Edgeworth-Box

As Edgeworth box (after Francis Ysidro Edgeworth ) is called in the microeconomics a graphical tool that is used to intuitively the general equilibrium of a pure exchange economy ( pure- exchange economy) from two individuals in the two-goods case investigate. An Edgeworth box consists of the set of indifference curves of the two considered individuals who are each wrapped in the positive orthant of their associated quantities quantities diagrams, diagonally composed mirror-inverted, so that the coordinate axes form a box (box).

Construction

In Figure 1, only the coordinate axes ( and not the Indifferenzkurven ) are to illustrate the structure first shown. The coordinate system with the pointing upwards and to the right direction Saxony belongs to household 1, the other to household 2 As a pure exchange economy is considered ( not in production), the dimensions of the Edgeworth box are always ex ante defined: equivalent to the length exactly the sum of the available (and thus potentially tradable ) units of good 1, so the sum of the features of one person with one good, and the facilities of person 2 Good 1. The same applies to the height of the box which corresponds to the sum of the equipment of both people with good 2.

Each point within an Edgeworth box has just taken four coordinates because is determined for both households each, about how much each of them has on both goods. Each point within an Edgeworth box describes the same reason, a full allocation.

Denote the vector features of the person; he recorded is equipped with Good 1 and Good 2 In Figure 1, a point has been exemplary drawn, which marks the beginning of Features 1 2 Budget and Budget. Accordingly, the purpose of setting an Edgeworth box you now may imagine that from this point exchange transactions are made, leaving in their wake the households the orange dot and gradually converted into an equilibrium. This process is described in the following section.

Exchange process and sample

Figure 2 shows the lower part of an Edgeworth box and consists of some indifference curves of Budget 1 ( as indifference curve is defined as the locus of all quantity combinations of goods - in this case of good 1 and good 2 -. , Which cause the same level of utility )

In this example it is assumed that both households have identical preferences. If we then consider in Figure 3, the Edgeworth box, so can the exchange process illustrate: The (red ) dot top left select the output allocation, ie, the initial equipment of households 1 and 2 Consider now the indifference curve of household 1 (blue), passing through the point; she reveals that the benefits of one household is from his initial endowment 4. Each bundle of goods that (and thus at a higher indifference curve ) is above this indifference curve is obviously preferred by household 1 (blue). The same is true for household 2 (green): He, too, preferred bundle of goods that lie on higher indifference curves (note that the coordinate system is known to be shown in mirror image - higher indifference curves for two household thus located below the bolded green curve).

From this consideration it follows that each point represents better within the lens-shaped area between the bolded green and blue indifference curve in Figure 1, both households compared to their respective initial endowment. Each point within the lens is, in the language of welfare economics, Pareto- superior ( also: a Parato - improvement) to the initial allocation, because without that a household would be worse off at least one household will be better off.

Perform the households now such exchange by, they are new to any point within the "lens". One can then again do the above reflection to see that again there is a new, smaller lenticular surface in general for each of these points, which is Pareto- superior regarding the new allocation. This does not apply for each point. If you look around on the (red) dot in the center of Figure 3, then there exists there is no Pareto improvement more: If you want to budget 1 (blue) provide better and on a higher indifference curve "lift", this is only possible by one worse off household 2 (green).

Determination of Pareto optimality - the contract curve

If only vaguely referred to a certain point as an example of a Pareto optimum in the preceding section, as can the amount of these efficiency points also accurately describe. In fact, there are an infinite number of Pareto- efficient allocations. Their characteristic is that in these points two indifference curves (namely, a household of one and a budget of 2) touch. If one wants to find full Pareto optimality within an Edgeworth box, so you have to just go through all the indifference curves of a household and mark that point where they just barely touched any indifference curve of the other household. By connecting those points then as is done in Figure 4, a curve is obtained, called the contract curve of the exchange economy. It contains all the Pareto- efficient allocation of the economy. Figure 4 illustrates this: from the lower right (red ) point is within the corresponding sectional area, all points on the contract curve Pareto optimality and is that part of the contract curve which passes through the area ( indicated by the orange dots ) for each household also Better a desirable position relative to the initial allocation.

The contract curve is generally not straight. In the example, this follows from the specific form of the utility function and the fact that households have identical utility functions.