Welfare and state intervention, taxation Inequality Pareto efficiency The theorems of welfare

Welfare and state intervention, taxation Welfare theory is a particular aspect of economics, which attempts to measure and influence welfare at the level of the economy, and not the individual What makes it particular is that it typically contains normative aspects (value judgments) Ex: How can you determine a “fair” allocation ? But it is an important part of economic theory And an important part of an economist’s job!

Welfare and state intervention, taxation Measuring inequality Pareto efficiency The theorems of welfare The effects of taxation

Measuring inequality Why is inequality an important issue? Why is it important to be able to measure it? Inequality is often important from a public perception point of view Therefore it is important as a policy issue, so it needs to be measured properly From the point of view of positive theory, inequality is not really the issue, efficiency is remember the “cool head & warm heart” idea of Samuelson

Measuring inequality First, there are different types of inequalities Income : minimum wage in France € annually vs. 6.57million € for the CEO of l’Oreal in 2004 (he’s worth it…) Wealth : Bill Gates’ 59 Billion $ vs. an unskilled labourer (his only asset is the value of his time) Ability : Zidane, Federer, Eminem vs. adults with untreated learning disabilities Not all can be easily measured or modified by public intervention The typical focus is on income/wealth inequality

Measuring inequality The following data gives the distribution of income over the US population  Source: US Census Bureau Share of income by quintiles YearLowestSecondMiddleFourthHighest ,691523,249, ,89,61624,346, ,310,316,924,843, ,211,117,524,442,8

Measuring inequality Let’s see what this table says in terms of the evolution of inequality : Income inequality has increased over the period Share of income by quintiles YearLowestSecondMiddleFourthHighest ,691523,249, ,89,61624,346, ,310,316,924,843, ,211,117,524,442,8

Measuring inequality There is a much easier way of visualising this data: The Lorenz curve Definition The Lorenz curve is the plot of the cumulative share of income This variable is not really intuitive in a table, but very useful in a graph  You can find the share of income of any given percentage of the population

Measuring inequality Let’s calculate the cumulative shares for 1998: Share of income by quintiles YearLowestSecondMiddleFourthHighest ,691523,249,2 Cumulative share ,612,627,650,8100

Measuring inequality Plot of the curve : The green line is the even distribution The red is the Lorenz curve It gives the share of income of any given % of the population

Measuring inequality Let’s add the curve for 1968 as a comparison

Measuring inequality Let’s add the curve for 1968 as a comparison There is less of a “bulge” in the Lorenz curve Income was more equally distributed in 1968

Measuring inequality Lorenz curve provides an easy, visual way of identifying changes in the distribution of income It also provides a numerical measure of inequality The Gini coefficient (or Gini Index) This coefficient allows us to rank any set of distributions from the most unequal to the most equal

Measuring inequality The Gini coefficient is calculated as follows: It tells us what percentage of the distribution space is occupied by the “bulge” of the Lorenz curve The higher the percentage, the more unequal the distribution A B

Measuring inequality Extreme case N°1: The distribution of income is perfectly even A=0 The Gini coefficient is 0 if there is no inequality B

Measuring inequality Extreme case N°2: The distribution of income is perfectly uneven B=0 The Gini coefficient is 1 if there is perfect inequality A

Measuring inequality Evolution of the Gini coefficient of income Source: World Bank, K.W. Deininger BrazilCanadaCosta Rica FinlandJapanNether -lands ,60*0,320,50,30,340, ,550,320,480,320,340, ,57**0,330,47*0,310,36*0,28* ,590,280,460,26*0,380,3 Notes * 1976 ** 1983 *1983*1991*1985*1983

Welfare and state intervention, taxation Measuring inequality Pareto efficiency The theorems of welfare The effects of taxation

Pareto efficiency Definition of Pareto efficiency (Vilfredo Pareto) : An allocation is Pareto-efficient if it is not possible to make an agent better off without making an other agent worse off A Pareto-improvement: Makes at least one agent better off, all other agents begin equally well-off as before. A Pareto efficient allocation is one where there are no possible Pareto-improvements

Pareto efficiency This can be analysed more intuitively using an “Edgeworth box” This is a theoretical tool used to examine the trading decisions of: Two agents: 1 and 2 Trading two goods A and B Main advantage: it is based on consumer choice theory

Pareto efficiency Good A Building an Edgeworth box Agent 1Agent 2 Good B A max B max A max B max

Pareto efficiency Good A Building an Edgeworth box Agent 1Agent 2 Good B A max B max A max B max

Pareto efficiency Good A Building an Edgeworth box Agent 1 Agent 2 Good B A max B max A max B max

Pareto efficiency Agent 1 Agent 2 A max B max A max B max Any point within the box is a possible allocation It divides the total amount of goods A and B available between agents 1 and 2 But how do we determine which ones are Pareto efficient, and which ones are not ?

Pareto efficiency Agent 1 Agent 2 A max B max A max B max Let’s re-introduce some indifference curves and an allocation (X) Is X Pareto efficient ? No, because by trading goods, both agents can move to a higher indifference curve ! X → Y is a Pareto- improvement Y, however, is Pareto efficient. Y X

Pareto efficiency Agent 1 Agent 2 A max B max A max B max So all the points where the indifference curves are tangent are Pareto- efficient. Joining them up gives the set of all the possible Pareto-efficient allocations. This is know as the “Contract Curve” Y X

Welfare and state intervention, taxation Measuring inequality Pareto efficiency The theorems of welfare The effects of taxation

The theorems of welfare There are 2 “fundamental theorems of Welfare” They are also due to Pareto They can be analysed using the Edgeworth box Although they might seem a little “dry” in their definitions, they are crucial to understanding : Why economists see free markets as a social optimum, Why there can nevertheless be a role for public intervention.

The theorems of welfare The 1 st fundamental theorem of welfare All competitive market equilibria are Pareto- efficient. In other words, a competitive market will exhaust all the possible gains from trade This is illustrated by the example we saw in the Edgeworth box: people are willing to trade until their indifference curves are tangent and there are no further gains to trading.

The theorems of welfare The 1 st fundamental theorem of welfare However, as we saw previously with the contract curve, this does not tell us anything about the other desirable properties of the equilibrium The Pareto-efficient allocation might not be “fair” Remember, if Agent 1 owns everything and Agent 2 owns nothing, this is an efficient allocation, but maybe not a socially desirable one!

The theorems of welfare The 2 nd fundamental theorem of welfare If preferences are convex, there is always a set of prices such that each Pareto-efficient equilibrium is a market equilibrium for appropriate initial endowments With convex preferences, the Pareto-efficient allocation is determined by the tangency of 2 indifference curves Remember basic consumer choice: this slope will also give the relative prices!!

The theorems of welfare The 2 nd fundamental theorem of welfare Agent 1 Agent 2 A max B max A max B max ∙Imagine we are at X, But we’d rather be at Z, in terms of fairness. ∙The theorem tells us that because preferences are convex, there exists a set of relative prices (the dotted line) which supports this equilibrium ∙Z can be achieved simply by redistributing the initial endowment to Y Y X Z

The theorems of welfare Implications of the 2 theorems 1 st : Under the assumption of competitive behaviour, markets with selfish agents can achieve the highest possible efficiency 2 nd : Under the assumption of “well behaved” preferences, the allocative role of prices (scarcity) is separate from the distributive role (the constraint on your level of consumption) The 2 can be separated: The state can redistribute the initial endowments, and leave the market to allocate efficiently

Welfare and state intervention, taxation Measuring inequality Pareto efficiency The theorems of welfare The effects of taxation

The 2 nd fundamental theorem of welfare tells us that we can move to a different Pareto-efficient allocation by redistributing the initial endowment In practice, this would amount to taxing the initial endowments and redistributing as necessary But in reality, there is a problem What is an “endowment” ? How do we tax it ?

The effects of taxation For most people, the basis of their endowment is the amount of labour they could sell on the market It is not a simple bundle of goods (as in the Edgeworth box) So taxing their income, (the labour they have sold) affects the relative price of labour (the wages) This can in turn affect the decision to sell labour The tax distorts the relative prices, and there is an efficiency loss

The effects of taxation This effect is not too large, as labour supply decisions are not that sensitive (as we have seen in week 5) But this points out the difficulty of going from the theoretical results to the practical reality Another problem is when taxes / subsidies affect the price of goods directly. (ex, VAT) The distortion on prices can be very important in this case Read about the example of Iraq in Varian, p.306

The effects of taxation P Q Q1Q1 P cons. P prod. T Unit Tax Deadweight loss S D

The effects of taxation P Q Q1Q1 P cons. P prod. Unit Subsidy Deadweight loss S D