Archive for December, 2013

Policonomics »

Explore keplr-apps.net for a collection of tools that enhance your blockchain experience, including wallet management and decentralized application support.

Dec 26

Lope Gallego

Pigouvian tax

Pigouvian taxes are corrective taxes levied on each unit of output an externality-generator agent produces. It is named after economist Arthur C. Pigou, who developed the idea in his book “The Economics of Welfare”, 1920. Pigouvian taxes are used in order to diminish the ugly consequences of externalities, specially in highly polluting industries.

Consider the diagram below, which shows the graphical representation of a negative externality problem using a polluting factory as an example. The horizontal axis or x-axis measures the amount of output produced by the polluting factory and the vertical axis or the y-axis measures monetary units. The marginal benefit curve (MB) represents the marginal benefit of the factory for each level of production which declines as the amount of output increases. The marginal private cost curve (MPC) shows the marginal cost of the factory as output rises. The more the factory produces, the more it pollutes and hence the bigger the negative effects, which is represented by the marginal damage curve (MD). Lastly, the marginal social cost (MSC) represents the total marginal cost for the whole society, and is constructed by adding together the private costs (which directly translate to higher prices) and social costs.

In this scenario, we have a negative externality equal to E, and the equilibrium is set at an output level of Q_A at a price P_A. A Pigouvian tax could be imposed, in order to eliminate such negative externality. This tax would decrease the output produced to Q_S, and increase price to P_S, being this a socially efficient equilibrium. Consumer surplus decreases A+C+F, while producer surplus decreases by area B+D+G. Government will gain a tax revenue equal to area A+B+C+D, drawn in light red in the diagram. Finally, external agents will gain E+F+G. Therefore, the net effect is E:

-(A+C+F)-(B+D+G)+(A+B+C+D)+(E+F+G)=E

The negative effects of the externality are therefore eliminated using a Pigouvian tax. However, a critique can easily be made: it looks like Pigouvian taxes reduce the willingness to produce. Indeed, the careful implementation of Pigouvian taxes require them to be imposed on the polluting aspect of the factory, rather than directly impose them on output levels. Obviously, it can be really hard to actually make this distinction.

Dec 18

Lope Gallego

Externality

Externalities are the benefits or costs that arise when the decision to consume or to produce generates some positive or negative impact on the environment affecting the welfare of others in a way that is not transmitted through prices or via market mechanisms. When the market price does not truly reflect the real price in which the externality should be considered, there is a loss of efficiency.

As previously stated, it is important to have in mind that externalities can be linked both to an improvement of the utility for individuals but also to its damage. The former are known as positive externalities and an example of one would be the vaccination of an individual that would prevent having a disease and at the same time avoid the spread of the disease to others. On the other hand negative externalities are those that reduce utility and a common example is the air pollution produced by many factories.

The diagram below shows the graphical representation of a negative externality problem using a polluting factory as an example. The horizontal axis or x-axis measures the amount of output produced by the polluting factory and the vertical axis or the y-axis measures monetary units. The marginal benefit curve (MB) represents the marginal benefit of the factory for each level of production which declines as the amount of output increases. The marginal private cost curve (MPC) shows the marginal cost of the factory as output rises. The more the factory produces, the more it pollutes and hence the bigger the negative effects, which is represented by the marginal damage curve (MD). Lastly, the marginal social cost (MSC) represents the total marginal cost for the whole society, and is constructed by adding together the private costs (which directly translate to higher prices) and social costs.

The socially efficient output Q_S in this case is located at a lower quantity and at a higher price than the actual output Q_A. Whenever market mechanisms do not properly transmit price there will be a loss of efficiency. If it were a positive externality being produced, the opposite would not necessarily occur. It is true that the optimum social would be to set a higher output but price could be lower, equal or even higher than the private optimum depending on the location and slope of the curves.

Several solutions have been proposed in order to reduce inefficiencies created by externalities:

Pigouvian tax: this corrective tax is levied on each unit of output an externality-generator agent produces. This tax is equal to the marginal damage at the efficient level of output (t on the adjacent diagram).

Subsidies: in a polluting industry, firms are paid not to pollute (the government pays a subsidy equal to s, the green rectangle). This method works in a similar way to a tax but this time the government spends money instead of collecting it, while it is the other way for firms.

Cap-and-trade: the basic idea behind this measure is to create a market, where there are a limited number of pollution permits, which allows the firms that pollute less to sell the permits they do not use to other firms that pollute more. This system of tradable pollutions permits will benefit low pollutant firms and penalize high pollutant ones.

Dec 12

Lope Gallego

Nicholas Kaldor

Nicholas Kaldor, 1908-1986, was a Hungarian born, British economist. He graduated from the London School of Economics and Political Science in 1930, and was there where he taught until 1947. Keynesianism influenced many of his ideas, especially those concerning welfare economics, the field of economics where his contributions became more popular.

During the 1930s, and following the example of his colleagues Hayek and Hicks, Kaldor contributed to enlarge mainstream neoclassical theory. In his “Welfare Propositions of Economics and Interpersonal Comparisons of Utility”, 1939, he made his own contribution to compensation criteria, developing what is nowadays known as Kaldor’s criterion. According to this principle a reallocation in the distribution of income can be more efficient when those that are better off, can compensate those who are worse off.

Kaldor contributions also include “A Classificatory Note on the Determinateness of Equilibrium”, 1934, where he analysed cobweb models, and which tries to explain the reason of periodic price fluctuations in certain types of products, taking into account supply, demand and price formation. In agreement with keynesianists, he referred to economic growth based on speculation as being undesired as it will provoke, in a medium-long run, a fast and sharp economic fall.

Dec 9

Lope Gallego

General equilibrium

A market system is in competitive equilibrium when prices are set in such a way that the market clears, or in other words, demand and supply are equalised. At this competitive equilibrium, firms’ profits will necessarily have to be zero, because otherwise there will be new firms that, attracted by the profits, would enter the market increasing supply and pushing prices down. Following the first fundamental theorem of welfare economics, this equilibrium must be Pareto efficient. Both will have a fundamental relation as a mechanism for determining optimal production, consumption and exchange.

Initial approach:

Let’s consider an economy where there are:

Two factors of production: capital (K) and labour (L).

Two goods: good X and good Y.

Two agents: A and B

The economic problem that is faced needs to find the most adequate allocation of factors of production in order to produce goods X and Y and how these goods will be distributed amongst consumers A and B. This configuration will be such that there will be no other feasible configuration that will allow an increase in any individual’s welfare without decreasing the other individual’s welfare.

In order to achieve Pareto optimality, a certain set of assumptions need to be held.

-The production function needs to be continuous, differentiable, and strictly concave. This will result in a convex set of production possibilities, also known as production possibility frontier Its shape shows an increasing opportunity cost as we need to use a higher number of resources in order to produce a larger amount of a certain good.

-Consumers’ preferences need to be monotonic, convex and continuous, showing how individuals’ welfare increases with a greater amount of goods, but with a decreasing marginal utility.

–Perfect and free availability of information.

-There has to be an absence of externalities and public goods so the utility of individuals depends directly and uniquely from their possession of goods X and Y.

Production optimisation

The optimisation problem in production relies in the maximisation of total output production taking into consideration that it is subject to a limited amount of capital and labour. Analytically,

We can start by looking at the production of goods X and Y as two different optimisation problems. The firm will have to decide what quantity of capital and labour allocate to the production of good X, as shown on the left side of the diagram below, but also what quantity of capital and labour assign to the production of good Y, as shown on the right. These curves are the isoquants corresponding to each production process.

These two diagrams can be plotted together using what is known as the Edgeworth box, which makes it easier to compare quantities of capital and labour used, while also comparing quantities of goods X and Y being produced. Indeed, it’s not only easier to analyse, but also makes more sense, since the total available quantities of capital and labour are given.

The solution to this problem is related to the marginal rate of technical substitution (MRTS). A higher efficiency will be achieved if the reallocation of a unit of labour or capital from one good to another leads to a higher production of the former. When the marginal rate of technical substitution is equal for both goods, it means that all available inputs are being used, which translates into a purely efficient production process.

Graphically, if we plot all these points we construct what is known as the contract curve (blue curve in the Edgeworth box). These represent all Pareto efficient distributions, such as F, G or H. I is not Pareto efficient, since going from I to either G or H would result in an increase in the production of one of the goods without giving up the production of the other. From this curve we can derive the production possibility frontier, which shows the quantities of goods X and Y being produced, as shown in the following diagram. It must be noted that both the contract curve and its derivative, the production possibility frontier, show all the solutions that are Pareto efficient from the firm’s point of view. Only when considering input and output prices will we be able to determine a unique solution (because of the concavity of the production possibility frontier).

Consumption optimisation

Bundles of goods cannot be ranked in a reliable way without knowledge of the distribution of the products, especially if a bundle has different amounts of each good. There may be some bundles that have more products of a good but less of another. The optimisation problem will be to maximise the utility of individuals A and B subject to a limited total amount of goods X and Y. Analytically,

In this case we have to achieve the optimal distribution of two, already produced goods (X and Y) between two individuals (A and B). We can follow the same step by step method used before. Here, we’ll plot indifference curves corresponding to the amounts of goods X and Y consumed by A (on the left), and the amounts of goods consumed by B (on the right).

Again, we use the Edgeworth box to graph the different distributions that can be given between two individuals, A and B, and two goods, X and Y. The further the indifference curve is from the origin, the higher the level of utility enjoyed by the consumer.

Although all the points in the graphic are feasible, not all are efficient, given the utilities and preferences of consumers. The indifference curves join all the points that give consumers the same level of utility. By connecting all points of tangency between the indifference curves of both individuals, the contract curve is constructed and represents all Pareto efficient allocations. The tangency between indifference curves is the point where both consumers have an equal marginal rate of substitution for goods X and Y, and are therefore not willing to trade between them, as it would result in a lower utility.

Global optimum

Until now we have only considered different parts of the economy, and not the economy as a whole. The optimisation problem faced this time is similar to the previous one, although this time an additional restriction is added, since we are here considering both production and consumption: the production level also needs to be efficient.

As this optimisation problem is based on the previous one, we have the same marginal rate of substitution equalisation, but also these two must be equal to the marginal rate of transformation, the PPF’s slope,

These solutions are multiple, since there are various points where the condition holds. However, if we consider output prices (given by the consideration of input prices mentioned before), we are able to consider a unique solution. In the adjacent diagram, if output prices were to be P_X and P_Y, the equilibrium would be point E. However, if output prices were instead P’_X and P’_Y, the equilibrium would be point E’.

Let’s say that prices are set at P_X and P_Y, and that the equilibrium point is E, as seen in the diagram below. Consumers A and B will consume both goods X and Y in different amounts. These amounts are given by the equilibrium in consumption, point E on the contract curve. We have also equilibrium in the production process, given by point E on the production possibility frontier. We know this is a general equilibrium because the marginal rate of substitution is equal to the marginal rate of transformation; or, in other words, the slopes of the indifference curves are equal to the slopes of the production possibility frontier.

Competitive markets result in an equilibrium position such that it is not possible to make a change in the allocation without making someone else worse-off. In reality there are many Pareto optimums and we cannot state that one is better than the other. Even if one consumer got all of the production and the other one none, we cannot say it is an inefficient distribution if all resources are being used efficiently. This is the reason why some economists believe it is an incomplete criterion. However, there are others, such as Milton Friedman and the advocates of the Chicago School, for whom this proves that the economy will act efficiently without the need of government intervention.