The exchange theory is most vital and practical theory in Advanced Microeconomics. Such theory is firstly formulated by F.Y. Edgeworth. He has assumed that there are two individuals and they exchange two commodities with each other. In the market, there are many commodities supplied and many commodities are exchanged. Two individuals bargain with each other to exchange commodities. Every individual always look for best contract at which both woul.d be better off. At the contract time, each individual finds the best deal which they look.
Edgeworth had a precise formulation of barter processes for the simple two-good economy. The process of barter dealt with by Marshall and Edgeworth consist of successive bartering between individuals until the position was reached at which no barter was possible for each individual to become better off. Edgeworth graphically showed that the equilibrium reached by the process depended upon the path of bartering as well as the amount of goods initially held by each individual.
The process of barter, therefore, constitutes a strong contrast to Walras’s tatonnement process. Walras’s process is a provisional market process by which competitive equilibrium is attained, and the equilibrium reached by it is determined solely by the initial holdings, independently of the path of the process.
In the Edgeworth figure, there are two individuals 1 and 2. The x̅i and x̂i, denote individual i’s consumption endowment and net demand respectively of commodity x where i = 1,2. The total endowment of commodity x is x̅ = x̅1 + x̅2. In addition to this, individual 2 possess some amount of a commodity y, where y̅i. and ŷi. are i’s consumption endowment and net demand.
This theory gives the indifference curves to explain the both consumers preference for two goods. The figure shows the length of the horizontal side of the box. It represents the total endowment of commodity x. The length of the vertical side of the box represents the total endowment of y.
A point in the diagram shows the four consumption values for two individuals. They are (x1, y1, x2, y2).
These values satisfy the feasibility conditions as follows:
The individual who achieve total utility from consumption of each good is equal to the total endowment. In the box diagram, we can measure individual 1 ‘s consumption of x which is right ward from the origin o1. It is the bottom left hand corner of the box diagram. The 2’s consumer’s consumption of y is measured leftward from the origin o2 at the top right hand of the box. Consumer’s consumption of y2 is measured vertically downward from o2 in diagram. There are four consumption co-ordinates at each point in the box diagram.
They are presented in the following figure:
In the figure 6.4, *α shows as a point which has 4 consumption values that is (x1, y1, x2, y2). It is written in the above paragraph. Now x̅ can be written slightly different as x̅ = x̅1 + x̅2. It is a medium consumption of total endowment of both commodities. Similarly, for y commodities, the total endowment can be written as y̅ = y̅1 + y̅2. Above equation is the median consumption of y commodity of both commodities. In the diagram, we can draw 1’s indifference curves with reference to origin 01and 2’s indifference curves with reference to origin of O2 Such indifference curves are named as I1 and I2 in the diagram.
The point ∝ indicates that the initial endowment point has the co-ordinates (x̅1, y̅1, x̅1, y̅2). In the diagram, the indifference curves I01 and I02 are passing through total endowments of two individuals. Before doing any trade on and indifference curves, the consumers are located at point ∝.
Edgeworth Hypothesis (EH):
Edgeworth Hypothesis is based on the two assumptions:
1. There are only two individuals in this hypothesis. They will always agree to an exchange of the commodities. Their agreement to an exchange of commodities will take place at least of the individual which will be better off and no one worse off.
2. Both individuals in Edgeworth hypothesis will not agree to an exchange if it makes any one worse off than what they are now.
The Edgeworth hypothesis is very clear and there is no any possibility of failure in it. Both the individual’s will agree to exchange commodities and bargain for better gains out of exchange. The Edgeworth hypothesis assumed that each individual is rational in his/her thinking. At the end of bargaining, both will agree to exchange commodities. Such exchange between the two individuals will make at least one better off and no one worse off.
In figure 6.4, we move along with 1 giving 2 y in exchange for x. It means suppose individual is buying x from 2 then 1’s individual is making him/her better off and 2nd individual is no worse off. Both individuals can become better off only if 1st individual buys from 2nd with payment falling between those implied by moving along and those implied by moving along. Such movements along with two indifference curves allow trading between two individuals. Therefore it will help and trade will take place between two individuals.
In order to decide the exchange process for two individuals, we require the cc’ line in the diagram. Such line is a locus of points and sometime it is called as contract curve. They are the tangency of the indifference curves of the consumers in the area bounded above by and below by. The assumption strict convexity shows that any given pair of indifference curves for the two parties or two consumers.
It will have no more tangency point. In the diagram, there is no point of cc’ in the area which is bounded by and, which can be a tangency point. All points of cc’ must be the points of intersection. Any point of interaction on cc’ line makes one individual better off.
Both individuals should agree by sliding along the two indifference curves. Before exchange ∝ point is not an equilibrium point on cc’ line, there is no equilibrium outcome out of exchange process between two individuals. On the other hand, a point cc’ cannot be improved upon if both individuals reach at particular point. Then a move on cc’ line is not possible. At such point, they are ready to exchange the goods. At this point at least one consumer is better off.
In the diagram, any direction of curve leads to a lower indifference curve for at least 1 individual. In the figure, it is not possible to move from one point to another point along cc’ line. Such possibility makes one individual worse off. The line cc’ in the diagram satisfies the Edgeworth hypothesis. The line cc’ line is called as contract curve. Such contract line is a set of possible contracts for exchange of commodities which any individual finally makes.
1. Arbitrary Explanation:
The Edgeworth exchange theory does not satisfy how the consumers get from point ∝ to a particular point on cc’ line. It is artificial explanation to make the two consumers better off. Edgeworth suggested that this is only possible solution or it is an accident which forces for the consumers to exchange the commodities and make each one better off.
2. Artificial Explanation:
In the theory, two hypotheses are inflexible. Such assumption shows that both consumers bargain with each other to sign a contract. Such contract is available on contract curve. There is no any other point which is other than contract curve. It is not possible to change contract.
3. Static Theory:
Explanation of theory is more static than dynamic. Theory does not give the particular point as equilibrium. It is a jet of points rather than as a particular point. Both consumers are ready to agree exchange both commodities but at different points. Therefore there is no particular point of satisfaction or solution. Therefore such model is called as an ‘intermediate’ model because it results into set of points.
4. Narrow View:
Theory explains only two commodities and two consumers. Such explanation is narrow and it does not represent the entire market behavior. Sometime both are not agreeing to exchange commodities. In modern world there are number of substitutes which are available. It does not mean market has stopped functioning. The theory has not explained that if both consumers are ready to exchange commodities with other consumers. Both consumers wants maximum gain therefore they continue bargaining till they get the satisfactory substitution.
Before the bargaining both consumers are equilibrium at α. Suppose both are bargaining and the process gets end at point’s e. Then the line ∝ϵ defines a price ratio. Consumers 1 pay 2 the amount y̅1 ⎯ y*1 in exchange for X*1 ⎯ X̅1 of x and so the implied equilibrium price of x is,
The equilibrium can be defined as by the slopes of the lines from cc to the curve cc’. It is below the slope of ∝c’. Such explanation shows that 1 is buyer of x. The lower is the price then better of he is.
5. Continuity and Strict Convexity:
The consumer preferences must satisfy continuity and strict convexity.
In the diagram, any point on cc’ can be generated as follows:
Through endowment constraints and non-negative constraints has a utility value of 2. It varies between the values of utility. It is corresponding to indifference curves and I2 . It is hard to construct the cases on cc’ line and it coincides with an edge of the box.