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Edgeworth Box

1.7K views01:27 min

Francis Edgeworth introduced the Edgeworth Box to study how two participants allocate a fixed amount of two goods between them.

It starts with two standard graphs, one for each participant. Since one’s gain is the other’s loss, one graph is flipped and combined with the other. This forms a box where each point shows both participants' allocations.

Imagine two individuals, Taylor and Alex, sharing ten apples and eight oranges. The Edgeworth Box maps all possible ways to distribute these goods between them.

It assumes perfect divisibility, meaning goods can be divided into infinitely small units, allowing precise and flexible allocations.

The box has a fixed size determined by the total amount of goods. The horizontal axis represents the apples, while the vertical axis represents the oranges.

One corner of the box shows Taylor having all the goods, while the opposite corner shows Alex owning everything. A point within or on the sides of the box depicts a specific allocation.

Moving along the box’s edges or within it adjusts the allocation. Giving one person more of a good reduces the share for the other, illustrating trade-offs in distribution.

Overview

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The Edgeworth Box, introduced by Francis Edgeworth, is a graphical tool used to analyze the efficient allocation of resources between two entities, such as consumers or producers. It focuses on the distribution of two goods between two individuals within a controlled framework, offering insights into exchange efficiency and market equilibrium.

The box's dimensions are determined by the total quantities of the two goods being analyzed. For instance, if two individuals, Jamie and Morgan, share 12 bananas and 10 pears, the Edgeworth Box will map all possible ways to distribute these goods between them. The horizontal axis represents bananas, while the vertical axis represents pears. Each corner signifies an extreme allocation, with one individual possessing all goods at one end and the other individual at the opposite corner.

The Edgeworth Box assumes goods are perfectly divisible. This divisibility allows for precise and flexible allocations. Every possible distribution of goods is represented within the box. A point within the box indicates a specific distribution of goods, with each individual's share represented by the distance from the respective axes. For example, a point halfway along the horizontal axis indicates both individuals have six bananas. The vertical position of the point shows how the 10 pears are distributed between them.

Allocations change as points move along the edges or within the box. For instance, if Jamie gains more bananas, Morgan’s share decreases. This highlights trade-offs, where redistributing goods between individuals involves balancing gains and losses.

The Edgeworth Box shows all possible allocations and helps identify points of Pareto efficiency, where no individual can improve their situation without making the other worse off. These efficient outcomes form the foundation for analyzing market interactions and equilibrium. This foundation supports further analysis of market interactions and equilibrium.

Transcript

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