# Edgeworth box

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The '*Edgeworth* box is an economics tool, named after its inventor Francis Ysidro Edgeworth (1845-1926), which enables the economist to analyze the situation of two individuals and two goods *a* and *b* and how both individuals might exchange quantities from their intitial endowment between each other.

## Economical analysis using the Edgeworth boxEdit

The Edgeworth box depicts the set of all feasible allocations of goods between those two consumers *i* and *j*. An allocation is a pair of consumer bundles *x ^{j} = (x_{a}^{j}, x_{b}^{j})* and

*x*. An allocation is considered

^{i}= (x_{a}^{i}, x_{b}^{i})*feasible*if the total consumed quantity is equal to the total quantity available:

- x
_{a}^{j}+ x_{a}^{i}= e_{a}^{j}+ e_{a}^{i} - x
_{b}^{j}+ x_{b}^{i}= e_{b}^{j}+ e_{b}^{i}

Because the Edgeworth box describes the consumers' preferences too, it contains all relevant information about the exchange. The consumers' preferences are affected by the following assumptions:

- all individuals maximize their utility;
- all preferences are convex and monotonic;
- the utility of a person is dependent of the consumption of another person.

More precisely, the Edgeworth box allows the Economist to simply observe if an allocation is Pareto-optimal, i.e. if two persons could improve their situation by trading/exchanging (without worsening the situation of any other market actor).

In the Edgeworth box diagram the **contract curve** depicts all those points where there is no possibility of advantageous trade between the two consumers. This means that on all points of the contract curve

- it is impossible to improve the situation of one person without worsening the other person's situation (criterion for Pareto optimality);
- all marginal rates of substitution (MRS) are equal.

Therefore, it is economically rational to expect that the two market actors *i* and *j* will interact (trade) with each other until they reach some point on the contract curve. Which point exactly is finally reached, strongly depends how the negotiation power is distributed between both parties negotiating and what type the market on which the interaction takes place actually is.

## LiteratureEdit

- Pindyck, Robert S.; Rubinfeld, Daniel L.: Microeconomics, 7th edition, Prentice Hall, 2009.