(x) Q x v x , Q x = 0 There exists wich maximizes the net surplus z x , z Water comes from upstream : and from incoming flows (rainfalls) : x Spatial flow dynamics: z x =− min Q x , Q x x z x 1
Recommend
More recommend
