Question

Bernard has a weekly income of 10 dollars and he only consumes apples and bananas . When the price of apples is 2 dollars and the price of banana is 1 dollar, he consumes 3 apples and 4 bananas. Last week, the government announced that due to an expected shortage in apples, the consumption of apples is limited to only 1 unit for 1 person. After new law, Bernard started to consume 1 apple and 8 bananas . Do these choices violate the WARP ? What about SARP ?

Answer 1

In the above situation let us first state the given terms

1. Budget = $10 (Assuming that Bernard spends all his income)
2. There are only two commodities_ Apples and Bananas
3. Prices of both the commodities are given such that,

1 unit of apple costs $2

1 unit of banana costs $1

It is clear that, at the prevailing price when both the commodities are freely available, 3 apples and 4 bananas are consumed. Hence, the budget constraint will be

(Qty of A).(Price of A) +(Qty of B).(Price of B) = $10

(3.2)+(4.1) = $10

6+4=$10

Since Bernard buys more bananas as compared to apples hence we can conclude that bananas are preferred to apples.

When the government applied the quota on apples, the new bundle became

(1.2)+(8.1) = $10

In this situation, there is a strong preference to bananas although Bernard is bound to consume only one unit of apple.

Hence in both the situations, Bananas are preferred to Apples. This satisfies the Weak Axiom of Revealed Preference (WARP).

NOTE: WARP defines consistency in decision making. If bundle A is preferred to B in a certain bundle, then A will be preferred to B in a different bundle too. If a consumer chooses B, then it is assumed that A might not be available at that point of time. This does not violate WARP.

On the other hand, Strong Axiom of Revealed Preference (SARP) defines transitivity in decision making. It is usually applied in the case of 3 bundles. For example, if Bundle A is preferred to B and bundle B is preferred to C, then A will always be preferred to C.

But in the above case, if bananas are preferred to apples, then it can never be a case when bananas will not be chosen as against apples.