Contract curve

The contract curve is a concept in economics and refers to the curve in an Edgeworth box that connects all Pareto- optimal solutions for the exchange of two volumes of goods between two households. In production theory, there are, in contrast to the household theory, two companies swap the two input factor quantities between them.

The economic agents A and B try with the goods to change their initial endowment X and Y such that their utility is maximized. Both exchange until market equilibrium is reached. A Pareto- optimal market equilibrium exists when no one can increase its utility without lowering that of the other.

Geometrically, the curve connecting all points where the indifference curves of the two economic agents affect ( she therefore identical marginal rates of substitution have ).

The black line represents the contract curve, the blue curves are exemplary indifference curves of an economic agent A, the orange curves, the corresponding indifference curves of B.

In theory, economic agents can get all the points on the contract curve through exchange. Once a point on the curve is reached, no more change occurs because one of the two individuals would be in a worse position by swapping in any case.

Which point is actually reached depends on what initial equipment have the individuals of both goods and utility functions which they possess.

The contract curve does not necessarily pass through the two corners of the Edgeworth box run.

On the points Konktraktkurve meet both the first and the second Wohlfahrtstheorem Wohlfahrtstheorem.

It is important to note that the purely contract stresses optimum distribution curve from the viewpoint of efficiency. It does not address issues of distributive justice. This limitation is particularly important when a model results to real situations to be transferred - not an efficient point may well be preferred by all participants because other aspects play a role.

Example

On a desert island Robinson and Friday live from the outside world cut off. Robinson has an initial endowment of 40 coconuts and 10 fish, while Friday is equipped with 10 coconuts and 40 fish. More goods are not of concern.

Both islanders have a utility function of. This means that both strive for the possession of coconuts and fish in an identical number. Obviously, the Anfangsaussstattung not fulfilled this wish. Will Trade approved, both will try to improve their bundle of goods.

The other hand, commands a benevolent dictator Redistribution, resulting, for example, the following bundle

• Robinson: 30 fish, 30 coconuts and Friday: 20 fish, 20 coconuts
• Robinson: 25 fish, 25 coconuts and Friday: 25 fish, 25 coconuts
• Robinson: 20 fish, 20 coconuts and Friday: 30 fish, 30 coconuts

So no further trade will be sought. Both have ( according to their means ) get optimum benefit bundle and can not be further improved without fish or coconuts to steal from others, and to reduce its benefits so.

Therefore, no more Pareto improvements are possible, the distributions shown are Pareto-optimal.

The contract curve represents the sum of all Pareto- optimal distributions, so in this case it is all distributions in which both Robinson and Friday have each identical number of coconuts and fish.

In the Edgeworth box (see drawing above) the contract curve would in this example, the shape of a straight line from the lower left ( Robinson has 50 fish and coconuts, Friday nothing ) to top right ( Robinson has nothing, Friday 50 fish and coconuts ) accept ( the three sample distributions mentioned then lie on this line ).