Topic 3 - efficiency

Public Economics 2013-‐2014 Topic 3: Efficiency Manon Cuylits

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Part II: Efficiency and market failures

Topic 3 – Efficiency “All in all, climate change must be regarded as market failure on the greatest scale the world has seen” N. Stern (2006) The market efficiency can face 4 types of issues:

1. No perfect competition: when we have monopolies, oligopolies, etc. there’s no efficient outcome possible

2. Asymmetries of information1 3. Public goods and externalities

1. Introduction

v Market and the role of governments v Main issue: do markets perform well? v Goal: have a general framework to organise thoughs about the desirability of

various governmental actions v Welfare economics framework: branch of economic theory concerned with the

social desirability of alternative economic states

2. The concept of efficiency Rappel:

les courbes d’indifférence:

NB : On parle de courbes d’indifférence et de boite d’Edgeworth dans l’hypothèse d’une économie sans production, une économie d’échange.

1 On parle d’asymétrie de l’information en économie quand lors d’un échange, certains participants ont des informations pertinentes dont les autres ne disposent pas.

Ici, on a les 3 courbes d’indifférences d’Alice. Où que l’on se trouve sur la courbe d’indifférence, on tirera la même satisfaction, qu’on ait plus 10 de food et 5 de drink ou 5 de food et 10 de drink par exemple. Ici, on voit qu’il y a plusieurs courbes d’indifférence. L’humain préfèrera toujours avoir +, donc plus la courbe de satisfaction sur laquelle on se trouve est élevée, plus la satisfaction de l’humain (Alice ici) sera élevée.


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La boite d’Edgeworth

Robinson et Vendredi vont donc échanger jusqu’à ce qu’il n’y ait plus d’échanges mutuels avantageux possibles. Une fois arrivés à ces points, on atteint des « optimum de Pareto », ils se situent au croisement des courbes d’indifférence des deux individus.

Concept of efficiency

Pareto Improvement = Reallocation of resources that makes at least one person better off without making anyone else worse off.

Ici on a les courbes d’indifférence de Robinson, et celles de Vendredi représentées dans l’autre sens. Les deux vont vouloir maximiser leur satisfaction et donc se retrouver sur la courbe d’indifférence la plus élevée possible. Plus on va vers le coin en haut à droite, plus la satisfaction de Robinson augmente, et plus on va vers le coin en bas à droite, plus la satisfaction de Vendredi augmente

Making Bob better off while not making Alice worse off

Making Alice better off while not making Bob worse off


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Pareto efficient allocation = allocation such that no person can be made better off without making another person worse off. In case of efficient allocations, there are no wasted resources. (See appendix for more information)

As we can see it above, the condition for Pareto efficiency is to have indifference curves that are tangent. Thus MRSAD,F = MRSBD,F è(MRSAliceDrink,Food = MRSBobDrink,Food) è Intuition (example): when MRS differ across individuals, there’s an incentive to trade. Marginal Rate of Substitution (MRS) = the rate at which the individual is willing to trade one good for an additional amount of another. è Le taux marginal de substitution c’est le nombre de biens « food » qu’un individu est prêt à céder en échange d’une unité supplémentaire de biens « drink » (ou l’inverse), cela peut aussi être la quantité minimale de bien « food » que l’individu exige pour céder un bien « drink » (ou l’inverse).

If we let the market go, we can move to another location that will improve the situation of at least one actor without deteriorating the situation of another one è this it the concept of Pareto Efficiency


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Economy with production

We have to decide how we organize the production. We can decide between producing more food and less drink, or producing more drink and less food. We have to reach efficiency in production, not only in consumption. In our economy, it’s the same: we have to decide whether we should produce more medical services and fewer cars for example. If we could do better for some people without doing worse for other people, it would mean we might organize our economy in that way and reach a situation that would be more efficient. Marginal Rate of Transformation = the rate at which the economy can transform one good into another one (slope of the production possibilities curves). Condition for efficiency within production: MRTD,F = MRSAD,F = MRSBD,F è without this equality, we don’t have efficiency. If the society is not organized in a good way, it means there’s room for changes that could make it more efficient. As a condition for efficiency, the slope between 2 goods (food and drink) should be equal to the marginal rate of substitution of the different customers. è Intuition:

Up to now, we just talked about allocations of resources. How to organise a society so as to reach a Pareto efficient allocation? And do market economies lead to Pareto efficient allocation?


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3. The first fundamental theorem of welfare economics The first fundamental theorem of welfare economics: “as long as producers and consumers act as perfect competitors, that is, take prices as given, then under certain conditions (see later) a Pareto efficient allocation of resources emerges” Key role of prices: Actor Consumers 𝑀𝑅𝑆!,! =

𝑃!𝑃!

• PD = Price of D • PF = Price of F

Producers 𝑀𝐶! = 𝑃! 𝑎𝑛𝑑 𝑀𝐶! = 𝑃!

𝑃!𝑃!

=𝑀𝐶!𝑀𝐶!

= 𝑀𝑅𝑇!,!

THUS 𝑀𝑅𝑆!,! = 𝑀𝑅𝑇!,! è Condition for efficiency è If you let people do what they want to do, you’ll have an enforcement of property rights, and then you let the market go. You’ll have an organization of the society that will be efficient, meaning that we won’t be able to improve the satisfaction of some users without diminishing the one of others. BUT, therefore, we need some conditions to be fulfilled: we need perfect competitions + other conditions (see later). Those conditions are not actually met. This takes place through the crises of resources, of the goods we sell. The prices are giving signals and are orienting the economy: supply/demand law. è If the supply is lower and the demand is higher, the price will rise. It means that only the people valuing the price of the good really high are going to pay for this good. This is done in order to avoid wasting resources (efficiency). In a nutshell, a competitive economy (decentralisation, Adam Smith ‘invisible hand’) leads to efficiency, and that’s really powerful. There’s a key role of prices. There’s a role for a government: even under perfect competition and when there are “certain conditions” that are met, there’s a role for a government:

• Protect property rights so that markets can work (ex: justice), that the minimal role of a government

• Deal with fairness/equity

4. The role of fairness/equity Among Pareto efficient (PE) allocations, which one? (see Edgeworth box) Observation: a non-‐Pareto Efficient allocation (ex: y that’s not on the contract curve) might be preferred to a Pareto Efficient allocation (ex: x or z that are on the contract curve) from the society’s point of view.


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Tools: Utility possibilities curves (UPC) and social indifference curves (social welfare functions).

Social indifference curves (SIC) and social welfare functions (SWF):

𝑊 = 𝑓 𝑈!"#$% ,𝑈!"#

𝑤𝑖𝑡ℎ 𝑈!"#$% 𝐹,𝐷 𝑎𝑛𝑑 𝑈!"#(𝐹,𝐷)

Social welfare framework = social welfare functions: you have to decide for everyone. If you look at people in terms of their utilities, you have to take some decisions to allocate the resources, then you have to aggregate so you have the utilities of everyone. Satisfaction can come from the fact you’re wearing nice clothes, driving a nice car etc. but it could also come from the fact you look at nice landscapes, etc.

Here, we might think an allocation such as y is not efficient, because it’s not on the contract curve, but actually, it is efficient (same for x and z that are on the contract curve). The contract curve = the maximum utility we can give to Alice or Bob

Here we see the utility possibilities curves: • The utility is maximal for

Alice if you give everything to Alice

• The utility is maximal for Bob if you give Bob everything

How do you compare the utilities of different persons? It’s a tricky question. We’ll look at the social indifference curves (SIC). If we have the utility of A and B, we have the same satisfaction, so the same W. Each curve is a social difference curve and The map = the social indifference curves


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Here, you look at the utility of everyone (the utility of Bob and the utility of Alice) and then you try to find one number: W. This number will depend on what you put in the utilities of Bob and Alice (cars, etc.). Then you can decide to do something else: You could decide you’d like people to be more taking care of older people, etc. è you search for the greatest/highest W.

More on social welfare functions: two extreme cases

♥ Utilitarianism: W = U1 + U2 + … + UN

♥ Maximin criterion: W = min (U1 + U2 + … + UN)

Le maximin = maximiser le sort de la catégorie la plus défavorisée, le sort de ceux qui ont le moins.

Half-‐half

B has some utility and A has none: A is starving

Level of utility: Here we could decide to give all the utility to A or all the utility to B, or to be just in the middle: half-‐half

Here we take the minimum within all the utilities of all the people (John Rawls): We look at the poorest person. If we want to raise the social welfare, we have to raise the satisfaction of the poorest person, so we have to allocate more resources to the poor people.


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Choice of the fair (and efficient) allocation:

5. The second fundamental theorem of welfare economics The second fundamental theorem of welfare economics: “Any Pareto efficient allocation can be attained by making a suitable assignment of initial endowments2 and letting people trade with each other”. Hence, interventions on market themselves is not necessary, redistributing income is enough.

Initial endowment: If we start from such an allocation and let the market work, Alice will give some of her drinks to Bob, in exchange with Bob’s food, so Alice will have fewer drinks and more food, and Bob will have more drinks and less food than at the beginning. Here we let the market work, we just have to redistribute endowments. The government redistributes income mainly through thanks to taxes: they redistribute through the tax system.

2 Dotation initiale

If I’m a social planner, I will look at all these curves and chose the level at which the utility is the highest. Here we have: ♥ The utility possibilities curve ♥ The indifference curves The point where curves meet is more efficient that the rest of the utilities curves. This is the point where this is the best at the society point of view.


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GDP = Gross Domestic Product = what is produced in a year. Half of the GDP is subject to taxes. The government has the power to take half of the GDP and to redistribute it through various allocations (example: the fact that education is free until 18 years old, etc.). We really benefit from the money redistribution. The public intervention is really significant and powerful è the government taxes income, with higher taxes for people with higher revenues. The taxes are not proportional taxes but progressive taxes: if we have an income of 10, we will pay 1 of taxes, but if we have an income of 100, we will pay more than 10 of taxes.

Equity-‐Efficiency trade-‐off Problem: government needs some way to reallocate resources and those mechanisms usually induce inefficiencies (e.g. income tax) Thus, in practice, there is to some extent a trade-‐off between efficiency and equity. The 3 main ways to collect money =

♥ VAT ♥ Tax income ♥ …

When we use tax income to collect money, people that are working know they will have much less than what they have truly earned while working. It does not encourage them to work much. It’s the same for VAT, if someone likes something, the fact he has to pay VAT when he buys it is a disincentive event. The government has to find a way to deal with that problem of disincentive events.

Redistribution of initial endowments

è When we have a tax system, we need to create efficiency because the tax system creates a disincentive. If we want to move from an allocation we think is not fair because Alice has everything and Bob has nothing, if we do not move ON the curve, we lose some efficiency.


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Excess burden of taxation: the window tax example 1696-‐1851: “when the window tax was introduced, it consisted of 2 parts:

• A flat-‐rate house tax of 2 shillings per house and • A variable tax for the number of windows above ten windows.

Properties with between ten and twenty windows paid a total of four shillings, and those above twenty windows paid eight shillings”. è Depending on the number of windows we had on our house, we had to pay more or less taxes. This could create a disincentive to having windows. This was not the purpose of having such a taxation system.

6. Conditions under which markets do not lead to efficiency Back to the first fundamental theorem of welfare economics: possible market failures.

• Imperfect competition: Imperfect competition arises when agents have the ability to influence the price of a commodity (monopoly, oligopoly, product differentiation, etc.) It leads to prices above marginal costs or above marginal productivity. Conditions for efficiency are violated. For example, in the case of monopolies, prices are above the marginal cost: it means companies are capturing rents, they could produce more, so it’s not efficient. Ex: the electricity market: there are some measures taken on the concentration of producers, it has an impact on the price.

• Asymmetric information: Asymmetric information is present when a party engaged in an economic transaction has better information about the good and service traded than the other party. Ex: insurance against the possibility of becoming poor. Everyone doesn’t know the same things. Ex: social security -‐ example of a public intervention: there’s asymmetric intervention. In Europe, we have a social security system very well developed compared to other countries. Many people will have the possibility to be insured (private insurance); however, many people don’t have the possibility to be insured because they are too poor and, moreover, it’s not efficient, it is not covering all the sorts of disease. There’s asymmetric information between the doctor and the patient for example.

• Public Good: A public good is a good that is non-‐rival and non-‐excludable in consumption, for example the roads. è Un bien public est un bien que chacun peut consommer en même temps, en même quantité et dans sa totalité. On ne peut pas exclure quelqu’un de l’accès à ce bien (non-‐excludable), si quelqu’un utilise ce bien, cela n’empêche personne de l’utiliser aussi (non-‐rival), et au niveau de la production, le cout marginal = 0, cela veut dire que pour une personne supplémentaire utilisant ce bien, le cout est nul, cela ne change rien qu’une personne en plus utilise la route par exemple.

• Externalities: An externality is an activity of one entity that affects the welfare of another entity in a way that is outside the market. Ex: airplane noise pollution.


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On parle d’externalités dans une situation économique ou l’acte d’un agent influe positivement (externalités positives) ou négativement (externalités négatives) sur la situation d’un autre agent non-‐impliqué dans l’action, sans que ce dernier ne soit totalement compensé ou n’ait à payer pour les dommages et bénéfices engendrés. Exemple d’externalités négatives : la pollution Public goods and externalities are dealing with the existence of public goods and the fact that we have externalities. When there are public goods, the market will never be efficient. NB: in asymmetric information, public good and externalities, markets are missing.

7. Conclusion Two criteria to evaluate the state of an economy (an allocation of resources):

• Efficiency (Pareto efficiency): no waste • Equity/fairness: social welfare function approach

“Role” of markets: Competitive markets lead to efficiency when there is a market for each and every commodity (i.e. no imperfect competition, no public goods, no externalities). Role of a government:

• Enhance efficiency: deal with market failures (imperfect competition and missing markets) and minimal role of property right protection

• Enhance equity: deal with distributional issues Possible trade-‐off between efficiency and equity.

Appendix 1: a note on social choice How do we, as society, choose a (desired) point along the UPF3? We need a “social choice function (SCF)”, an ordinal ranking of the alternatives.

• What criteria should such a function have? • How do we choose which function is the right one?

A social planner is a kind of cop. How do we decide what to do? We do vote/elect politicians. They have programs regarding intervention on the market. They are writing laws intervening on the economy: the allocation of resources includes fiscal instruments è they do define a program with more taxes on companies, more redistributions, etc. for example. è The way those things (programs) take place in reality = through democracy, etc.

3 Utility Possibility Frontier


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Arrow’s impossibility theorem (no question at the exam)

• Pareto principle: “If at least one individual prefers option x to option y and no one strictly prefers y to x then society prefers x to y”

• Universal domain: The SCF should work for any set of individual preferences (no matter how weird).

• Non-‐Dictatorship: The SCF should not depend solely on the rankings of one individual

• Independence of irrelevant alternatives: The ranking of x and y should only depend on individual rankings of x and y and not on the preferences of individuals over x and z (nor y and z).

Arrow: Any SCF should be complete and transitive and satisfy these four criteria. However, no SCF can satisfy these four criteria

Condorcet’s Paradox (as an illustration of Arrow’s impossibility theorem) Rankings of alternatives, example

• Liberals: Green Park > Public housing > Private housing • Labour: Public housing > Private Housing > Green Park • Conservatives: Private Housing > Green Park > Public housing

Consider majority rule as a “social choice function”: When considering two policies, select the one that more people prefer. This will satistfy PUDI. But in the case above, the choice will depend on the way these are paired (as in Rocks-‐ Paper-‐Scissors). “Society prefers” Green Park to Public housing, Private housing to a Green park, and Public housing to Private housing. è Social preferences are not transitive.

Appendix 2: Pure exchange economy

• 2 goods: Food and Drink • 2 people: Alice and Bob

Note: results hold for many people and commodities è The Edgeworth box:


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Alice

Bob

Together A possible initial location

Each point is a basket of goods (food and drinks). è Same level of satisfaction for any basket on a given indifference curve.

Topic 3 - efficiency

Economy & Finance

Transcript of Topic 3 - efficiency