Competitive market – one where both buyers and sellers are price takers. Equilibrium price and equilibrium quantity If a competitive market is not in equilbrium, excess demand or supply will tend to move it towards equilibrium. Practise: Calculate the equilibrium price and quantity when demand and supply functions are linear. Comparative statics – what happens to equilibrium price and quantity if demand or supply curves shift?

The incidence of a tax – will the buyer or seller bear the burden? The incidence does not depend on who pays the tax, formally. The more elastic supply is, the more of the tax burden falls on the consumer. The more elastic demand is, the more of the tax burden falls on the producer. Deadweight loss – a tax does not only mean that resources are shifted from one party to another. It also affects behaviour.

tax t = Pd - Ps P* = before tax price, Pd = price paid by consumer, , Ps = price paid to producer S’ S Pd P* t Ps

A is tax paid by consumers C is tax paid by producers B is loss of consumer surplus because consumption is reduced D is loss of producer surplus because production is reduced A+C is a transfer, B+D is a social loss S’ S B A D C t

An outcome A is Pareto efficient is there is no way of making any one person better off without making at least one other person worse off. Let’s say that an outcome A is ranked higher than an outcome B if nobody prefers B to A and at least one person prefers A to B. An outcome is said to be Pareto-efficient if no other outcome is ranked higher in this sense.

LIMITATIONS OF THE PARETO CRITERION Obviously, there will be lots of outcomes that are neither ranked higher nor lower than A because some people are better off and some are worse off. The Pareto-criterion is about efficiency, given the existing distribution of resources, it has nothing to say about whether the way resources are distributed is good or bad With different endowments there would be other Pareto-efficient outcomes.

Vilfredo Pareto vs charles dickens ….to-day, for instance, Mr. M'Choakumchild [the teacher] was explaining to us about Natural Prosperity.’ [said Sissy]* … And he said, Now, this schoolroom is a Nation. And in this nation, there are fifty millions of money. Isn't this a prosperous nation? Girl number twenty, isn't this a prosperous nation, and a'n't you in a thriving state?’ 'What did you say?' asked Louisa. 'Miss Louisa, I said I didn't know. I thought I couldn't know whether it was a prosperous nation or not, and whether I was in a thriving state or not, unless I knew who had got the money, and whether any of it was mine. But that had nothing to do with it. It was not in the figures at all,' said Sissy, wiping her eyes. 'That was a great mistake of yours,' observed Louisa. (From Charles Dickens ”Hard Times”, 1859) * Sissy and Louisa are students in a utilitarian school. Louisa does well in school, Sissy does not.

AND this takes us into the contents of Chapter 33: The Economics of Welfare

Chapter 33 Welfare We have looked at individual welfare represented by utility functions. What can we say about the welfare of a whole society? Assume, to start with, that we can define a Social Welfare Function (SWF) – a utility function for the whole society.

Can we see what it takes to maximise the utility of a whole society (social welfare) like we did with utility of an individual? It is a good idea to have Pareto efficiency – if one person can be made better off without hurting anybody else, fine.

Social Optima & Efficiency Upf is the set of efficient utility pairs. Higher social welfare Social indifference curves

Take a society with two individuals. To give either of them higher utility requires resources. Resources are limited. All the Pareto efficient combinations form the utility production frontier. Each point corresponds to a different distribution of resources between A and B. A negatively sloped upf means that more utility for A implies less for B. A concave (to the origin) upf implies that the more utility a distribution has already given A, the less utility A has to give up to increase B’s utility by a certain amount.

Social Optima & Efficiency Upf is the set of efficient utility pairs. Social optimum is efficient. Social indifference curves

A point which is not on the upf (not pareto-efficient) cannot be optimal. But which point on the upf is optimal depends on the SWF.

How does a society choose its SWF? Different economic states will be preferred by different individuals. How can individual preferences be “aggregated” into a social preference over all possible economic states?

Can we analyse social welfare by adding individual utilities?

First question: Can we make interpersonal comparisons of utility? The utility function is only a way of representing a preference ordering. The value taken by the utility function is arbitrary in the sense that different functions can take different values but still represent the same preferences. We can compare the choices two persons make but not directly measure their level of utility.

For example: Assume that one person had the utility-function If another person had the utility-function and a third the utility-function they would always make the same choices.

This means that the classical utilitarian welfare function (Bentham) is only one of many possible ways of aggregating preferences over individuals.

What when can we mean by ”a social welfare function” (SWF)? As a social welfare function W we can take a function of the individual utilities that is such that it is increasing in each individual’s utility. I. e. in a situation where least one individual is better off and no-one worse off, W should take a higher value.

”In a situation”?? The SWF is a function of the utilities of individuals. But the utilities of individuals is a function of the total distribution of goods in the whole society. So the SWF depends on the amount of each good that each person consumes. If there are n consumers and k goods, utilities depend on n*k variables.

A simpler special case: If the individual utilities only depend on their own consumption we have a Bergson-Samuelson SWF If we have a Bergson-Samuelson SWF and there are no consumption externalities the results from the Edgeworth box hold.: All welfare maxima are competitive equilibriums, and all competitive equilibriums are welfare maxima for some SWF In actual research and applications the Bergson-Samuelson SWF is often used; easy when it comes to calculations. But at the price of defining away that people may care about other people’s welfare.

Again, what can we mean by ”a SWF”? A SWF is a weighting formula which produces a number which is higher for preferred bundles It is a function of individual utilities Ranks different allocations that depend on individual preferences An increasing function of each individual’s utility Where the SWF hits its maximum, social welfare is maximized

Like utility functions for individuals, SWFs should rank alternatives. They are preference orderings – ordinal rather than cardinal.

Second question: Can we deduce a social preference ordering from the preferences of individuals? Different economic states will be preferred by different individuals. How can individual preferences be “aggregated” into a social preference over all possible economic states?

An idea would be to let people vote. But that is not as simple as it seems. Condorcet’s paradox. Arrows impossibility theorem. (More on voting in a later chapter.)

What should the Bergmans have for dinner? The Bergman family’s dinner preferences: More preferred Less preferred

The outcome depends on the order in which the vote is taken. In a majority vote: Chicken beats fish. (Both Mum and child prefer chicken.) Fish beats meatballs. (Both Mum and Dad prefer fish.) Meatballs beat chicken. (Both child and Dad prefer meatballs.) The outcome depends on the order in which the vote is taken.

No socially best alternative! Majority voting does not always aggregate transitive individual preferences into a transitive social preference. What if we let the Bergmans assign points (1 to the best, 2 to the second best, 3 to the third best) instead?

Result of ”Bergman food contest”? Chicken: 1+3+2 Fish: 2+3+1 Meatballs: 3+2+1 Draw!

Manipulating Preferences As well, most voting schemes are manipulable. I.e. one individual can cast an “untruthful” vote to improve the social outcome for himself. Again consider rank-order voting.

Manipulating Preferences These are truthful preferences. Child introduces a new alternative and then lies

Manipulating Preferences These are truthful preferences. child introduces a new alternative and then lies.

Manipulating Preferences Rank-order vote results. Chicken-score = 8 Fish-score = 7 Meatball-score = 6 Soup-score = 9 Meat-balls win!!

Desirable Voting Rule Properties 1. If all individuals’ preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. 3. Social preference between x and y should depend on individuals’ preferences between x and y only.

Kenneth Arrow’s Impossibility Theorem: The only voting rule with all of properties 1, 2 and 3 is dictatorial. Therefore if we want a non-dictatorial voting rule we have to skip one of them.

Same goes for the SWF – we would like it be such that: 1. If all individuals’ preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. 3. Social preference between x and y should depend on individuals’ preferences between x and y only.

Social Welfare Functions 1. If all individuals’ preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. 3. Social preference between x and y should depend on individuals’ preferences between x and y only. Give up which one of these?

The usual choice: 1. If all individuals’ preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. 3. Social preference between x and y should depend on individuals’ preferences between x and y only.

Social Welfare Functions 1. If all individuals’ preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. There is a variety of voting procedures with both properties 1 and 2.

Social Welfare Functions ui(x) is individual i’s utility from overall allocation x. Utilitarian: Weighted-sum: Minimax:

Varian: Fair Allocations Some Pareto efficient allocations are “unfair”. E.g. one consumer eats everything is efficient, but “unfair”. Can competitive markets guarantee that a “fair” allocation can be achieved?

Fair Allocations If agent A prefers agent B’s allocation to his own, then agent A envies agent B. An allocation is fair if it is Pareto efficient envy free (equitable).

Fair Allocations A B C Has Would want Equal endowments and trade does not necessarily  fair allocation Maybe the trading opportunities are not the same for all agents if there are a limited number of them. A B C Has Would want B or C can increase their utility by trading with A, but not both of them.

Fair Allocations Many agents, same endowments. Assume trade is conducted in competitive markets for all goods. The post-trade allocation will be fair.

Fair Allocations Endowment of each is Post-trade bundles are and Then and If A would envy B, A could just buy B’s bundle instead!

Rawls: The minimax choice is usually attributed to John Rawls. According to Rawls the choice of which of two social states is preferable should be made under the ”veil of ignorance”: Which society would you choose to live in if you have no idea which position you would hold in it!

According to the minimax criterion the social welfare of society is taken to be related to the income of the poorest person in the society, and maximising welfare would mean maximising the income of the poorest person without regard for the incomes of the others.

Amartya Sen: W = Income*(1-G) here G is the Gini index, a relative inequality measure, 0 ≤ G ≤ 1. (G = 0: Income is equally divided G = 1: One person gets 100% of income.)

There are many other possibilities: To maximise the sum of incomes  maximising the average. (Ignores distribution.) Another simple possibility is to maximise the median. One option would be two choose only distributions such that each individual is above some minimum. More technically complex: Forster, Dworkin etc.

The choice of SWF is a normative choice. What would you choose? Equality or inequality? Or how much equality? Or what kind of equality?

Different ideas of fairness Equality of opportunity versus equality of outcome. Equality of income, capabilities (Sen) or happiness. The choice is a matter of values – what do you prefer?

Example: Assume that there are n individuals and that total incomes are Y = y1+ y2 +…+ yn Assume that all individuals have the same utility function u(y) which are increasing in y and with decreasing marginal utilities. Assume that the SWF = u How to maximise the SWF?

Solve the Lagrange-problem Max u(yi) Subject to yi = Y L = u(yi) –λ(yi – Y) First order conditions for each i

This implies that u’(y1) = u’(y2) =… u’(yn) And this implies that y1= y2 = …= yn because u is strictly increasing (one-to-one) The conclusion is that SW is maximised when incomes are equal. Do you agree? Arguments for and against?