 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 the individual preferences? Please remember, there are no restrictions on the individual preferences. Every individual can decide how he or she will choose between all the different options. So, let's put this in a set of different equations. Let's say that there is an N-person society. N-people and let's say that there are, you know, we talked of potatoes, onions, travel, air conditioning, a whole set of different goods. Let's assume a composite material good x. That material good has x1, x2, xm, different goods, goods services. 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. We could, this is remember, this will actually 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 divisibility. So, we could look at 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 individuals. So, when we talk about the utility well-being of every individual, 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 there will be N such utility functions. Now, let's look at, when we look at, is it possible to substitute x for E? Can we, if you consume more of x, if you are consuming more fossil fuels, there are going to be more emissions and so on. So, pure biocentrists will say that you don't 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, x for E. And in the case of extreme anthropocentrists, you would not want to give up anything in terms of your goods for the environment. So, you don't 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 will also can 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 the future generation. And this 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 in concept we think of when we take the decision which is a long-term decision, it is also the utility of future generations which is involved. 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 individual 1 and it is the whole bundle of consumption goods that one that individual consumes and that is a 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 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 1 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 we will see under what conditions can we have a unanimous choice under what conditions how will we have trade-offs and what are the ways in which we can make these choices. The 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 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 so let us look at the situation let us look at the graph so what we have done here is n individuals in a 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 and b and this shaded region represents the feasible region of all possible combinations so when we compare w with z you will find that a's utility for z is greater than a's utility for w so it is better of w with z in the case of b also b's utility for z is more 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 x and r a's utility in x and b a's utility in r are both the same so as far as 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 preferred to x when we now compare x and s you find that a's utility in s is more than a's utility a's utility in s is more than a's utility in x and b's utility remains the same again s is Pareto preferred similarly y but if we look at this curve you will find that the this represents from this curve there is no feasible solution of Pareto improvement so this curve represents locus of all the best points which are Pareto preferred this is also called the Pareto frontier so essentially we can talk about z being Pareto preferred to w and y being Pareto preferred to x so in principle when we write this we can talk about 2 consumption bundles a dash being x dash and e dash and a double dash as x double dash e dash and the group of people i is equal to 1 to n with utility function if for the group as a whole a dash is Pareto preferred to a double dash that will mean that every individuals 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 a equivalent situation no one gets affected no one loses off in terms of the utility there are many other situations where actually some lose and some gain and there is a modification which we try to do for the which is called the potential Pareto improvement 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 it is compensated and based on that this is equivalent at least equivalent for A we can have a situation where A is 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 to the people who are affected that the net benefits outweigh the costs and this is the whole concept of the potential Pareto improvement so in this what we do is we allow transfer of resources amongst the individuals to increase the unanimity of opinion regarding the option so for instance suppose 80% of the population prefer an option A to B while 20% prefer B to A and according to Pareto criterion we cannot say whether A or B is preferred but suppose the 80% can transfer significant resources to B and suppose the resources that transfer is large enough so that unanimity can be reached on option A so there is a compensation where B can agree that okay we will go ahead and everyone agrees to do that 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 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's look at this point when we look at B is getting most of the benefits so what we do is transfer 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 XBE 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 balance 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 were not for the project because their utility was decreasing now their utility is remaining constant hence 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 preferred to A double dash we compare A dash Y minus Z to A double dash Y and if A dash Y minus Z is Pareto preferred then this is a potential Pareto improvement so this increases the options that we have and we compare 2 bundles as we said so that A dash Y minus Z is Pareto preferred to A double dash Y then A dash is a potential Pareto improvement now so this is clear 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 utility increase more they transfer some resources their utility their part of that increase in utility is shared with those who are losing out with the result of unanimity so this is called potential Pareto improvement now the third third situation is called the Kaldor Hicks compensation principle and this is 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 actually made now 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 hypothetically transfers could be made 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 really happens in many cases we identify based on cost benefit saying that compensation even after compensation the project is profitable but then we do not do the compensation so then there is this kind of issue and this is what even this is the problem with the kind of sometimes the economic calculation 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 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 we will look at the utility so we would like to compare the society with a welfare function welfare function means there are any individuals each individual has its own utility u1, u2 to un when we compare 2 different sets of preferences where we look at 2 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 or equal to the is greater than the utility for B then A is socially preferred to B where W is called Bergson-Samuelson social welfare function there are different ways of creating this social welfare function and there are many different function values if you look at the metamite social welfare function this is just a weighted average so we basically say un we call this as theta1, u1 plus theta2, u2 plus and so on thetaN, un where thetaI 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 and egalitarian function function could be where we have equal weights 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 John Rawls who is a philosopher and a thinker said that the utility function should be where we are maximizing the minimum utility so the poorest individuals utility should be first maximized so with this we have let us just take stock of what we have done we have looked at this choices between environment and development we have looked at the philosophical basis and the perspectives we looked at a few problems a few problem context and then we talked about pareto preferen they pareto 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 Kaldor compensation principle so these are three methods of choices pareto preferen pareto compensation and then the Hicks Kaldor 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 environment 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 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