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Difficulty: MediumBarter System and Its Problems

A market trader in an economy operating under a pure barter system deals in five distinct commodities: cassava, palm oil, yam, cocoa, and maize. In the absence of a monetary unit of account, what is the minimum number of relative exchange rates the trader must determine to evaluate all direct commodity-to-commodity trades?

  1. A
    5
  2. 10Answer
  3. C
    20
  4. D
    25

Answer

10 relative exchange rates are required to evaluate all direct commodity trades among five goods.
In a moneyless barter system lacking a standard unit of account, every good must have a relative price in terms of every other good. The formula to calculate the unique pairs of exchange rates among nn commodities is n(n−1)2\frac{n(n-1)}{2}. Substituting n=5n = 5 gives 5×42=10\frac{5 \times 4}{2} = 10. Money solves this inefficiency by reducing the total required prices from n(n−1)2\frac{n(n-1)}{2} to just nn prices expressed in a single monetary unit.

Step-by-Step Solution

1
Identify the formula for determining the number of relative exchange rates in a barter economy without a standard measure of value.
The formula is Number of exchange rates=n(n−1)2\text{Number of exchange rates} = \frac{n(n-1)}{2}, where nn is the total number of distinct commodities.
Because there is no common unit of account (money), every commodity must be directly priced in terms of every other unique pair of commodities.
2
Substitute n=5n = 5 commodities into the formula.
Number of exchange rates=5×(5−1)2=5×42=10\text{Number of exchange rates} = \frac{5 \times (5 - 1)}{2} = \frac{5 \times 4}{2} = 10
Each of the 55 commodities must be paired with the remaining 44 commodities, divided by 22 to avoid counting reciprocal trading ratios twice.

Key Concept

Lack of a Standard Measure of Value (Unit of Account) in Barter
Estimated Time:1m 0s
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Topics

Barter System and Its Problems

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