Discuss Jevon’s equation of exchange.
⇒With the help of the law of diminishing marginal utility Jevon’s arise at the equation of exchange and keeps the condition of consumers equilibrium and gives the basis of his theory of exchange. His equation of exchange states that in equilibrium the ration’s at which the two commodities are must be inversely proportional to the final degree of utility. He derive the equation of exchange in the following manner.
Individual A has quantity ‘a’ of corn
Individual B has quantity ‘b’ of beef
Now, individual A will continue to exchange corn for beef and individual B beef form corn as long as each things that the loss of utility by surrendering a unit of one commodity is less than the gain of utility by acquiring a unit of other commodity.
Suppose A parts with ‘X’ unit of corn in return for ‘Y’ units of beef after this exchange the position is A possesses: (e-x) of corn + y of beef
B possesses: x of corn + (b-y) of beef
If ϕ and Ψ represent the final degree of utilities (MO) of corn of and beef respectively, then the final degree of utilities of A & B will be
Φ(a-x)+ Ψ, y
Φ x+ Ψ2(b-y)
Continuous barter of units of corn and beef between A & B will reduce the final degree of utility of the commodities acquired and raise the utility of surrender one. Finally a stage is reached when the final degree of both the commodities to an individual becomes equal. This is the equation level.
Thus A maximizes his utility when Φ(a-x).dx= Ψ1, Y.dy
Or (Φ(a-x))/(Ψ1,Y)=dy/dx-------------(i)
B maximizes his utility when Ψ2 (b-y).dy= Φ2x.dx
Or Φ2x/(Ψ2(b-y))=dy/dx------------(ii)
This is the equation level of both the individuals.
Now, if-dy/dx=y/x then we can write (Φ(a-x))/(Ψ,y)= Φzx/ Ψ2(b-y)
This is the equation of exchange of Jevons. We can also show, this exchange with the help of a diagram as follows
Initially, the trading body A possesses Oa of corn. A increase in A/s holding of corn by aa/ simultaneously represent a decrease in A’s holding of beef by the same amount aa/. But A benefits by trading beef for corn because he receives more utility aa/gh by acquiring additional corn of aa/ amount then the loss of utility aa/f e by giving up same amount aa/ of beef. Thus A’s net gain is efgh. A will continue to give up beef for corn until equation is each at point c, where the marginal utilities of the two commodities becomes equal. Similarly B will continue to give up corn in exchange for beef until the equation c is reached. At point C both the trading bodies A and B are in equation and there is no further gains from trade and the trade ends
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