 been looking at the issues related to utility, comparing utility and preferences across individuals and in general the idea of going from utility for individuals to group choices or social choices and we looked at different possibilities of having social welfare functions and we carry on with this to try and look at the question that starting with the knowledge of individual preferences over a whole set of different outcomes, is there a general way of aggregating this into a social preference or an ideal way in which we can get a social preferences that is reasonable and this is the problem that has exercised several economists and thinkers and one of the persons who did some pioneering work in this was Professor Kenneth Arrow and Professor Kenneth Arrow got the Nobel Prize in Economics in 1972 and the Nobel citation basically says for his pioneering contribution to general economic equilibrium theory and welfare theory and the paper, one of the papers that enabled him to get this prize was the paper that he had written in 1950 called A Difficulty in the Concept of Social Welfare and so the theorem that he proposed is called Arrow's impossibility theorem and it is a very powerful result that he showed and basically what he started off is he started off with a set of axioms if you want to make a choice and if you want to look at individuals, their choices and can these be used to have a way in which we can have an ideal social choice and the interesting thing that he showed and he proved was that it is impossible to have a social choice which meets all the requirements of an ideal choice mechanism unless you want to individually compare utilities, utilities between different individuals if they are to be compared and quantified. If you just want to do it in terms of ordering then it is not possible to have a social choice mechanism which is ideal and this is extremely powerful result and for those who are interested you can go into the original paper and read it, we will just talk about a few points which come from it. So, his conclusion was that interpersonal comparison of utilities has no meaning and that there is no meaning relevant to welfare comparisons in the measurability of individual utility. So, basically he said that if you have a social choice mechanism that mechanism and ideal social choice mechanism should have the following characteristics and the six characteristics completeness, unanimity, non-dictatorship, transitivity, independence of irrelevant alternatives and universality and so if you look at what these mean in the case of completeness it means that all social alternatives can be compared and that essentially means that all the alternatives when we are looking at all possibilities can be compared, so all the entire set of choices is possible and unanimity means that if everyone prefers a particular option if all the individuals prefer a to b, society will prefer a to b and this is sort of an obvious statement. Non-dictatorship means that it should not happen that one individual controls all social decisions, so that means no one should always get their way and transitivity we talked about this when we talked of preference, if a is preferred to b and b is preferred to c implies that a would be preferred to c. The fourth option that is there, fourth axiom is that the there should be independence of irrelevant alternatives that means society's choice between a and b does not depend on the introduction of a third option and so it does not depend on other alternatives. Now we can see very clearly that this need not always be true, you see this in the form of elections, if there is an election between two candidates and a third candidate comes in then there is choice between those two candidates often gets spoiled and it affects it, so in reality this does not happen, to give you another example of this let us say that three professionals early working professionals they are sharing an accommodation, so if you have this you had Inder, Ram and Ashish all three of them say in a flat and it is being decided that we want to paint the flat. So we have these preferences, Inder has a preference where prefers painting black to white and yellow, these are the three choices we are looking at, black, white, yellow in the case of Ram, white is preferred to black, preferred to yellow, Ashish prefers black to white to yellow. So in this particular case if you see it will be appropriate to paint both two of them have black as the best preference and Ram has preference of black over yellow, so from all these points it would be appropriate to paint the room black. Now suppose we have a different choice where Ram's choice is now replaced and Ram's choice now is white, preferred to yellow, preferred to black, now if you look at it what happens is two I have a preference now there are two blacks and there are you know there are there is there are two whites, two blacks the decision gets modified, changed but it could be we can look at black or white but if here now you have the option you have a statement which says that Ram essentially hates black. So there is an intensity of a preference where Ram does not want it to be black in which case the choice which we get is we will go for white but the fact that Ram has such an intensity of dislike for black is affecting the decision between black and white for all of black, white and yellow for the choice. So this is often what happens is that you would have these kind of issues which are there in reality and universality means that any possible individual ranking of alternatives is possible that means that whatever choice mechanism you should have is suppose we have an N set of people each one can have a whole set of different preferences and so Arrows Impossibility Theorem states that there is no rule satisfying the six axioms for converting individual preferences into a social preference ordering and this has been shown with some examples and proof by Arrow in his pioneering work. So this implies that there is no need theory of social decision making and this has of course very severe implications in terms of that means that there will always be trade offs there will be winners and losers and it is not possible to have in general it has been shown that it is not possible to have a social choice mechanism where individuals have different preferences and it comes out into a need preference where everyone gets an improvement and this has been in future work this has been relaxed with the idea that if you can measure and compare utilities and then quantify under certain conditions you can show that you can have this kind of a social decision making but the implication of this is that in general whenever we talk about society making decisions there would be winners and losers and there would be trade offs involved. And so we would now move forward with this and try to see when we talk about the Pareto optimality and we look at the markets how do we try and get the optimal kinds of solutions. So in general when we talk about we this is from Colster if you had two different goods we could have we had talked about this earlier where we have a we can see that you have these indifference curves which represents constant utility function and this is increasing and then depending on the budget constraint between the two goods we have the marginal rate of substitution between these two goods. This is for a particular individual similarly for other individuals there would be marginal rates of substitution. So there is this theory and in this course we will not go into this theory but you can go into this if you are interested you can look at the whole concept of the Edgeworth box and the idea is that if you look at two individuals who have a different utility functions and based on the utility functions they will have different marginal rates of substitution between the two goods. We could then the two individuals with the utility functions we can see if individual A will exchange with individual B so that overall the utilities get improved and this is where we can remove the inefficiencies in exchange and with the result that we can then go to something which is called between A and B we can get a set of preferred options and in a based on the kind of resources which are there this is the preference region. This curve represents the limit in terms of these are all Pareto dominant points. Any of these points is Pareto preferred over any other point which is on the interior and movement between these points would the utilities would get modified but basically we cannot have any improvement if you are on any of these points it is not possible to have any Pareto preferred move where the utility of A or B one of the utilities gets reduced so it is not possible to have any Pareto improvement when you are on this curve and this is these are all Pareto dominant this frontier is called the Pareto frontier and the Pareto frontier is defined as all allocations for which there are no allocations that are Pareto preferred and so an allocation is supposed to be efficient if it lies on the Pareto frontier and so that is the definition of efficiency that means that no movement is possible with any Pareto preference and which means that either we showed this for two individuals but this can be generally extended for any individuals and with this result that we can look at these are the two sources of economic inefficiency in exchange and inefficiency in production. We can analyze it using the Pareto frontier example we can look at creating the Pareto frontier and looking at the fact that the marginal rates of substitution would be equal and would be equal to the prices. So if there are two individuals the marginal utility the marginal rate of substitution of A with respect to marginal rate of substitution of B this would be equal if there is efficiency in trade so that there is no incentive for trade and this would also be equal to the ratio of the prices. So this is in terms of efficiency of trade in a similar fashion we can look at the efficiency in production if there are different sources of production for instance if we look at the production of garbage disposal and wine if you look at this and you have different kinds of production possibilities we can find the marginal rate of transformation in terms of machinery or equipment so that you reduce you have more garbage disposal or you have manufacture more wine and you can see that these marginal rates of substitution would be equal so that you can reduce the efficiency you can inefficiency in production can be minimized and so that the marginal rate of transformation between in this case a bad and a good or you can talk about garbage disposal which becomes a good and so on. So in general what we are looking at is we are looking at a marginal rate of transformation between pollution and the good should be the same for all producers if this is not true then we can actually get an improvement by producing more of good A as compared to good B. So similarly in the case of pollution where we are looking at pollution as a bad or pollution control as a good marginal rate of pollution control should be the same for all firms that means the per unit cost of pollution control would be equalized across different firms there are different ways in which we can represent goods and bads and for instance if you talk about garbage garbage is created in the household level garbage is created in the in terms of pollutants at the industry level at the commercial level and that is something that has no value for us it is a bad garbage on the other hand can be shown as a so you can look at a bad and a good and we can represent it in terms of supply and demand or we can convert the bad into a good by talking about the removal of pollution so pollution control or garbage disposal. So there are two ways in which we can draw supply demand curves and this is shown in Colstad you can see quantity of garbage consumed and the price of garbage if you look at the price would be negative because this is the negative price of garbage consumed but if you convert this so in terms of in a normal way in which we analyze supply and demand for a good we would like to have a positive price then we can talk about garbage disposal and this will be having the same kind of mechanism that we talk of in terms of demand and supply and so this is another way of representing so we can either represent it as a bad or we can represent it as a good by converting it into garbage disposal pollution control and depending on your on the way in which you find it convenient you can do either of these two representations the sign of the price will change but in all other aspects the analysis will remain the same. So now let us look at when we talk about the market and market trying to get the reduce the efficient the inefficiency minimize and not have any inefficiency in trade or inefficiency in production we can look at the market and the equilibrium that is formed from a market. So there are certain assumptions that we have when we talk in terms of a market the first assumption is that you have complete property rights what do we mean by complete property rights if we are looking at we want to look at a pen if this is my pen I have purchased it and I own this pen and then I can which means that I have a property right over the pen similarly when we are looking at let us say a house or something a product or you are buying something to eat you have you have complete property rights over that and when we look at something like a negative thing like garbage if there are rules that prevent the you are if we are responsible for the garbage that we create and we cannot just litter it and dispose it anywhere if there are proper laws then there are complete property rights and that complete property rights is essential implementation of that complete property rights is essential for us to have the ability to buy and sell the goods and to have the ability to try and find out what will be the demand under different kinds of conditions. So that is the first kind of assumption and that assumption is valid for most of the goods and services that we are considering the second assumption is atomistic participants atomistic participants means that there are a large number of small participants so there are many different suppliers there are many different consumers why is this required this is required so that no one individual has that much demand that he or she can affect the overall dynamics and the setting of the price and with the result that this is the this can someone's utility does not predominate and this is one of the assumptions which is there similarly there should be there cannot be multiple there should be many suppliers one supplier cannot have a monopoly and then you and affect the whole thing and this is one of the things which is an approximation in many cases this is violated and that is why then there are problems with the market and then you need to have regulation complete information now complete information means that every producer has information about the different kinds of conditions about the conditions of the market about the conditions of the demand similarly every consumer knows what is the prices which are available in different markets and this is often not there there is asymmetry in information so that often the end user and then there is this leads to middleman people who get a benefit because they use this asymmetry in information to be able to get some kind of a leverage and get some revenue and profit and the fourth thing is that we presume that there is no transaction cost there are no cost for entry or exit you want to start manufacturing something you can just go ahead you can if you want to make something and transfer it to the consumer again there are no transaction costs in reality of course there are transaction costs and this of course creates make some modification in this so there are these two theorems of welfare economics and I will just state them we are not going to look at it in too much detail but basically we are looking at in a competitive economy we are talking of a market equilibrium and the market equilibrium results in a Pareto optimal solution there are no it is on the Pareto frontier there is no inefficiency in the trade or no inefficiency in production and so we get a Pareto optimal solution no further improvement is possible of course this is the ideal case of market equilibrium when all these conditions are established in terms of the requirements for transparency in terms of complete information for non-atomistic participants it is also the second theorem of welfare economics says in a competitive economy any Pareto optimum can be achieved by market forces provided the resources of the economy are appropriately distributed before the market is up allowed to operate so the market does not have anything to talk about the distribution and in case the distribution is unequal then the solution which is there will result in being unjust and unfair however these that solution may not result in any it may be a Pareto optimal solution and it may be something which is from a market point of view it is efficient and so the economics when you talk about efficiency is only looking at overall whether any improvements are possible through efficiency in trade or efficiency in the production transformations and it depends on the pre-existing distribution so the market often will tend to perpetuate and accentuate the status quo and just to give you an example of this is an extreme example there is an there is a memo which was written by one of the economists in the World Bank way back in the 1990s it is a very controversial memo it was a memo written by Lawrence Summers and Lawrence Summers wrote and he was the chief economist of the World Bank when he wrote this memo subsequently Lawrence Summers also served with the US government and was also the president of the Harvard University but just look at the memo and what it says and then we will come up with this is just to illustrate to you the fact that a market economy need not necessarily result in something that is ethical or that is correct or fair so this is a memo which was written in December of 1991 it is there on different websites and I am just going to read this out to you talks about dirty industries and of course when there was a big controversy about the memo Lawrence Summers said that he was just he mentioned he did not mention it very seriously it was just to illustrate some of the facts which are there in the economic calculations he sort of backtracked but the fact is this was a memo which he sent to others in the World Bank so the memo says dirty industries just between you and me should not the World Bank be encouraging more migration of the dirty industries to the less developed countries so the idea is that instead of having the industries polluting the developed countries they should actually be polluting the developing countries and then he goes ahead to talk about three reasons the first reason is the measurements of the costs of health impairing pollution depends on so if you look at health impairing pollution we are saying how many days of labour loss what are the kind of increase because of loss of work increasing morbidity or loss of life increasing mortality so it depends on the foregone earnings from increased morbidity and mortality from this point of view a given amount of health impairing pollution should be done in the country with the lowest cost which will be the country with the lowest wages since it has lowest cost and lowest wages that would mean that the impact would in money terms would be much much lower than it would be in a developed countries and I think the economic logic behind dumping a load of toxic waste in the lowest wage country is impeccable and we should face up to that so you can it is a shocking argument but it is an argument which is being made based on an economic terms so this is point one the second point that he made is costs of pollution are likely to be non-linear so that means in a country or a region which has very low pollution the initial cost of abatement or the initial cost of that pollution is likely to be very low so the non-linear initial increments of pollution probably have very low cost and then he goes on to say I have always thought that under populated countries in Africa are vastly under populated their air quality is probably vastly inefficiently low compared to Los Angeles or Mexico City so the idea is that those who have less pollution are from an economic point of view under polluted so you can just see what is the kind of argument which is being made only the lamentable fact so much pollution is generated by non-tradable industry so what he is saying is that it is unfortunate that when you talk about industry we cannot transport the pollution and so we look at transport electrical generation it is happening locally and the unit transport costs of solid waste are so high prevent world welfare enhancing trade in air pollution and waste so the what is being proposed from an economic view point is that it would be it is been proposed that we should trade and move the pollution from the urban from the cities which are highly polluted and which have high wages and take them to regions where the there are where the cost of the damage is relatively low and you can see that very clearly from an ethical point of view from a fairness point of view all these arguments are completely wrong but from an economic point of view this is and this is one of the biggest problems with economics and it continues to be that several people do realize this but you can actually see that someone actually makes arguments like this in an official document and a memo. The third point that he makes is the demand for a clean environment for aesthetic and health reasons likely to have very high income elasticity concern over an agent for instance that causes one in a million change in odds of prostate cancer obviously going to be much higher in a country where people survive to get prostate cancer then in a country where the under 5 mortality is very high much of the concern over so essentially what he says is if in regions where there is higher income higher quality of life and higher people survive for longer they their demand for clean environment would be much higher and they would be willing to pay much more so then they are basically say he is again arguing for trade in goods that will be the pollution will increase in developing countries but it will increase their welfare so the production is mobile consumption of the good quality air is non-tradable and so he anticipated that this would create a controversy and people would oppose it and so he is the last sentence that he says say that the problem with arguments against all of these proposals for more pollution in LDCs intrinsic rights to certain goods moral reasons social concerns lack of adequate markets could be turned around and use more or less effectively against every bank proposal for liberalization and this is one of the problems which has been there with many of the multilateral agencies and their proponents often the economics which when we talk in terms of equilibrium and market equilibrium does not consider anything in terms of what is fair or what is moral and it just looks at the efficiency from a Pareto frontier perspective please keep in mind this is not the final perspective the perspective has to have an issue of values and ethics and morality and so this is just to word of caution to say that whenever we do all of this calculations we can calculate the cost and the economics but then we should have to see overall what is fair and what is just and what is the right thing to do.