Perfect Substitutes Edgeworth Box Contract Curve

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Exploring the Perfect Substitutes Edgeworth Box Contract Curve in Economics

In microeconomic theory, an Edgeworth box or exchange diagram is a graphical representation of two individuals` preferences and endowments in a two-commodity exchange economy. The Edgeworth box shows the possible allocations of the two commodities between the two individuals that are consistent with the efficient use of resources and the satisfaction of both parties. The shape of the contract curve, which connects the tangency points of the indifference curves, depends on the degree of substitutability or complementarity between the two commodities. In the case of perfect substitutes, the contract curve takes a simple form that allows for a useful analysis of the distribution of gains from trade.

Perfect substitutes are two commodities that a consumer considers interchangeable in terms of their usefulness or value, regardless of their price ratio. For example, if a person only wants to consume apples and bananas, and either one satisfies the same amount of their total utility, then apples and bananas are perfect substitutes for that person. Mathematically, perfect substitutes have a constant marginal rate of substitution (MRS) that equals the price ratio of the two commodities. This means that the consumer is willing to trade one unit of either commodity for one unit of the other at any price ratio, as long as their budget constraint allows for it.

The Edgeworth box for the perfect substitutes case is a rectangle with equal sides, representing the total quantity of both commodities in the economy. Each individual`s indifference curves are straight lines with a slope equal to the price ratio of the commodities. The contract curve is also a straight line that connects the points of tangency of the indifference curves from both individuals, passing through the midpoint of the rectangle. The slope of the contract curve is the harmonic mean of the slopes of the two indifference curves, which is simply the average of the two prices. The contract curve determines the set of efficient allocations of the commodities that both individuals can agree upon, given their initial endowments. Any point inside the contract curve is Pareto inferior, meaning that one individual can be made better off without making the other worse off.

The perfect substitutes case has some interesting implications for the distribution of gains from trade. Suppose that both individuals start with an equal endowment of each commodity, and that the initial price ratio is different from the slope of their indifference curves. In other words, they do not have the same MRS as the market price. Then, there exists a mutually beneficial trade that increases the total quantity of both commodities consumed, and makes both individuals better off. The trade consists of exchanging some units of the cheaper commodity for some units of the more expensive one, until the relative prices adjust to the common MRS. In this case, the gains from trade are symmetric, because both individuals have the same bargaining power and are willing to exchange the same amounts of the two commodities.

However, if the initial endowments are unequal, the gains from trade may not be symmetric anymore. Suppose that one individual has more of one commodity and less of the other than the other individual. Then, the contract curve shifts towards the side of the more abundant commodity, because the marginal utility of that commodity for the first individual is lower than the other`s. In this case, the first individual has a stronger bargaining position and can capture a larger share of the gains from trade. This is known as the principle of comparative advantage, which suggests that trade between countries or regions with different natural or human resources can lead to mutual gains, but not necessarily equal gains. The contract curve for perfect substitutes illustrates this principle in a simplified setting.

To sum up, the perfect substitutes Edgeworth box contract curve is a useful tool in economics for analyzing the optimal allocation of resources and the distribution of gains from trade in a simplified exchange economy. The constant MRS property of perfect substitutes allows for a rectangular and symmetric Edgeworth box, with a contract curve that is also a straight line passing through the midpoint. The contract curve reflects the efficient allocations that both individuals can agree upon, given their initial endowments and preferences. The perfect substitutes case illustrates the principle of comparative advantage, which suggests that differences in initial endowments can affect the distribution of gains from trade, even when both parties benefit from the exchange.