Water Resource Economics C H A P T E R A W A T E R D E M A N D, S U P P L Y, A N D A L L O C A T I O N

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1 Water Resource Economics C H A P T E R A W A T E R D E M A N D, S U P P L Y, A N D A L L O C A T I O N

2 Reader, based on Griffin (2006), Text

3 Organization 1. Costs of water supply 2. Efficiency for a single water user 3. Aggregation of demand using marginal net benefit functions 4. Aggregate efficiency (and opportunity costs)

4 Objectives 1. Understand how an economist views the possible allocation of water. 2. Grasp and apply the concept of efficiency using marginal costs and benefits. 3. Understand how to apply efficient allocation with multiple water users. 4. Apply the concept of efficient water allocation to simple cases. 5. Apply an economic perspective to analysis of water allocation.

5 Introduction This chapter covers the fundamental economic theory required to analyse water resources planning and management. It is based on the standard economic notions of demand, supply, and allocation. Because water is not an ordinary economic good, some of the economic concepts and treatments are tweaked to accommodate for water peculiar characterstics. The goal of the chapter is for students to understand how an economist views the possible allocations of water by water suppliers over water users. The focus is on water quantity rather than water quality.

6 Economic approach Demand: interpretation as marginal benefits, marginal willingnes-to-pay (WTP) Derived from utility function - downward sloping = diminishing returns Supply: marginal costs of production Derived from production function - upward sloping = decreasing returns to scale Market equilibrium: find the price where demand equals supply

7 WTP

8 Market equilibrium

9 Surplus Consumer surplus: the total value (WTP) attached to the demand minus the cost of purchase as WTP is higher than price for all but the last ( marginal ) unit, CS is positive Producer surplus: the total revenue from sales minus the cost of production as production cost is lower than price for all but the last ( marginal ) unit, PS is positive Sum of consumer and producer surplus: marginal versus total net benefits --> welfare or net social value.

10 Opportunity costs

11 Invisible hand Adam Smith 1776: maximisation of individual welfare contributes to maximisation of social welfare. Market takes care of an efficient allocation of scarce means: sum of consumer and producer surplus maximal. This only holds if social costs = private costs.

12 Market failure No socially efficient/optimal allocation of scarce means through markets if: 1. There are not markets for all goods and services. 2. There is imperfect competition on some markets. 3. Economic activities generate externalities. 4. Public goods exist. 5. Property rights are incompletely assigned. 6. Transactions do not occur under perfect information. 7. Not all firms maximise their profit. 8. Not all individuals maximise their utility (bounded rationality). 9. There are transaction costs.

13 Economics and water a. The field of economics is concerned with the allocation of scarce resources. b. Movie tickets, bus seats, clean air, water. c. Allocation to users with demand for water. d. Role of prices Characteristics of water: 1. Location 2. Time 3. Quality 4. Quantity Complicate the invisible hand.

14 Efficiency Economists often seek to achieve efficiency of resource use a) Allocative efficiency b) Neutral economic efficiency c) Aggregate economic efficiency A leading social objective, although can be disputed Alternative: maximize efficiency under fairness or distributive constraints Often used principle for efficiency is Pareto-optimality. Applied to water: A given allocation is Pareto optimal when there is no alternative allocation of water that makes everyone (weakly) better off.

15 Costs of water supply Usually a single organization: a) Water utility or water district manager b) Privately or publicly owned c) Maintains treatment and distribution network d) This translates into our prime variable of interest: supply costs Water supply costs consist of a.o.: a) Investment and maintenance of delivery infrastructure b) abstraction of surface or groundwater using pumps and conveyance c) treatment of water to remove or deactivate various contaminants d) transport of water via the delivery infrastructure

16 Costs of water supply We assume that the total cost of operating a particular supply organization is a welldefined function of the amount of delivered water W. We capture this assumption by introducing the function C(W) that defines water supply costs as a function of delivered water. Some usual assumptions on C(W) are: a) No costs for natural (untreated) water b) Every level of W is achieved using least-cost technology c) The costs of supplying W=0 is zero: all costs are variable d) Costs increase strictly in W e) Marginal costs are convex due to (i) returns to scale and (ii) capacitly limitations

17 Total and marginal (convex) supply costs

18 Marginal cost function is supply function The marginal cost function of water supply is equal to the water supply function One problems is that, in practice, costs are not only related to W, but relate also to e.g. costs of delivery infrastructure investments, which are clearly independent of W. The main message is: 1. The cost function C(W) portrays cost-effective action by the supplier 2. For any given amount W, this function gives us the lowest total costs of supply 3. Efficiency requires operating on this function

19 Single water-using agent a) We distinguish between demand by firms and demand by consumers. b) Difference: firms derive profits, while consumers derive utility from water use. c) Both concepts can be captured by demand functions d) Demand functions, as opposed to supply function, measure the benefits of water use. e) Logical counterpart of the supply function C(W).

20 Single water-using agent Start with firms, story is equal for household consumers a) Each firm can be considered to have a production function f() of the form y=f(w,x 1,x 2, x n ), a) y is production b) w is the input of water into production c) x 1,x 2, x n is the input of n other items such as fertilizer in agriculture. b) Fixing x 1,x 2, x n at arbitrary levels, we write y=f(w). c) Where the marginal supply function is convex, we have that the marginal production function is concave. d) Obtain this from its derivative to w, which gives the marginal product of water y e) At low levels of w, additional units of water create inreased production at an increasing rate, while at high levels of w, additional units of water create inreased production at a decreasing rate.

21 Total and marginal (convex) supply costs

22 Single water-using agent 1. Assume a market price p for output y 2. The cost of water supply to the firm is given by c(w) 3. Ignore other inputs for the moment 4. Then, a profit-maximizing firm must maximize p f(w) c(w). 5. Solution is such that the marginal benefits of water p y are equal to the marginal costs MC=c (w*) of water use.

23 Optimal water use with one agent

24 Single water-using agent: demand 1. Water demand function tells how the firms desired use of water changes in response to the value of water 2. For calculations, see module and reader 3. This relation is expressed by w=d(p)

25 Water demand firm

26 From firms to consumers One notable difference: consumers do not maximize profits. Instead, consumers maximize their utility subject to an income constraint. Utility is an abstract concept that measures the satisfaction from consuming goods. Alternatively, utility is the metric that we use to compare consumption of different bundles of goods based on individuals preferences Technically, it is sufficient to make the following assumption: Each consumer consumes water `as if he or she is maximizing his/her utitility. Otherwise, the analysis is rather similar to that of firms: water consumption such that their marginal benefits equal their marginal costs of water consumption.

27 Single water-using agent: utility

28 Utility function Three important features 1. More water is preferred to less 2. Diminishing marginal utility of water use 3. Invariance to order-preserving transformations (which implies, for instance, that the unit of measuring utility is irrelevant)

29 Water demand consumer

30 Water demand Conceptual differences between 1. A change in demand: this is a shift in the demand curve 2. A change in quantity demanded: this is a move along the demand curve Note that demand is a function rather than a number. That is, demand depends on price. This distinguishes the economic perspective on water demand from other perspectives, which may use terms like water needs or water requirements. Those are non-economic terms.

31 Aggregating demand We have now established water supply and demand for a single firms or consumer. We are one step closer to determining the efficient allocation of water for an entire society. Next step: aggregating all water demand by firms and consumers in one water demand function and subsequently solve the allocation using the supply function. Some problems though: a) differential processing, which affects which types of water can be combined b) water reuse, which requires information on hydrological processes c) non-rivalness, which changes the method of combining demands.

32 Aggregating demand Having passed these obstacles, one can add demand functions. Suppose following demand functions for 3 agents: w 1 =D 1 (p) for agent 1 w 2 =D 2 (p) for agent 2 w 3 =D 3 (p) for agent 3 Then aggregate demand is D(p)=D 1 (p) +D 2 (p) +D 3 (p) That is, horizontal addition, because water use is rival. The resulting demand curve may be interpreted as a marginal benefit function or willingness-to-pay curve, which are almost identical concepts in the current context.

33 Aggregating demand

34 Aggregating demand The total benefits of water use can be estimated by integrating this function over the complete interval [0,w*]. Changes in total benefits can be estimated by taking the appropriate definite integral below or above w*. Similar calculations can be made with respect to the marginal net benefit (MNB) function, which combines the marginal benefit and marginal cost functions

35 Optimal water allocation for a society Primary perspective from a society point of view: aggregate efficiency (or Kaldo-Hicks efficiency) From this perspective, the total value of water should be maximized. This includes firms profits and consumers utility. Assuming one water supplier, this can be captured in the maximization problem max B 1 (w 1 )+B 2 (w 2 )+ +B j (w j ) C(w 1 +w 2 + +w j ) subject to a water constraint B i denotes benefits (i.e. profits or utility) to agent i. It is no surprise that the solution to this maximization implies that the marginal net benefits MNB are equal for each agent.

36 Optimal water allocation for a society An aggregately efficient allocation of water implies that the value of water to each firm and to each consumer is equal, given the hydrological constraints. Obviously this is an ideal situation that is hard to reach in practice. Nevertheless we are interested in describing this situation, in the abstract terms of sipmle analytical models, because it allows to assess clear trade-offs in policies for water management and planning.

Introduction Question Bank

Introduction Question Bank 1. Science of wealth is the definition given by 2. Economics is the study of mankind of the ordinary business of life given by 3. Science which tells about what it is & what