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Jun 15

Lope Gallego

Pareto optimality

This efficiency criterion was developed by Vilfredo Pareto in his book “Manual of Political Economy”, 1906. An allocation of goods is Pareto optimal when there is no possibility of redistribution in a way where at least one individual would be better off while no other individual ends up worse off.

A definition can also be made in two steps:

-a change from situation A to B is a Pareto improvement if at least one individual is better off without making other individuals worse off;

-B is Pareto optimal if there is no possible Pareto improvement.

This can be easily understood using an Edgeworth box. Starting from point C, two Pareto improvements can be made:

-from C to D: individual 1 would increase its utility, since a further indifference curve would be reached, while individual 2 will remain with the same utility;

-from C to E: individual 2 would maintain its utility while individual 2 increases theirs.

Once we are at point either D or E, no further Pareto improvements can be made. Therefore, D and E are Pareto optimal.

Following the same steps for every indifference curve, we can say that every point in which indifference curves from different individuals are tangent is Pareto optimal. The curve that links these infinite Pareto optima is called the contract curve.

Video – Edgeworth box:

Jun 13

Lope Gallego

Production possibility frontier

The production possibility frontier (PPF) represents the quantity of output that can be obtained for a certain quantity of inputs using a given technology. Depending on the technology, the PPF will have a certain shape.

As you can see on the adjacent figure, this PPF (blue curve) slopes downwards. This slope, which equals the marginal rate of transformation between X and Y, shows us how, in order to increase the output X, the quantity of Y must decrease. In fact, the marginal rate of transformation measures the tradeoff of producing more X in terms of Y.

This frontier determines the maximum output (of both X and Y) that can be obtained given the technology. Production at point A will produce more quantity of Y and less of X than production at point B. However, both are technically efficient, since they maximize the output. For example, production at point C is technically inefficient because, at any point on the PPF, more combined output is produced using given the technology. Also, point D is unattainable given the technology, being this is the reason why it is outside the PPF.

The PPF can be derived from the contract curve on an Edgeworth box. In this box, we see the quantity of inputs (K, L) being used in the production of each good (X,Y). In fact, we can see how, for each quantity of each product, the quantity of each input can change. The isoquants (green curve for X, red for Y) determine how much a certain input has to increase in order to compensate the decrease in the other input, maintaining the quantity of output produced unaltered. The slope of these curves is given by the marginal rate of technical substitution of each output.

The points where the isoquants of different outputs combination intersect, which are Pareto-optimal, allow us to draw the contract curve, from which the PPF can be derived. Since the technology is given, only one PPF can be derived from the contract curve (as opposed to the case of the utility possibility frontier).

Video – Production possibility frontier:

Jun 11

Lope Gallego

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.