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Microeconomics Question from Walter E. Williams:Edit

Imagine a community of two individuals. Individual A's endowment shows him rich in good X and relatively poor in good Y. Individual B's endowment is just the opposite. Heretofore unknown exchange opportunities become available and known and the exchange rate for good X and Y that appears (it matters none to you from whence this exchange rate come) is equal to neither A nor B's subjective exchange rate. Explain analytically the nature of the gains from exchange. Would each member of the community benefit from exchange or is there a possibility that a loss might be incurred? Why?

AnswerEdit

(This is not the Fisherian 2-period Model)

Autarky

Step one: Autarky

  • Under autarky an individual can go from his/her endowment point (e) to a point which maximizes utility under the constraint of a production possibility frontier (C1). This is a movement along the frontier.
Trade2

Step one

  • When trade is introduced a new point of interest is created. A point like Q is the place where an individual can maximize income subject to a given price ratio. This price ratio dictates what bundle of resources the individual will produce assuming that maximizing income is desiered.
Benefits2

Step three: The Benefits of trade

  • Once trade is introduced another possible point is reached. On a give budget line (income held constant) a move to the highest utility curve is possible. In this case, the individual has choosen to maximize income and then maximize utility subject to this constraint.
Wealth Effect
  • The wealth effect shows clearly the increase in utility from the inital position to the final position.
Total
  • In this diagram we have seen an increase in utility but we have also seen an increase in the efficency of society -- wealth creation.


Finally there is a wealth improvment, for the individual and for society. Q* and C* are the individual’s productive and consumptive optima in the absence of trade. When a market emerges, and trade becomes possible, an individual will begin to produce at the point where MRTS = MRS, and where this is equal to the slope of the budget constraint, Q**. This is the new productive optimum made possible through exchange. The new consumptive optimum is at C**. Gains from exchange due to specialization are equal to (y2-y1) + (x2-x1). The exchange is financed by giving up y3-y2. Everyone will be made at least as happy, or better off, as long as trade is voluntary.

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