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Module 1: Arrow's Theorem and Demand Curves

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Biocentrism and Social Welfare Function

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And then normally there is a process where they invite public comments and then, but many times they get mired in some kind of controversy, but we are trying to look at this in terms of how do we compare and how do we choose. (Refer Slide Time: 14:54) So, we would like to look at the kind of different philosophical perspectives. So, we look at essentially three perspectives, biocentrism and which focuses on the fact that every living organism has an intrinsic value. Then there is a second perspective, which is a sustainability perspective where we want to preserve the health of the ecosystem. The third perspective is a human-centric, or anthropocentrism. So, depending on your value system, whether it is biocentric or sustainability or anthropocentrism, it will result in different kinds of choices. And of course, in general, people will have a multiplicity and you will not be extreme on any of these, but it is good to understand philosophically what are the differences between these three perspectives, and then precautionary principle if you know that there are likely to be problems you may want to just take the safe we out and try to see that we can preserve the environment and yet have some development. In the case of biocentrism, we will talk about intrinsic value and instrumental value and they will define what is biocentrism. (Refer Slide Time: 16:22) So in biocentrism, we are saying that the biologic world is the centre of the value system, all living beings have intrinsic value, regardless of their instrumental value. So, what is the instrumental value? Instrumental value refers to the usefulness of an object or an individual or a being. So, it is the instrumentals is the usefulness that if it can serve as an instrument for achieving some useful objects and that is what is instrumental value. So, only those things which can serve some useful objective will be said to have an instrumental value and in the case of biocentrism, we say that all living organisms have an intrinsic value, irrespective of whether or not they have any use, irrespective of whether or not they have any instrumental value. So, something can be useless and still have intrinsic value. Example, the smallpox virus so in a biocentric world, the smallpox virus has a value and you would not want to destroy it however we consider that to be the smallpox virus is useless and has a negative value and damages but we in the biocentric world we think that, all life, all of life is important and we want to perceive, we want to preserve life. So, similarly, if you have a biocentric view of the world, even if you have someone who is a known murderer, you would not prescribe a death sentence because you feel that life itself has a value. And even though that person has a negative value in society, you would continue to keep that person in prison, but you would not destroy it because life itself has an intrinsic value. And we would like to, so, this is one extreme, and this would mean that if you have a biocentric viewpoint of the world, you would try to not only preserve individuals, but you would also like to preserve all kinds of all the organisms. And so that is one kind of perspective, philosophical perspective one which one we have. The second perspective that we talk about is the sustainability perspective. (Refer Slide Time: 19:14) Sustainability perspective initially was proposed by Leopold, way back in 1949, talks of the land ethic, the health of the ecosystem are of paramount importance. So, you want to make sure that the land remains fertile, that the land remains beautiful and we would like to keep it in that fashion. So, in the case of sustainability, we are looking at an environmental policy being right, only if it preserves the integrity of an ecosystem and wrong if it does not. So, the question is, is this consistent with natural resource use for humans? It could be, so, it depends on it provided the use does not degrade the environment. For instance, fishing is acceptable but overfishing is not because if you overfish, the entire population of fish in the rivers would vanish and that is not sustainable. The logging is acceptable, cutting of trees, but provided the long term health of the forest is not affected or it is not jeopardized. And so this is consistent, however, if you look at fishing, fishing will not be consistent with the biocentric view of the world because the life, living fishes have their value and you will not be allowed to damage that. Sustainability term is commonly used but often not precisely defined. (Refer Slide Time: 21:03) We often approach sustainability from what is not sustainable. So, a few decades back the Brundtland Commission defines sustainability as development that meets the needs of the present without compromising the ability of future generations to meet their own needs. And this is, of course, mostly a human-centric dfinition but when we are talking of the land ethic and the sustainability, we are looking at also the sustainability of the overall ecosystem. (Refer Slide Time: 21:32) Robert Solow has defined sustainability as making sure that the next generation is as well off as the present generation and ensuring that this continues for all time. What are the two important aspects of sustainability? The first is the degree to which natural capital can be viably replaced by human capital. So, we always started with having things available in nature. We have several different processes and natural cycles, the history of human development have been where we have made our ways of doing things and mimicking nature. So, we replace natural capital by human capital, by technology, by materials, by devices. And so this is to what per cent to, you know to what extent can we do this and we do this essentially to make our lives more comfortable. The second part of sustainability is that we, the present generation has an obligation to future generations and so we also looking at sustainability in terms of how do we fulfil that obligation so that future generations can enjoy at least the same quality of life that we enjoy. So, the man-made capital, when we talk of machines, building. So for instance earlier we used to have to daylight and you can have ventilation but now we create lights, artificial lights, we condition the air in the buildings, and then we imitate nature and we can do that so, that we can control and we can increase our comfort. So, manmade capital and most importantly now we are looking at knowledge and information as being substitutes for natural capital, particularly natural resources. There are limits to this of course and there are physical requirements which are not necessarily going to be substitutable. So, the question is, are sustainability and biocentrism consistent? In many cases, they are not so, for instance, hunting can be acceptable from a sustainability viewpoint, it may be desirable to reduce the overpopulation and there may be a limiting condition in which different ecosystems and different species can coexist in a certain. So it may be natural from an ecosystem and a sustainability viewpoint to have hunting but it is not acceptable for biocentric. So, we saw two different perspectives, the first one was biocentrism, the second one was sustainability. (Refer Slide Time: 24:48) Let us look at the third, the third perspective, which is anthropocentrism. So, anthropocentrism is a human-centric viewpoint and the thinking is that only human beings matter and the environment is only there for one purpose, to provide material gratification for humans, this is also an extreme kind of thing. But if you see how human civilization has been progressing, we behave as if everything is there for us and we are doing, we can exploit it as long as it serves our purpose. So, anthropocentrism only provides an instrumental value to the environment that means the environment is important only so far as it is useful to us. So, if there is air pollution which affects human health, then we should be concerned about it. But if we are polluting the ecosystem and it does not affect humans, but it is affecting the rest of this civilization then we are not concerned about it. So, this is an extremely selfish and human-centric viewpoint, which is often which is fairly reflects how development is occurring today. The other slight variant of this is utilitarianism, where we talk about the wellbeing that people attained from the environment and this could be materialistic, spiritual, instrumental or intrinsic. So for instance, if the Californian Gnatcatcher if we talked about, which was talked about as an example in Kolstad book is something which does not have an environmental, useful value. And we are not very clear about its contribution to the ecosystem in terms of what is the impact on humans. But it may have a utilitarian value because several people may be happy that we have this species and it has not become extinct. People may come and visit and see the California Gnatcatcher even if you are not in that locality, the very feeling that we have actually, the perception that it has been saved and it is there is a forest may give you a good positive feeling and you may get a utility of that and that is from a utilitarian perspective. So now, the question is, individuals have different belief systems and then based on those belief systems they will have preferences and make choices. We now want to look at how we aggregate and make social choices from different individual values. So, what are the methods for making decisions about specific projects or regulations that have some adverse environmental impact, based on individual preferences? Please remember, there are no restrictions on individual preferences. Every individual can decide how he or she will choose between all the different options. (Refer Slide Time: 01:11) So, let us put this in a set of differential equations, let us say that there is N person society, there are N people okay, n people and let us say that there are, you know we talked of potatoes, onions, travel, air conditioning, a whole set of different goods, let assume a composite material good x, that material good has x1, x2, XM, different goods, good services okay, each individual is consuming all of this in addition to this. So, there is an individual state of preferences, how many clothes, how much food, how much entertainment, all of this comes in this and then in addition to this will be e, e is the quality of the environment, this is remember this will have multiple attributes, we can talk about the air quality, we can look at particulate matter, we can look at global emissions in terms of CO2, we can talk about it in terms of the visibility. So, it could be a the quality of water, the quality of the soil. Now, the idea is that this e, the x was dependent on every individual, so every individual would have a range of different values of x and would also have in the utility, some value for the environment, the environment quality is going to be common for all the n individuals, right. So, when we talk about the utility wellbeing of every individual. (Refer Slide Time: 03:21) So there are two things, the composite good ‘x’, which has those m different components and the environment e and so each individual has a utility which is a function of xi and e. So, x1 e, x2 e and so on for each individual, there will be a utility function and then they will be n such utility functions okay. Now let us look at when we look at, is it possible to substitute x for e, can we? If we consume more of x, if you are consuming more fossil fuels, there is going to be emissions, and so on. So, pure biocentrist will say that we do not want to have anything where any ecosystem or the species is getting, species biodiversity or any life is getting spoiled. So, there will be no substitution for x for e. And in the case of extreme anthropocentrism, you would not want to give up anything in terms of your goods for the environment. So, you do not want to substitute any e for x, these are both extreme conditions, but in actual practice, there will always be this trade-off. So, also remember, whenever we are talking of choices, we talked about the n individuals and their choices. However, the future generation and the utility that they will enjoy, right will also come into the utility function that means utility xi, e and the utility of future generations, where uj is the utility of person, j in a future generation and this is, of course, makes it all that much more difficult. And this is where now you have this whole situation where you have children coming up and opposing the governments in terms of the inaction related to climate change, you have Greta Thunberg telling world leaders that we need to think about the future and we do not have the right to spoil the choices for the future. So, these are tricky things, but to in concept, we think of when we make the decision which is a long term decision, it is also the utility of future generations which is involved. (Refer Slide Time: 06:03) So, we will now try to look at how do we choose between two bundles, there are two bundles of goods, two options A x dash e dash, where x dash is x1 dash, x2 dash, each of this x is x1 is for individuals one and it is the whole bundle of consumption goods that one, that that individual consumes and that has we said, it is a array of m different goods and services. So similarly, so this is a composite good as we said, xn dash and e dash. This is one option, the second option is x double dash, e double dash alright, so the question is should we choose A or should we choose B? Should the society choose A or should the society choose B and what conditions should we choose? And the question is how do we generate a set of societal preferences over different bundles given individual preferences over the same bundles. So, each individual will have a preference x1 dash and e dash, individual one has x1 dash e dash as compared to x1 double dash, e double dash, x2 dash e dash, x2 double dash, e double dash and here we are we will see under what conditions can we have a unanimous choice, under what conditions how will we have tradeoffs and what are how we can make these choices. (Refer Slide Time: 08:21) So, this problem was first solved in a sense by Wilfredo Pareto, an Italian economist who talked about the concept of Pareto optimality. And the idea was that we could get a situation where you cannot have an improvement where everyone benefits and so that become then you have the condition of Pareto optimality where there is no possible change where everyone benefits and everyone will be agreeable to it. So, we look at the Pareto criterion is what he defined. This has found applications in many different fields and we will talk about it in the utility field. (Refer Slide Time: 09:02) So, let us look at a situation, let us look at the graph, so what we have done here is we have simplified it, we talked about n individuals in the society, now we are looking at two individuals. So, we have A and B, and you have different combinations of in the case of W look at each point, each point is a combination of resources which gives us A’s utility and B’s utility. There is a distribution of resources between A and B and this shaded region represents the feasible region of all possible combinations. So, when we compare W which with Z, you will find that A’s utility for Z is greater than A’s utility for W. So it is better off, A better off followed with Z, in the case of B also B’s utility for Z is more, the utility is more than that of W. So, what we say is both A and B are better off and this Z is said to be Pareto preferred over W. Similarly, if you look at X and R, if you look at E and R, A’s utility in X and A’s utility in R are both the same, so as far A is concerned X and R are identical, but for B the utility for R is greater than the utility for X. So, for A is indifferent to this, but for B this is better so, this is also R is Pareto prefer to X. When we now compare X and S, you find that A utility in S more than A utility, A’s utility S is more than A’s utility in X and Bs utility remains the same, again S is Pareto preferred similarly, Y, but if we look at this curve, you will find that this represents from this curve, there is no feasible solution of Pareto improvement. So, this curve represents the locus of all the best points which are Pareto prefer, this is also called the Pareto frontier. So, essentially we talk about Z being Pareto preferred to W and Y being Pareto prefer to X. (Refer Slide Time: 12:12) So, in principle when we write this, we can talk about two consumption bundles, a dash being x dash and e dash and a double dash is x double dash e dash and the group of people i is equal to 1 to n with utility function defined over the consumption bundle. (Refer Slide Time: 12:29) If for the group as a whole a dash is Pareto prefer to a double dash, that will mean that every individual for every I, Ui of a dash greater than equal to Ui a double dash and for at least, at least one individual so, that means everyone is either better off or equal, it could be that all are equal, a dash is equal to a, a dash is equal to a double dash utility, at least for one individual the utility increases. Then what we say is that a dash is Pareto preferred over a double dash, which means that everybody is at least as well off in terms of the utility and at least one person is better off with a dash than in a double dash, so the Pareto criteria will have unanimity, everyone will opt for a dash, everyone will opt for a dash, because they are either equivalent or they are better off. So, this is the Pareto criterion and, of course, this is restrictive, it will be only in a very small subset of cases where you can have this where everyone is better off or they are in the equivalent situation and some are better off. So, for some it improves, no one gets affected, no one loses off in terms of the utility. There are many other situations where some lose and some gain and there is a modification which we try to do for which is called the Potential Pareto improvement. (Refer Slide Time: 15:05) So, for instance in the case of X and if you look at X and R and we are moving from X to, if you look at the benefit that we are getting in terms of moving from X to Z, we are getting a benefit B’s utility increases very significantly, A’s utility decreases so, the question is the amount of increase that B has if B compensates A to account for the loss in utility that A has. So that is compensated and based on that, this is equivalent at least equivalent for A then we can have a situation where A also okay with the new option and since B gets so much improvement in utility, they can transfer something back to A. So, that this is happening and this is the principle which is used for dams when we talk about resettlement, we try to give compensation for to the people who are affected and with the result that the net benefits outweigh the costs. And this is the whole concept of the potential Pareto improvement. (Refer Slide Time: 16:48) So, in this what we do is we allow the transfer of resources amongst the individuals to increase the unanimity of opinion regarding the option, so for instance, suppose 80 per cent of the population prefer an option A to B, while 20 per cent prefer B to A and according to the Pareto Criterion, we cannot say whether A or B is preferred. But suppose the 80 per cent can transfer significant resources to B and suppose the resources transfer is large enough so, that unanimously can be reached an option A. So, there is compensation where B can agree that okay, we will go ahead and everyone agrees to do that. (Refer Slide Time: 17:25) So, in order to do this, what we say is that in addition to x and e, we also have another resource y and this y could be something which is tradable, for instance, money. So, that we are looking at a certain amount of y and we have transfers in y which are Zi that means, for instance, in the example that we had where A has a certain amount of money yA and B has an initial amount of money yB we transfer. Since, A is getting, if you look at this graph, you remember sorry, B is getting most of the benefits. Let us look at this point when we look at B is getting most of the benefits, so what we do is B transfers money to A, so this will be Z. So, this becomes yA plus Z and this becomes yB minus Z. So, with the result that because now the initial thing was xA, e, yA now, it becomes xB, e. The utility with this additional resource can be such that it is equal to the more than or equal to this. So, you transfer that much resource, so that these become equivalent and with the result that the utility of B is also increasing, even though it is transferring a certain amount of money because it is getting so much additional benefit. So, if it is possible to do this such that the sigma of Zi is going to be equal to 0. That means, there is no money or no additional resource coming from outside the system this resource is balanced within the system it is traded so that we compensate those whose utility is decreasing. And the individuals whose utility is increasing compensates this overall if you can do that so that the utility of those who in the earlier case was not for the project, because their utility was decreasing. Now their utility is remaining constant and it becomes after compensation, it becomes a Pareto preferred choice. So, then, that is the situation that we can look at. So, we look at the condition where we are comparing a dash y minus z is Pareto prefer to a double dash. (Refer Slide Time: 20:40) We compare a dash y minus z to a double dash y and if a dash y minus z is Pareto preferred then we say that this is a potential Pareto improvement. So, this increases the options that we have and we compare two bundles as we said vector of transfers so that a dash y minus z is Pareto prefer to a double dash y then a dash is a potential Pareto improvement over y. So, this is clear that we can compensate and in the compensation at the result of that, finally, every individual utility either increases or remains constant. Some of the individuals who had the utility increase more they transfer some resources, their utility, their part of that increase in utility shared with those who are losing out with the result that now there is unanimity. So, this is called Potential Pareto improvement. Now, the third situation is called the Kaldor Hicks Compensation Principle and this is a little controversial. This talks about the fact that if transfers could be made to achieve unanimity, that means if we can have a choice where we transfer from the gainers, some tradable resource to the losers so that the losers utility remains constant with the result that there is a net gain and every single individual is okay with the project. If that can be conceptually done, and it works, then the choice is socially desirable, even if the transfers are not equal actually meet. But this is highly controversial because in actual practice when you look at individuals and societies, there is already a significant amount of inequality and what is mentioned here is that if the project is such that it is possible to make these transfers then societally this project results in better utilities. And the idea of equity compensation, links with the idea of equity is decoupled from determining whether the choice is a good idea or not, the choice is a good idea or not if the hypothetical transfers could be made, and this would be then Pareto preferred even though the transfers are not made, so, this is a fine sort of argument, but in actual practice, this is what happens in many cases. We identify based on cost-benefit, saying that compensation, even after compensation the profit, the project is profitable, but then we do not do the compensation. So, then there is this kind of issue and this is what often you know, this is the problem with the kind of economic, sometimes the economic calculations. (Refer Slide Time: 24:23) Then another mode of choice is voting and voting means that every individual is asked to vote on the project and this rule does not need unanimity. So, it is more flexible than the Pareto condition but the majority rule cannot take into account the intensity of preferences. So, often majorities may decide some things which may not necessarily be correct in terms of principles of natural justice. And so, now the next thing that we will look at is we will try to create some kind of a social indifference curve. (Refer Slide Time: 25:01) We will look at the utility that we have for so, we would like to compare the society with a welfare function. (Refer Slide Time: 25:10) Welfare function means there are n individuals. Each individual has its utility u1, u2 to un, when we compare two different sets of preferences, where we look at two bundles, and a and b and we would try to see, we put a welfare function where we calculate the value of the utility for all the n individuals for a and the value of this utility for all the n individuals in b. And if we say in comparing this, that this utility is greater than you utility for b, then a is socially preferred to b, where W is called the Bergson Samuelson social welfare function. There are different ways of creating this social welfare function and there are many different function values. (Refer Slide Time: 26:13) If you look at the Benthamite social welfare function, this is just a weighted average. So, we say, un we call this as theta 1 u1 plus theta 2 u2 plus and so on theta n un where theta I greater than or equal to 0, they are all positive. And we sum this up so, this is some weighted average, some weighted values, and we can decide what are these weights depending on this, of course, an Egalitarian function could be where we have equal weights. (Refer Slide Time: 27:24) We can also try to see that we want to minimize the deviation from the, so you have this Egalitarian function which you can see here is the sum of ui minus ui minus minimum ui, so that the deviation from the minimum is we try to see that, we try to reduce the gap between the average value and the minimum value and this can be an Egalitarian social welfare function. (Refer Slide Time: 27:49) John Rawls who was a philosopher and a thinker said that utility function should be where we are maximizing the minimum utility of any individual so, the poorest individuals utility should be first maximized okay. So, with this we have, let us just take stock of what we have done, we have looked at these choices between environment and development. We have looked at the philosophical basis and the perspectives, we looked at a few problems, few problem contexts and then we talked about the Pareto preference, the Pareto something being Pareto preferred and something where we can have a transfer and we can then use this with the transfer we can get a Pareto preferred option. Then we looked at the Hicks Kaldur compensation principle. So these are three methods of choices Pareto prefer, Pareto compensation and then the Hicks Kaldur compensation principle. We then also looked at voting, after doing that, we then said that let us look at all the utilities and create a social welfare function where we get the welfare of the overall society. Please remember, in actual practice, these are all conceptual constructs by which we understand how we are making the tradeoffs. And it is difficult to construct some of these utility functions, but conceptually this is useful to us to understand what kind of tradeoffs and possibilities are there. You may want to look at from your locality or your state or the context that you are familiar with, try to identify problems where we talk about energy and development and the environmental impacts, look at the kind of tradeoffs which are there, look at what kind of who are the stakeholders and how would you identify what are the kind of utilities. And also think in terms of the value that we talked of e. How do we characterize and put one quantitative value to talk about the quality of the environment, that is a difficult task often, we are going to look at there is in the next module, we will look at the concept of Arrows theorem where he talked about the impossibility of social choice. We will talk about that and then we will move forward to define public goods and private goods.