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# Revealed preference theory

Explain the Revealed Preference Hypothesis. How can you derive the law of demand through Revealed Preference Theory?

Meaning of Revealed Preference Theory:- It is that theory which reveals his actual behaviour toward his preference for a combination of goods.

In other words :- It reveals that consumers actually consume goods which are preferred by him. Which goods may be alternative out of his collection goods.

Consumer reveals his preference for a particular combination of goods out of the alternative combinations available to him.

According to Baumol,  “If a consumer buys some collection of goods A, rather than the available collection B, C, D, etc. It turns out that A is more expensive than others. Now We can consider that A has been revealed to be preferred to others”.

Derivation of Demand Curve through Revealed Preference Theory

Samuelson and Marshallian have used the term revealed preference theory of demand.

Samuelson’s law of demand, his revealed preference hypothesis, established the relationship between price and demand by assuming that income elasticity of demand is positive. As ‘Any goods demand of which is increased when income is increased. And Shrink in demand when its price increases’.

There are two parts of revealed preference theory

• Direct or positive relationship between income and demand
• Inverse relationship between price and demand.

Revealed Preference theory can be explained with the help of two different situations.

1. Fall in price of a Commodity
2. Rice in a price of a commodity

( 1 ) Fall in price of a commodity:- We will understand it from the following figure.

1. In which ( AF ) represents the price line. Consumer chooses a combination of goods X and Y indicated by point E ( EL of Y and OL of X ).
2. Now Consumer reveals his preference by Choosing.
3. Let us Suppose that when the price of X falls, Price of Y remains the Same, so that his price line shifts to AG.
4. Then Consumer reveals his preference toward X goods. And New Combination shifts From E to E1 from two effects of price Change, as Income and Substitution effect.
5. This can be done by drawing a price line A1 and F1 through point E. This price line parallel to price line AG Showing the same price Ratio.
6. Since then the combination is still available to him. Because he will not choose any Combination to the left of E due to being inferior to E. He will buy such a combination ( in case the substitution effect is Zero )
7. Otherwise he will Choose any combination on EF1. Such Z, Which includes a larger quantity of X. Which is possible due to the substitution effect.
8. But, demand for X increases as a result of a decrease in price. This establishes the law of demand.
9. However, consumers move on the new price line AG. The new revealed preference position E1 involves a larger quantity of X, Resulting from the fall in price. As MN indicates income effect.

Thus, Price effect LN = LM ( Substitution Effect ) + MN ( Income Effect ). Thus, the theory of preference directs the derivation of the demand curve as the price of X falls, more of X is Purchased.

( 2 ) Rice in Price of a Commodity:- Let assume a consumer spends his entire income on two commodities X and Y. Now we can understand it from the following figure.

1. Now the price line is represented by AF. The consumer chooses the combination on point E. This means he prefers this combination.
2. Let Assume Price of X is increased and Price of Y remains unchanged.
3. Now New price line will be AG.
4. For the purpose of buying the same combination he will have to grant extra money at the higher price of X has been called over-Compensation.
5. Let us a line A1F1 will be Drawn parallel to AG so passes through E.
6. As consumer Choice of any Combination on EF1 Segment of A1F1 Curve will be inconsistent. Hence consumers will buy E Combination.
7. Otherwise, he will choose a combination of A1E segments Such as Z which Includes a smaller quantity of X. ( Namely OM )
8. The resulting position includes a small quantity of X due to Rice in its price.

Conclusions:- It is proved from the revealed preference theory that a Rice in Price will lead to fall in demand and vice versa. And Income effect is positive on the demand. As if income rises then demand will also rise. Now by analysing this whole question we are able to draw the demand through the revealed preference theory.

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