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Fundamental Theorem Of Welfare Economics Assumptions And Critical Thinking

There are two fundamental theorems of welfare economics.


-First fundamental theorem of welfare economics (also known as the “Invisible Hand Theorem”):

any competitive equilibrium leads to a Pareto efficient allocation of resources.

The main idea here is that markets lead to social optimum. Thus, no intervention of the government is required, and it should adopt only “laissez faire” policies. However, those who support government intervention say that the assumptions needed in order for this theorem to work, are rarely seen in real life.

It must be noted that a situation where someone holds every good and the rest of the population holds none, is a Pareto efficient distribution. However, this situation can hardly be considered as perfect under any welfare definition. The second theorem allows a more reliable definition of welfare


-Second fundamental theorem of welfare economics:

any efficient allocation can be attained by a competitive equilibrium, given the market mechanisms leading to redistribution.

This theorem is important because it allows for a separation of efficiency and distribution matters. Those supporting government intervention will ask for wealth redistribution policies.





Short History of Welfare Economics


B.Contestabileadmin@socrethics.comFirst version 2009   Last version 2018





Table of Contents




1.      Introduction

2.      Classical Economics (18th and 19th Century)

2.1 Definition

2.2 Classical Utilitarianism

2.3 Criticism of Capitalism

3.      Neoclassical Economics (since ca.1870)

3.1 Definition

3.2 Old Welfare Economics

3.3 New Welfare Economics

3.4 Social Choice Theory

3.5 Micro- and Macroeconomics

3.6 Neoclassical Synthesis

4.      Modern Development Economics (since ca.1950)

4.1 Definition

4.2 Neoclassical Theory

4.3 Capability Approach

5.      Happiness Economics (since ca.2005)

5.1 Definition

5.2 Criticism of Neoclassical Economics

5.3 Surveys

6.      On the Philosophy of Economics

6.1 Positive Economics

6.2 Normative Economics

7.      Conclusion




Appendix: In Interdisciplinary View on Happiness









Starting point

Classical utilitarianism started with the slogan “The greatest happiness for the greatest number”.

Welfare economics is supposed to increase national welfare.

Traditional approximations for welfare are

- income for the welfare of the individual

- GDP (calculated by the income approach) for the welfare of society.



Type of problem

Richard A.Easterlin, professor of economics at the University of Southern California found, as expected by most economists, that, within a given country, people with higher incomes are more likely to report being happy. However, in international comparisons, the average reported level of happiness does not vary much with national income (GNI) per person, at least for countries with income sufficient to meet basic needs (Easterlin Paradox, Wikipedia).

Does welfare economics contribute to happiness?




The history of welfare economics seems to confirm the following suspicion:


The mathematical maximization of welfare is extremely useful – as a form of employment for economists   (author unknown).


Whereas many branches and techniques of economics are indispensable, the mathematical maximization of welfare cannot live up to its promise.

Newer strategies have given up the idea to derive happiness exclusively from economic welfare:


The Capability Approach emphasizes that – once a decent level of economic welfare is reached – human rights become a major determinant of happiness.

Happiness Economics builds on empirical data about individual happiness instead of mathematical functions and bureaucratic indicators like the GDP and GNI.


With regard to economic welfare the hope rests on simulation models, which forecast the outcome of competing economic policies. Unfortunately, however, these models did not foresee the worst economic crises since the Great Depression.






1. Introduction



 Starting point

▪         Classical utilitarianism started with the slogan “The greatest happiness for the greatest number”.

▪         Welfare economics is supposed to increase national welfare.

Traditional approximations for welfare are

o   income for the welfare of the individual

o   GDP (calculated by the income approach) for the welfare of society.



Type of problem

Richard A.Easterlin, professor of economics at the University of Southern California found, as expected by most economists, that, within a given country, people with higher incomes are more likely to report being happy. However, in international comparisons, the average reported level of happiness does not vary much with national income (GNI) per person, at least for countries with income sufficient to meet basic needs (Easterlin Paradox, Wikipedia).

Does welfare economics contribute to happiness?




2. Classical Economics (18th and 19th Century)



2.1      Definition


The historical context of classical economics was the age of enlightenment, the French Revolution (1789-1799) and the industrial revolution.


1.      Classical economics is widely regarded as the first modern school of economic thought. It is the idea that free markets can regulate themselves. Its major developers include Adam Smith, David Ricardo, Thomas Malthus and John Stuart Mill (…) Adam Smith's The Wealth of Nations in 1776 is usually considered to mark the beginning of classical economics. The school was active into the mid 19th century and was followed by neoclassical economics in Britain beginning around 1870.

2.      Classical economists attempted and partially succeeded to explain economic growth and development. They produced their "magnificent dynamics" during a period in which capitalism was emerging from a past feudal society and in which the industrial revolution was leading to vast changes in society. These changes also raised the question of how a society could be organized around a system in which every individual sought his or her own (monetary) gain.

3.     Classical economists reoriented economics away from an analysis of the ruler's personal interests to a class-based interest. PhysiocratFrancois Quesnay and Adam Smith, for example, identified the wealth of a nation with the yearly national income, instead of the king's treasury. Smith saw this income as produced by labor applied to land and capital equipment. Once land and capital equipment are appropriated by individuals, the national income is divided up between laborers, landlords, and capitalists in the form of wages, rent, and interest.

(Classical economics, Wikipedia)


A notable current within classical economics was underconsumption theory, as advanced by the Birmingham School and Thomas Robert Malthus in the early 19th century. These argued for government action to mitigate unemployment and economic downturns, and were an intellectual predecessor of what later became Keynesian economics in the 1930s. Another notable school was Manchester capitalism, which advocated free trade, against the previous policy of mercantilism.

(History of economic thought, Wikipedia)




2.2      Classical Utilitarianism




The origins of utilitarianism are often traced as far back as the Greek philosopher Epicurus, but, as a specific school of thought, it is generally credited to Jeremy Bentham (1748-1832) (Utilitarianism, Wikipedia)


Utilitarianism retains the Epicurean view that humans naturally seek pleasure and avoid pain, but while Epicureans laud pleasure seeking and pain avoidance for their effects on the psychological state of the actor, utilitarians use it to express the consequentialist view that a good action maximizes pleasure and minimizes pain in the society (Epicurus, Science Encyclopedia)



Bentham’s utilitarianism

Bentham’s utilitarianism is based on the following assumptions:

1.      Each individual knows best what is good for him/her

2.      Each individual should decide him/herself in private matters

3.      The welfare of an individual does not depend on other individual’s welfare

4.      The welfare of each individual can be added in order to evaluate the total welfare of the society.

5.      Each individual has the same weight (rights) in collective decisions.

6.      Utility is interpersonally comparable

7.      The principle of competition increases welfare, if applied under the conditions of equal opportunity.

8.      Economic welfare correlates with general welfare.

9.      Utility can be measured by cardinal numbers and utility functions are linear.

[Kleinewefers, 37-38]

Utilitarianism was originally developed as a challenge to the status quo. The demand that everyone count for one, and one only, was anathema to the elitist society of Victorian Britain (Utilitarianism, Wikipedia).



Welfare function according to Bentham

In classical utilitarianism utility is a function of consumption. Consumption is measured in terms of preferences for goods and services. Utility is associated with the happiness which is created by consumption [Bentham, 120].

Let’s assume the society consists of two persons P1 and P2, who dispose of two goods G1 and G2. The welfare function according to Bentham would look as follows:

1.      Social welfare (W) is the total of the two individual utilities (U): W = U1 + U2

2.      The utility functions are identical for both persons. It is assumed that the utility (usefulness) of the two goods is the same for both persons.

3.      The utility depends linearly (factors a1, a2) on the quantities (q) of the goods.

U1 = (a1 x q11) + (a2 x q12)

U2 = (a1 x q21) + (a2 x q22)

where q12 = the quantity of good G2, consumed by person P1.

Under these premises social welfare should increase linearly with the Gross National Product (GNP).

[Kleinewefers, 40]




The development into maturity of classical liberalism took place before and after the French Revolution in Britain, and was based on the following core concepts: classical economics, free trade, laissez-faire government with minimal intervention and taxation and a balanced budget. Classical liberals were committed to individualism, liberty and equal rights. The primary intellectual influences on 19th century liberal trends were those of Adam Smith and the classical economists, Jeremy Bentham and John Stuart Mill (Liberalism, Wikipedia)

There is, however, a profound difference between liberalism and utilitarianism:

▪         Utilitarianism attempts to increase the total utility of the community. The individual is subordinated to this goal.

▪         Liberalism claims that individual actions are only restricted by the condition not to harm others.

How could Mill claim that liberalism is compatible with utilitarianism?


The key for compatibility lies in Mills interpretation of utility [Schefczyk]:

1.      Mill stands in the tradition of Epicurus and Bentham according to which happiness (respectively the absence of suffering) is the only rational goal of human behavior. Mill’s innovation was to introduce a ranking for different kinds of happiness. The ranking is justified by competence, i.e. by the judgment of experienced persons. The judgment if football is preferable to the opera can only be made by persons who made a positive experience with both kinds of events. People who don’t enjoy the opera (or don’t even know it) cannot morally valuate the corresponding kind of happiness; they lack a specific perception, respectively knowledge.

2.      Even if all competent persons accord in ranking pleasures then this ranking is still not generally relevant. The life of an individual cannot be improved by imposing an “official” ranking upon him/her.

3.      Most philosophers agree that the life of an unhappy human is preferable to the life of a happy pig. But Mill doesn’t conclude that we should invest all our energy in top-quality actions. All kinds of happiness reach a point of satiation and we should therefore attempt to diversify our engagements.


The liberal characteristics of Mill’s concept can be summarized as follows [Schefczyk]:

1.      Tolerance, accept that perception and experiences are different

2.      Informality

3.      The denial of external and internal perfectionism

On this basis Mill claims that liberty is a consequence of the utilitarian goal. Since humans are different, the pressure for conformity and the denial of individual liberty contradicts the interests of all humans.

The point in Mill’s argument consists in not only seeing other people as competitors but also as enrichment. Diversified experiences produce empirical data about possible kinds of happiness. The ethical ideal according to Mill is not restricted to tolerance, it is open and affirmative; a liberal is willing to learn and profit from other person’s experiences.




2.3      Criticism of Capitalism


The main critic of capitalism was Karl Marx.

▪         Communism emerged in response to the miserable living and working conditions of the working class in the new industrial era.The economic and political theory published in The Communist Manifesto (1848) and Das Kapital (1867) combined with the dialectic theory of history inspired by Friedrich Hegel (1770–1831) provide a revolutionary critique of nineteenth-century capitalism.

▪         Marx developed a theory of business cycles based on exploitation, alienation, capital accumulation and economic growth(see Marxian Economics). With every boom and bust, with every capitalist crisis, thought Marx, tension and conflict between the increasingly polarized classes of capitalists and workers would heighten. Ultimately, led by the Communist party, Marx envisaged a revolution and the creation of a classless society.

In 1917 Russia crumbled into revolution led by Vladimir Lenin. Lenin promoted Marxist theory and collectivized the means of production (History of economic thought, Wikipedia).

From now on there was a concrete example, how the Marxist theory could be implemented (respectively abused) in practice. Lenin’s centrally planned economy also marked the beginning of an endless competition between liberal and (partly) state-run economies. An attempt to reconcile Marxian economics with free markets was made in the 1920s in the context of market socialism. Market socialism combines the public, cooperative, or social ownership of the means of production with the framework of a market economy (see chapter 3.3).





3. Neoclassical Economics (since ca.1870)



3.1 Definition


Neoclassical economics is a set of solutions to economics focusing on the determination of goods, outputs, and income distributions in markets through supply and demand(Neoclassical economics, Wikipedia).




Neoclassical economics is conventionally dated from

1.      William Stanley Jevons's Theory of Political Economy (1871)

2.      Carl Menger's Principles of Economics (1871), and

3.      Leon Walras's Elements of Pure Economics (1874 – 1877).


These three economists have been said to have promulgated the marginal utility revolution or Neoclassical Revolution (…).

1.      Walras was more interested in the interaction of markets than in explaining the individual psyche through a hedonistic psychology.

2.      Jevons saw his economics as an application and development of Jeremy Bentham's utilitarianism and never had a fully developed general equilibrium theory.

3.      Menger emphasized disequilibrium and the discrete. Menger had a philosophical objection to the use of mathematics in economics, while the other two modeled their theories after 19th century mechanics.

(Neoclassical economics, Wikipedia)



Comparison with classical economics


Rational behavior

▪         Classical economists (…) accounted for economic phenomena like output, consumption, value of commodities, distribution of income.

▪         Neoclassical economists defined economics as a science which additionally could be capable of studying all human rational actions. All humans can be modeled as agents who search for getting the maximal satisfaction from their actions. The marginalist neoclassicals tried to develop general economic laws, imitating the rigorous methods used in physics (History of Economic Thought, Wikipedia).


Marginal utility is a consequence of rational behavior:

▪         Instead of the price of a good or service reflecting the labor that has produced it (as in classical economics)

▪         the price reflects the marginal usefulness (utility) of the last purchase. This meant that in equilibrium, people's preferences determined prices, including, indirectly the price of labor (…).

Consumers act rationally by seeking to maximize satisfaction of all their preferences. People allocate their spending so that the last unit of a commodity bought creates no more satisfaction than a last unit bought of something else (History of economic thought, Wikipedia)




3.2      Old welfare economics



Marginal utility

The concept of diminishing marginal utility has a long history (see Marginalism, Wikipedia):

▪         Daniel Bernoulli (1700-1782) published a formalization of marginal utility in 1738 (Expected Utility Hypothesis, Wikipedia)

▪         Jevons, Menger and Walras promulgated the concept of marginal utility, but did not invent it.

▪         It was Gossen who found a convincing mathematical formulation and Pigou (not Bentham) who introduced it in a welfare function.


Hermann Heinrich Gossen (1810-1858) was a Prussianeconomist who is often regarded as the first to elaborate a general theory of marginal utility (Gossen, Wikipedia)


One of the major representatives of the Gossen-type of economics was the English economist Arthur Cecil Pigou (1877-1959). According to his theory the welfare of a society can be measured by the Gross Domestic Product (GDP) and the distribution of GDP [Kleinewefers, 40-42].



Welfare function according to Pigou

Let’s assume the society consists of two persons P1 and P2, who dispose of two goods G1 and G2. The welfare function according to Pigou would look as follows:

1.      Social welfare (W) is the total of the two individual utilities (U): W = U1 + U2

2.      The utility function is identical for both persons. It is assumed that the utility (usefulness) of the two goods is the same for both persons.

3.      The utility function U = U (q1, q2) is of the Gossen type, i.e. the marginal utility decreases with increasing consumption.

Under a given GNP the maximum social welfare can be attained, if the goods are equally distributed among the two persons [Kleinewefers, 41].


As long as utility functions are assumed to be linear (as in Bentham’s welfare functions) it does not matter, if the welfare of the most or the least wealthy is increased. But if we assume a diminishing marginal utilityof welfare (as in Pigou’s welfare functions) then it makes sense to increase the welfare of the least wealthy. Under the influence of Gossen’s laws a part of the welfare economists turned towards egalitarianism without being particularly compassionate.The normative force of the French revolution’s fraternitéis not required to justify redistribution, as long as Gossen’s laws are seen as a kind of “natural” laws. Under the given premises redistribution is simply a consequence of the common goal to maximize the welfare of the community.


Pigous ideas are still effective in the actual discussions on

1.      Egalitarian utilitarianism (Pigouvian redistribution)

2.      Protection of the environment (Pigovian tax for pollution etc.)

The weakness of his theory lies in the assumptions that the utility functions of all individuals are equal [Herbener, 80] and that the society’s total income isn’t affected by the redistribution. If we take into account that the society’s total income is negatively affected by the redistribution (because hard working people lose the motivation to create additional income) then the optimal redistribution is rather prioritarian than egalitarian.




3.3      New Welfare Economics




Old welfare economics used the following assumptions:

1.      Utility can be measured in terms of money and is a measure for social welfare

2.      Utility is interpersonally comparable and summable.

These two assumptions were given up in new welfare economics [Clarenbach, chapt.2.6] [Herbener]. Pareto proved that utility is immeasurable from observations of behavior. Economists who accepted this proof (like Hicks) attempted to revise the theory of consumer behavior by excluding immeasurable concepts of utility. The analytical framework remained individualistic. All social phenomena (in particular market prices and the law of demand) had to be explained in terms of individual behavior.



Ordinal utility

Ordinal instead of cardinal utility is the major difference between old and new welfare economics [Kleinewefers, 42]. For a comparison see Cardinal Utility, Wikipedia.

When cardinal utility is used, the magnitude of utility differences is treated as an ethically or behaviorally significant quantity. On the other hand, ordinal utility captures only ranking and not strength of preferences (…). It would e.g. be possible to say that juice is preferred to tea to water, but no more. Neoclassical economics has largely retreated from using cardinal utility functions as the basic objects of economic analysis, in favor of considering agent preferences over choice sets (Utility, Wikipedia).


The first usage of ordinal utility is attributed to Vilfredo Pareto (1848-1923).

▪         Giving up cardinality (classical utilitarianism, assumption 9) means giving up the cardinal hedonistic scale.

▪         Utility is now defined by a set of individual preferences and cannot be interpersonally compared (classical utilitarianism, assumption 6).

▪         Without a common hedonistic scale utilities cannot be added (classical utilitarianism, assumption 4).

As a consequence there is no variable like “welfare” which could be maximized and distributed. Distributive justice was cancelled from the economist’s agenda.



Allocative efficiency

From now on economics concentrated on the search for allocative efficiency under the conditions of a given initial allocation and limited resources. These are the characteristics of an optimization problem.


Given a set of alternative allocations of goods or outcomes for a set of individuals, a change from one allocation to another that can make at least one individual better off without making any other individual worse off is called a "Pareto improvement". An allocation is defined as "Pareto efficient" or "Pareto optimal" when no further Pareto improvements can be made (Pareto efficiency, Wikipedia).


Two fundamental theorems of welfare economics are the following:

1.      A perfectly competitivegeneral equilibrium is Pareto optimal [Arrow, 97]

▪         The theorem captures the logic of Adam Smith’s invisible hand (Welfare Economics, Wikipedia)

▪         A corollary is that free trade is Pareto optimal among countries.

2.      Any Pareto optimalallocation can be attained by a competitivegeneral equilibrium.

For a more detailed description see General Equilibrium Theory


Pareto efficiency was criticized for two reasons:

1.      It does not require a "just" or equitable distribution of wealth. A simple example is dividing a pie into pieces to distribute among three people. The most equitable distribution is each person getting one third. However, the solution of two people getting half a pie and the third person getting none is also Pareto optimal despite not being equitable, because the only way for the person with no piece to get a piece is for one or both of the other two to get less, which is not a Pareto improvement (Pareto efficiency, Wikipedia)

2.      Varying initial allocations lead to varying optima, and there is no criterion to compare these optima. It is not even possible to compare the optimal solution for a specific initial allocation with the non-optimal solution of a different initial allocation. The only normative goal is to realize perfect competition in a perfect market in order to reach a pareto optimum [Kleinewefers, 43-44]. Obviously the Pareto optimization cannot be applied to practical politics because political decisions normally produce winners and losers. As a consequence, economics developed new optimization criteria which could be applied to cases with winners and losers.

Using Kaldor-Hicks efficiency, an outcome is more efficient if those that are made better off could in theory compensate those that are made worse off, so that a Pareto improving outcome results. For example, a voluntary exchange that creates pollution would be a Kaldor-Hicks improvement if the buyers and sellers are still willing to carry out the transaction even if they have to fully compensate the victims of the pollution.

(Kaldor-Hicks efficiency, Wikipedia)

Using the new efficiency criteria it was possible to compare a new situation with the status quo, but it was not possible to compare several alternatives and find the best one. The need to compare and rank a larger number of alternatives led to the development of new social welfare functions. There was, however, a competing movement in economics, which radically questioned the value of economic planning.



The economic calculation problem

The economic calculation problem is a criticism of using economic planning as a substitute for market-based allocation of the factors of production. It was first proposed by Ludwig von Mises in his 1920 article "Economic Calculation in the Socialist Commonwealth" and later expanded upon by Friedrich Hayek. In his first article, Mises describes the nature of the price system under capitalism and describes how individual subjective values are translated into the objective information necessary for rational allocation of resources in society. In market exchanges, prices reflect the supply and demand of resources, labor and products. In his first article, Mises focused his criticism on the inevitable deficiencies of the socialization of capital goods, but Mises later went on to elaborate on various different forms of socialism in his book, Socialism. Mises and Hayek argued that economic calculation is only possible by information provided through market prices, and that bureaucratic or technocratic methods of allocation lack methods to rationally allocate resources (seeAustrian School).

The debate raged in the 1920s and 1930s, and that specific period of the debate has come to be known by economic historians as the Socialist Calculation Debate. Mises' initial criticism received multiple reactions and led to the conception of trial-and-error market socialism (Economic Calculation Problem, Wikipedia).

The theory of Market Socialism combines Marxian Economicswith neoclassical economics after dumping the labor theory of value (History of economic thought, Wikipedia).

In response to the Economic Calculation Problem, Abram Bergson formally demonstrated that competitive outcomes may not lead to the best result. In the following he reconsidered the concept of a social welfare function and reintroduced distributive justice to the economist’s agenda.



New social welfare functions

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