Subject ECONOMICS

Paper No and Title 15 - Environmental Economics

Module No and Title 01_ Pareto optimality, competitive equilibrium and fundamental theorems of welfare

Module Tag ECO_P15_M1

TABLE OF CONTENTS 1. Learning Outcomes

2. Introduction

3. Importance of Environment for the economy

4. Utility function with environmental good 5. Pareto optimality as an instrument for collective choice 6. Feasibility of Pareto Improvement with compensation 7. From individual utility to social welfare function 8. Pareto Frontier and Efficiency 9. Summary

TABLE OF CONTENTS

T

1. Leaning Outcomes

• Understand the significance of studying environment in

economics

• Know the pareto optimality conditions and different

explanations

• Analyse different conditions using PPF

2. Why Environmental Economics

The nature has gifted us a variety of renewable and non renewable resources. These scarce resources can’t satisfy all of our unlimited wants. But the efficient use of

resources may provide all the necessities for present and future generations. Untreated sewerage waste drained into the river will pollute it which may affect the availability of drinking water, aquatic life and many more. A factory situated near a laundry shop, dirtying the air, will affect the launderer’s production of clean linen. A brick manufacturing unit near a mango farm will badly affect the quality of mango. All these examples illustrate the type of problems we consider in environmental economics. They have both positive and normative aspects of study. From a positive point of our area of interest may be to understand how the existing structure of institutions will lead the self interested factory owner, the institution responsible for the management of sewerage system and the owner of brick manufacturing unit, to undertake an action against their harmful impact on others. From a normative perspective one might be interested in suggesting policy interference for mitigation of these harmful consequences. Origin of environmental economics is related with the concept of market failure. Repairing of market failure needs government intervention. A policy interference by the government need the suggestions from environmental economists. 3 Importance of Environment for the economy We have to understand the importance of environment for the economy. Our economic system provides us the desired material goods and services for all our needs. This economic system can’t survive without the support of environment around us which includes various communities of insects, plants, animals and different other natural resources. The interrelationship and influence in a community of organisms and natural resources on each other is called an ecosystem. A pond ecosystem is an example of a very small ecosystem where everything from shallow water to various plants, fishes, frogs, rocky or muddy bottom, various insects etc. are interrelated and interdependent. This pond may provide so many things like water, fishes, algae, other plants etc. for the economy to be used for various purposes. If water charging in the pond or the aquatic life or anything else is badly affected it will also inversely influence economic activities of the people depending upon this pond. Similarly environment provides us the raw materials which are transformed into numerous commodities through various economic processes. Simultaneously it also provides direct services to all of us, by providing oxygen, air, water, sunlight, scenic beauty etc. The uninterrupted supply of these environmental goods and services is necessary for the existence of our economic system. But the conventional economics textbooks often ignore the economy-environment interrelationship¹, without considering this relationship an economic model or the picture is incomplete and misleading. The basic economic processes of extraction (for example mining of iron ore from iron mines), processing/fabrication (converting iron ore into steel and automobile) and consumption (using the automobile), all involve the generation of waste product that ultimately goes back into the environment (air, water or onto the land).

In most of our economic models and hence the textbooks, markets try to solve the problems of finding the efficient and right amount of production and consumption in terms of minimization of costs directly involved in the process of production and maximization of utilities in the consumption of market goods. But they do not try to find the right or of socially desirable amount of waste or the pollution. Our environment also acts upon the waste being produced by us. This natural process helps to clean up and

recycle the waste to be used again. But there is a capacity of nature to absorb the waste or the pollution. If the pollution crosses this capacity it starts affecting the producers as well as consumers by affecting the supply of environmental goods. As for the survival of present generations the production of market goods is necessary similarly for future generations the protection of environment is also necessary. Hence in environmental economics an important question is to find the right balance between protection and use of environment. 4. Utility function with environmental good The basic nature of a market good is different from an environmental good. Market goods are rival and excludable in nature while environment goods which are pure public goods are non rival and non excludable. If bread (a market good) is consumed by one person the same can’t be consumed simultaneously by another person. But the decrease in air pollution or the provision for clean water (an environmental good) in a particular area by controlling the industrial waste disposal will be enjoyed simultaneously by all the people of that area. Hence the total utility of a person will depend upon all the market goods consumed by him and the utility from environmental goods available for everyone. If we produce more of market goods (let’s denote market goods by x), it will be associated with more production of waste, hence there will be less of environmental protection (let’s denote the environmentai good by ‘e’, improvement in environmental quality means higher value for ‘e’ and vice versa). The utility of a person ‘i’ will depend on both, market goods x consumed by him and the environmental good e. Hence his total utility will be Uᵢ(xᵢ,e) where xᵢ represent all the market goods consumed by him during a period of time and e represent the environmental quality during same time period. Different people may consume different quantity of market goods but must consume the same amount of environmental quality as it is a pure public good. Fig. 1 shows a set of indifference curves with composite market goods and environmental goods. At low levels of x environment is less valuable hence the loss of utility because of a small decrease in x will be offset by a large quantity of e. As we move to higher values of x a smaller quantity of e will be required to offset the same quantity of composite market good x.

Fig. 1 Set of indifference curves for an individual. Higher indifference curves represent higher level of utility. When the consumption of market goods increases, the consumer values more to the environmental good where he is ready to give up x3x4 units of market good for a small quantity of e as compared to lower indifference curves where he will be ready to give up the same quantity of market good only for higher quantity of e. Assuming that there are N individuals in the society. Then a societal consumption bundle will include all the market goods consumed by each individual separately and the environmental good consumed collectively. If a represents a societal bundle such that a≡ (x1,x2,x3,……xN, e ) where x1 composite market goods consumed by individual 1, similarly x2 by consumer 2 and so on, e is environmental good collectively consumed by all. Similarly another societal consumption bundle aʹ will be represented by aʹ≡ (xʹ1,xʹ2,….xʹN, eʹ). Each individual is facing a tradeoff between market goods and environmental goods. Their utility depends upon both x and e. If the utility of market goods, U(x), increases then utility of environmental goods, U(e), decreases as higher production of market goods is associated with lower environmental quality. Hence to maximize the utility each individual has to find the right balance between x and e. Poor people will value market goods more than the environmental goods as they will be on lower indifference curve in Fig.1, while the rich who are on the higher indifference curve, will be more concerned for environment than poor.

5 Pareto optimality as an instrument for collective choice When the people are facing the tradeoff between market goods and the environmental goods, the collective decision making for the whole society becomes more difficult and complicated. The individual can choose about her consumption of market goods only. She may decide to help in protecting the environment but can’t decide a different consumption level of environmental goods for herself as compared to other people around her. A redistribution of market goods among the people of a society is possible by changing their relative prices but the same is not possible for environmental goods. We may increase or decrease the quantity of environmental good by changing the production of market goods. The same quantity of environmental good may have different utility for different individuals depending upon their income level, philosophical thoughts, level of information, education etc.

Assume that different levels of market goods being produced are xʹ, xʹʹ etc. for the society as a whole, then the associated levels of environmental goods for the society are eʹ, eʹʹetc. respectively. Now the societal consumption bundles may be represented as aʹ=( xʹ, eʹ); aʹʹ=( xʹʹ, eʹʹ); ……and so on. When xʹ quantity of market goods is being produced, all the N consumers will be consuming x1ʹ, x2ʹ, …xNʹ respectively. Similarly for xʹʹ quantity of market goods they will be consuming x1ʹʹ, x2ʹʹ, …xNʹʹ respectively.

Now we face the question of societal choice. Which consumption bundle should society choose aʹ or aʹʹ, if there are only two societal bundles? If every individual prefers aʹ over aʹʹ the society will also prefer aʹ over aʹʹ. Similarly even if every individual, except one who prefers aʹ over aʹʹ, equally prefers aʹ and aʹʹ, society will also prefer aʹ over aʹʹ. In both of these two cases there is no controversy. We can say that aʹ is Pareto preferred to aʹʹ if we use Pareto optimality criterion.

The Pareto Optimality Criterion states that an economic outcome is said to be Pareto optimal if any reallocation of resources can’t make someone better off without making another worse off. Explanation 1 For a group of people consisting of N members (i=1, 2, …..,N) with their respective utility function Uᵢ , decided by their consumption bundles, assume we have two societal consumption bundles aʹ=( xʹ, eʹ) and aʹʹ=( xʹʹ, eʹʹ). Then aʹ is Pareto preferred to aʹʹ for the whole group if for every individual Uᵢ(aʹ) ≥ Uᵢ(aʹʹ) and at least for one individual Uᵢ(aʹ) ˃ Uᵢ(aʹʹ). Suppose a society consists of only two individuals, Anish and Bina. Their respective utilities are represented by Ua(xa,e) and Ub(xb,e). Fig.2 shows their possible utility combinations in the utility space with limited available resources. The attainable utility combinations lie either on or below the Utility Possibility Frontier AB. Let’s compare two points G and H. Utilities of both is higher at point H as compared to point G. Hence H is Pareto preferred to G. Similarly F is also Pareto preferred to G as Anish’s utility remains unchanged but Bina’s Utility increases when we move from point G to point F. While comparing points K and H we can’t conclude that one point is Pareto preferred as compared to another point. To make Anish better off we have to make Bina worse off or to make Bina better off we have to make Anish worse off. There will not be a unanimous choice between points K and H for Bina and Anish. But the unanimity is possible between both of them while comparing points G and H or G and F.

Fig.2 Pareto preference for a society of two with utility possibility. Point F and H are Pareto preferred to G. Point J is non attainable while all the points on or below the utility possibility curve AB are attainable.

6. Feasibility of Pareto Improvement with compensation In Fig. 2 a unanimous choice for the society (this two member example may be extended to N members of the society) between point G and K is not possible. Moving from point G to K will be acceptable for Anish but not for Bina. Bina may accept only if she is being compensated by Aneesh and that compensation should be able to offset her loss of utility while shifting from point G to K. This compensation is possible only through market goods as environmental good can’t be exchanged between two consumers.

Fig. 3 Potential Pareto Improvement for a society of two. As shown in Fig. 3, the shaded area of triangle FGL shows all the points which are Pareto preferred to point G. But we can’t say for other points which are lying outside this triangle in attainable area. Comparing a shift from point G to K, the gain of utility for Anish is ΔUa and the loss of utility for Bina is ΔUb. If Anish compensates Bina by giving her y units of market goods, then both will agree only when for Anish ΔUa≥Ua(y) and for Bina ΔUb≤Ub(y). In case when compensation can make unanimity among the individuals for a particular societal bundle, we may say that there is feasibility for Pareto improvement. In our example of point G and K Bina who was loser got compensated from Anish and both agreed for this compensation of y goods we may say that K is potential Pareto improvement to G. The same example may be generalized for N number of people in societal group. Explanation 2 For a group of people consisting of N members (i=1, 2, …..,N)while comparing two societal bundles aʹ and aʹʹif there exists a vector of transfers from individuals such that the sum total of all the transfers is zero, y=(y1,y2,…,yN); ∑yᵢ=0 and (aʹ,y)=( xʹ1+y1,xʹ2+y2,….xʹN+yN, eʹ) becomes Pareto preferred to aʹʹ,then we can say that aʹ is a potential Pareto improvement over aʹʹ. With a large number of people in the society the feasibility of implementation of Pareto improvement criterion becomes very difficult. Nicolas Kaldor and John Hicks have suggested an alternative in Kaldor-Hicks compensation Criterion. Suppose that the Government wants to install sewerage treatment plant. Some people will gain because of the availability of clean water, while a few will lose because of bad smell in their surroundings. According to this compensation criterion if government asks the gainer whether they are ready to compensate the losers and their answer is yes then building of this plant is Pareto improvement hence good idea for the society. 7. From individual utility to social welfare function In Fig.1, all the indifference curves U1,U2,U3,U4 represent ordinal preferences of utilities for an individual. Using these we can draw the societal utility function which is also known as Bergson-Samuelson Social Welfare Function or the Social welfare function. According to each societal bundle aʹ or aʹʹ there is a consumption bundle for each individual. For example, if aʹ represent 100 units of market goods and a certain level of pollution, Anish and Bina are consuming 60 and 40 units of market goods respectively. Their utilities at point aʹ will be determined by their consumption of market goods and environmental goods. Anish’s utility at point aʹ may be represented as Ua(aʹ)=(60, eʹ) similarly for Bina Ub(aʹ)=(40, eʹ). Here 60 and 40 represent the utility for Anish from 60 units of market goods and for Bina from 40 units of market goods. The total social welfare at point aʹ will be determined by the individual utilities of all the members of the society which are Anish and Bina in our example. Hence Social Welfare Function W at point aʹ will be written as W= W(Ua (aʹ), Ub(aʹ)) and if there are N members so that i=1,2,…..N then W=W(U1 (aʹ),….., UN(aʹ))

If in comparing two consumption bundle aʹ and aʹʹ, W(U1 (aʹ),….., UN(aʹ)) ˃W(U1 (aʹʹ),….., UN(aʹʹ)) we can say that aʹ is socially preferred to aʹʹwhere W is Bergson-Samuelson Social Welfare Function. If a social welfare function exists to show social preferences we can also draw social indifference curves. Fig 4 shows such social indifference curves which are just like individual indifference curves. Point A is Pareto preferred to B and also represents higher level of social welfare. Point C is not Pareto preferred to B but represent higher level of social welfare.

Fig. 4 Social indifference curves representing different levels of social welfare 8. Pareto Frontier and Efficiency

Now let’s come back to Fig.3 with two member society. We have already discussed that the attainable area lies on or below the curve AB. We can see that because the point G lies below the Utility possibility curve AB, there exists the points like F, L, and all other points on curve between F and L which are Pareto preferred to G. At point F Bina’s utility increases without decreasing Anish’s utility and at point L Anish’s utility increases without decreasing Bina’s utility and on all the points between F and L utility of both is increasing. Similarly for all the points below the curve AB there is a possibility of Pareto improvement. But for all the points on this curve AB we can’t increase the utility of either Anish or of Bina without decreasing the utility of other’s. When the Pareto improvement is not possible the point becomes Pareto optimal. Hence all the points on curve AB are Pareto optimum that is why we may call this curve as Pareto Frontier. Explanation 3 Pareto frontier consists of all the allocations for which no improvement in Pareto sense is possible. We may consider an allocation to be inefficient if any improvement over that is possible. Point G is inefficient as improvement in allocation possible. Point F and L are not inefficient as any improvement in Pareto sense not possible over these points. Generalizing this to all the points of Pareto frontier we may say that: all the allocations on Pareto frontier are efficient or Pareto optimal and the allocations below the Pareto frontier are inefficient. -----------------------------------------------------------------------------------------------------------

1. Natural environment has a limited capacity to absorb the waste. Addition of excessive waste to land, water and air with unsustainable use and inappropriate management practices leads to severe deficiency of various inputs and other requirements for our economic activities which constraints the economic growth. This is also known as waste receiving limit to growth.

9. Summary

Most of our economic traditional theories and textbooks talk about efficiency in terms of

efficiency in the production of market goods and their consumption. Both, production

and consumption are associated with the production of waste (we may call it pollution).

Market goods give utility, pollution gives disutility, so total utility depends on both

market goods(x) and environmental good (e) (environmental good is a public good). The

challenge before us is to find a right balance of market goods and environmental good.

Now if we assume an economy with two consumers, both consuming market goods and

environmental goods, then Pareto optimality is a situation where we can’t make one

person better off without making someone worse off. If we can make some one better off

by compensating someone else, there is a feasibility of Pareto improvement; we call it,

‘Potential Pareto improvement’. All the points below utility possibility frontier are

potential Pareto improvement consumption bundles, and the utility possibility frontier is

Pareto frontier where we don’t have the feasibility of improvement even by

compensation.