# Equilibrium in the exchange economy - Microeconomics

## Equilibrium in the exchange economy

Suppose that in society there are only two consumers - consumer 1 and consumer 2 and two goods - and . Denote the non-negative initial stock of two consumer goods 1 as , and the initial stock of consumer 2 as . The cumulative quantity of each commodity available in a society can be expressed by the vector

Important features of such an economy can be analyzed using the "Edgeworth's box", familiar from the basic course of microeconomics. In Fig. 6.4 the number X1 is plotted for each horizontal line, and the number x2 for each vertical. The number X, for the consumer 1 increases from O1 to the right on the underside, and for the consumer 2 - from O2 to the upper side. Similarly, X2 for consumer 1 increases from O1 vertically up to the left, and for consumer 2 from O2 vertically down to the right.

Since the box sizes are rigidly defined by the size of the initial stocks, each set of four coordinates corresponds to a certain distribution of the total quantity of each commodity between two consumers.

For example, the point e denotes a pair of initial stocks e1 and e2. Any other point in the box reflects some other way of distributing stocks between consumers.

Suppose that consumer preferences are convex. In Fig. 6.5 the indifference curves of the consumer 1 increase in the right-up direction, and the indifference curves of the consumer 2 are left-down. Through each point in the box Edgeworth passes one curve of indifference of each consumer. The curve denoted by MN, is a subset of distributions in which the indifference curves of consumers passing through one point touch each other and is called the contract curve.

Fig. 6.4. Edgeworth's Box

Fig. 6.5. Equilibrium in the exchange between two participants

The solution of the problem of maximizing the utility of two consumers under the constraints imposed by the Pareto efficiency condition must correspond to the point where the marginal rates of substitution of two benefits in consumption for individuals A and B are equal . This is the point of contact of two curves of indifference of our consumers, which lies on the contract curve.

Depending on the degree of relative preference of goods or goods Y on the part of each individual (expressed by his marginal rate of substitution), the contract curve may bend more to the right or left corner of the Edgeworth box. For example, in Fig. 6.6 shows the contractual curve for the case when the individual A prefers the product X to a greater degree, and the individual B is the product Y.

Fig. 6.6. Contract curve for individuals with different degrees of product preference

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