Jun 11

Fundamental theorems of welfare economics

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.

Jun 9

Lope Gallego

Second best

Kelvin Lancaster and Richard G. Lipsey, in their article “The General Theory of Second Best”, 1956, following an earlier work by James E. Meade, treated the problem of what to do when certain optimality conditions (which must be considered in order to arrive at a Paretian optimum solution in a general equilibrium system) cannot be satisfied. The main idea in this article is that, when a constraint prevents the fulfilment of one of these conditions, the other conditions are in general no longer desirable. The optimum situation in this case can be attained only by neglecting the other conditions. Indeed, this new optimum is called “second best” because a Paretian optimum cannot be attained.

This can be easily understood using the diagram depicted in the article. We start by considering a typical optimization problem, with a given production possibility frontier (PPF) considered as a boundary condition, indifference curves (green curves, in this case representing a welfare function, ω) and the optimum where the PPF is tangent to ω (point P). Since this points lies on the transformation line and an indifference curve, it defines the production and consumption optima.

When we draw a new constraint condition (red curve), it can be easily seen that point P is no longer attainable. Q could be a second best solution, since it lies both on PPF and NewCC. However, as the authors point out, the second best point would be R, inside the transformation line. This is so because an improvement on welfare can be attained by moving to point R, since it lies on a further indifference curve (ω’’), and therefore means higher welfare.

The segment MN is technically more efficient than R, but since the points on this segment cannot be attained, R is the second best solution.

Jun 7

Lope Gallego

Welfare economics

Welfare economics are a part of normative economics which objective is to evaluate different situations of a given economic system, in order to choose the best one.

Its study can be traced back to Adam Smith, who related an increase of welfare with an increase on production, and to Jeremy Bentham, whose utilitarian views made him think that welfare was equal to the sum of individuals utilities or, in other words, to a “social” utility.

Traditional welfare economics is based on the work of three neoclassical economists. Alfred Marshall stated that consumer’s welfare was the consumer’s surplus, and therefore was measurable in monetary units. Vilfredo Pareto would criticize this cardinal view, and would be the economist who built a true theory of welfare economics in his book “Manual of Political Economy”, 1906: based on the principles of unanimity and individualism, he designed what nowadays is known as the Pareto Optimality, which would become the core of welfare economics. Later, Pigou wrote “The Economics of Welfare”, 1920, stating that a definition of social welfare must include both efficiency and equity.

During the XXth century, welfare economics developed quickly. Nicholas Kaldor and John Hicks’ compensation criteria, and its following critics by Scitovsky, Little and Paul Samuelson, which aim was to find some way of classification of different optima. Also Bergson’s social welfare function, and Kenneth Arrow’s impossibility theorem, proving the former could not be identified. The theory of second best, developed by Lipsey and Lancaster, aimed at finding an optimum when Pareto optimality could not be found. Finally, the increasing use of cost-benefit analysis marks the validity of welfare economics nowadays.

Apr 18

Lope Gallego

Phillips curve

In 1958, A. W. Phillips wrote a paper on Economica (London School of Economics), entitled “The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957”. Analysing data concerning money wages and unemployment rates in the UK, Phillips managed to draw a curve representing the inverse relation between these variables. It must be said that Irving Fisher had already pointed out a relationship between price levels and unemployment in his paper “A Statistical Relation between Unemployment and Price Changes”, 1926 (cleverly renamed later as “I Discovered the Phillips Curve”). The Phillips curve has evolved following other empirical studies, and is widely known nowadays, even though it has also been criticized.

In his article, Phillips drew a curve showing the inverse relation between the rate of change of money wage rates, as a percentage change per year () and the unemployment rate (U).

Two important things must be noted: the point where the curve crosses the abscissa, and the fact that the ordinate seems to work as an asymptote. The importance of the point of crossing must be highlighted (around 5,5%), since it is the rate of unemployment that an economy will have for a zero increase in the money wages. This point will be named, in further developments of the Phillips curve, Natural Rate of Unemployment and Non-Accelerating Inflation Rate of Unemployment (NAIRU). Regarding the asymptote, as the author pointed out, there was no data of higher rates of change in money wage, nor lower unemployment rates. It can be concluded that unemployment cannot be lowered beyond a certain level.

Two years later, Richard G. Lipsey would publish a paper in the same journal deepening the mathematics regarding the curve, as well as expanding Phillips’ research by doing further econometrical tests.

Also in 1960, Paul A. Samuelson and Robert M. Solow, in their “Analytical Aspects of Anti-Inflation Policy”, studied a similar relation, in this case using data from the United States. Although they used inflation (Π) instead of the rate of change in money wages, they came up with similar results. Even though the curve might seem different because of the scale used, the unemployment rate at price stability is the same as at money wage stability (around 5,5%), and there seem to be no way to lower unemployment beyond a certain level (around 1%).

It was in this paper that the Phillips curve was considered a “menu of choice” for the first time. This meant that, concerning policy making, governments would be able to choose between a low rate of unemployment with high inflation, and a higher rate of unemployment with lower inflation. However, as the authors pointed out, this menu had to be used only in the short-run, since certain policies or economic events might change the shape of the curve in the longer run.

In the mid 50s, and until the late 60s, the adaptive expectations hypothesis became popular, especially because of the works by Phillip Cagan and Milton Friedman. This hypothesis would endure almost unquestioned until the late 60s and early 70s, when economist Robert Lucas (among others) brought forward a rational expectations hypothesis, from earlier works by J. F. Muth.

Mar 29

Lope Gallego

Keynesianism

This school of economic thought, which focuses on macroeconomics, is mainly based on interpretations of John Maynard Keynes’ most important book, the “General Theory of Employment, Interest and Money”, 1936.

Keynes’ main thesis was that unemployment during the Great Depressionwas the result of a decreasing demand, and that the solution was to revive the economic system through public investment. A Keynesian policy would be one that promotes, for example, public works such as building dams or highways.

Supporters of Keynesianism, or Keynesian economics, believe that although businesses and private sector entities working on a liberal environment function in an efficient way, sometimes market failures may appear. For this, they support a certain degree of implication by the public sector in order to prevent these failures and restore the economy if they appear, through fiscal and monetary policies. However, they will give more credit to the former, the latter being more supported by Monetarists.

Keynesianism was the main economic doctrine from 1936 until the advent of Monetarism, with which it coexisted until the stagflation of the seventies.

Joan Robinson, Nicholas Kaldor and John R. Hicks, are just some of the great disciples of Keynes, and therefore Keynesian economists, mainly from the Cambridge School in its not neoclassical meaning, to name a few.

Mar 29

Lope Gallego

Alvin Harvey Hansen

Alvin Hansen Hansen was an American economist (1887-1975), professor at Harvard University and one of the main precursor of the New Economic Science or Keynesianism, in the U.S. In fact, Hansen is known for popularizing the IS-LM model.

Hansen, heavily influenced by the psychological environment of the Great Depression, also addressed the concept of steady stateand long-term stagnation.

Mar 29

Lope Gallego

John Richard Hicks

John R. Hicks

John R. Hicks was a British economist (1904-1989), professor at the London School of Economics, Cambridge University and University of Oxford. He took special interest on issues concerning microeconomics, growth, economic fluctuations and monetary theory. In his most famous work “Value and Capital”, 1939, Hicks referred to aggregation problems, interest rate, etc. It was also in this book where he developed further the comparative statics, the analysis in economics when describing two possible outcomes. His book “The Social Framework: an Introduction to Economics”, 1942, is a veritable treatise on structural analysis by means of social accounting.

However, Hicks is mainly known for the development of a general equilibrium model, based on J. M. Keynes’ “General Theory”, in which he analyzed four markets: goods, labor, credit and money, called the IS-LM model. This model, firstly named IS-LL, appeared in his article “Mr. Keynes and the Classics: a Suggested Interpretation”, published in 1937 in the journal Econometrica.

He was awarded the Nobel Prize in Economics in 1972, along with Kenneth Joseph Arrow, for his contributions to general equilibrium theory and welfare economics.

Mar 29

Lope Gallego

John Maynard Keynes

Keynes was a British economist (1883-1946), son of the economist and methodologist John Neville Keynes. J. M. Keynes first gained notoriety with his work during the Versailles Peace Conference, when he cleverly proposed in his book “The Economic Consequences of the Peace”, 1919, not to punish Germany to avoid future retaliation. Later, during the Great Depression, he fought the conservative views advocating for a restoration of the gold standard in the famous pamphlet “The Economic Consequences of Mr. Churchill”. After a series of papers on monetary issues, he published in 1936 the most important of his works, the “General Theory of Employment, Interest and Money”, which was the foundation of the then called New Economic Science, or Keynesianism. Keynes’ main thesis was that unemployment during the Great Depression was the result of the decrease in effective demand. Therefore, to achieve full employment, it was necessary to revive the economic system through public investment. In the last years of his life, J. M. Keynes participated in the negotiations of Bretton Woods, in 1944, leading to the creation of the International Monetary Fund.

At the Bretton Woods conference, where he was part of the British delegation, he raised the idea that the IMF should be constituted as a true worldwide central bank, capable of issuing paper currency for international payments, for which he proposed the name “bancor”. Most of the ideas mentioned in the “Keynes Plan” were not followed through, since they competed with the U.S. proposals specified in the “White Plan”.

Great disciples of Keynes, part of the Cambridge School, were Joan Robinson, Nicholas Kaldor and John R. Hicks, to name a few.

Mar 29

Lope Gallego

Chicago school

From the University of Chicago, and opposing Keynesianism, a number of contributions and doctrinal attitudes of authors can be identified, which turn back to neoclassical economics, are in favour of laissez faire and monetarism. Created around the 1940s, its main precursor is Milton Friedman, along with Frank H. Knight and Friedrich A. von Hayek, the latter acting as a liaison with the Austrian School.

The common view of the Chicago School focuses on the idea that governmental interventions should be at its minimum required, being deregulation the most desirable path. Another characteristic theory of the Chicago School is that the reduction or eradication of all types of regulation on business activities is beneficial for the economy as a whole. They support monetary policies when required by the economic environment, as they assume these to be more reliable and effective than fiscal policies.

The Chicago School based their assumptions on the concept of rational expectations. Milton Friedman defended that the price levels in a certain economy are always determined by the amount of money moving in circulation. According to the Chicago School, by acting and allocating resources in a rational way, people drive economic growth, while at the same time controlling price levels.

Mar 29

Lope Gallego

Indifference curves

Indifference curves are lines in a coordinate system for which each of its points express a particular combination of a number of goods or bundles of goods that the consumer is indifferent to consume. This is, the consumer will have no preference between two bundles located in the same indifference curve, since they all provide the same degree of utility. The indifference curves, as we move away from the origin of coordinates, imply higher consumption and, therefore, increasing levels of utility.

An indifference map is a combination of indifference curves, which allows understanding how changes in the quantity or the type of goods may change consumption patterns.

Francis Y. Edgeworth, developed the mathematics concerning the drawing of indifference curves in his book “Mathematical Psychics: an Essay on the Application of Mathematics to the Moral Sciences”, 1881, from earlier works by William Stanley Jevons. However, Vilfredo Pareto was the first economist to draw indifference maps as we know them nowadays, in his book “Manual of Political Economy”, published in 1906.

The first example of indifference map showed in the adjacent graph is the most common representation. It shows four convex indifference curves (red), showing each curve what amount of a good or bundle of goods x₁ the consumer has to give up in order to be able to consume more goods, or bundles of goods, x₂. This relation gives us the marginal rate of substitution (MRS) between these goods, which is the slope of the curve in each of its points.

Our second example is an indifference map with four parallel lines (green). This is the case for goods or bundles of goods, y₁ and y₂, which are perfect substitutes, since the lines are parallel and MRS = 1, that is the slope has an angle of 45º with each axis. It can also be the case for goods or bundles of goods that are perfect substitutes but in different proportions. In that case, the slope will be different and the MRS can be defined as a fraction, such as 1/2 ,1/3 , and so on. For perfect substitutes, the MRS will remain constant.

Our third example shows an indifference map with four indifference curves (blue) that represent perfect complementary goods, z₁ and z₂. This is, there will not be an increase on the consumer’s utility unless both goods increase in the required proportion. The best example of complementary goods are shoes, since the consumer’s utility will not increase when he or she gets a new right shoe without getting a new left shoe. Notice that the elbows are collinear, and the line crossing them defines the proportion in which each good needs to increase in order to have an increase in the utility. In this case the horizontal fragment of each indifference curve has a MRS = 0 and the vertical fractions a MRS = ∞.

These explanations of indifference curves can also be applied to production. In that case, the MRS turns into marginal rate of technical substitution and marginal rate of transformation.
Video – Indifference curves: