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Revealed Preference Theory Of Demand

Revealed Preference Theory of Demand

Introduction

            Prof. Samuelson’s Revealed Preference Theory is a behavioural ordinal utility study as different from the contemplative ordinal theory of Hicks and Allen. It is the third root of the logical theory demand and has been denoted by Hicks as the Direct Consistency Test under strong ordering. Thus theory analyses customer’s inclination for a combination of commodities on the basis of pragmatic customer performance in the market.

Choice Revealed Preference

            The Revealed Preference theory of demand of Samuelson is based merely on hypothesis and hence stated as ‘Choice Revealed Preference’. Keeping this detail into outlook a customer buys goods of two combinations one of the causes he likes it or is cheaper when compared. For instance when a customer chooses an article say X and buys it forgoing articles Y and Z, it may be of two causes that is article X is his liking or it is cheaper than the other two. Then, article X is said to be ‘Revealed Preference’ with the cause of liking.

Law of Demand

            The law of demand is determined without indifference curve and other constrained assumptions but merely with the ‘Revealed Preference’. There are certain postulations with which Samuelson’s Law of Demand is based.

Postulations – The customers’ likings do not alter, that the liking with one combination divulges his inclination for that. He chooses combinations with the prescribed price-earnings streak and any variation in relative prices will always escort to some variation in the articles he purchases. He prefers such that he gains more out of less price. His choices are based on strong ordering. There is always customer reliability in his performance. And the theory is based on the hypothesis of transitivity, nevertheless demotes to three term consistency.

Demand Theorem – Rise and Drop in Price

            Based on the above postulations, Samuelson states his theorem as demand theorem thus “Any good that is always to increase in demand when money income alone rises must definitely shrink in demand when its price alone rises.” It means that when earnings elasticity of demand is positive price elasticity of demand is negative.

            Likewise for drop in price, the definition goes like this “Any good that is recognised always to decrease demand when money earnings alone drops must definitely expand in demand when its price alone drops.”

Derivation of Indifference Curve From Revealed Preference

            Let us now discuss work of Samuelson on this topic of constructing indifference curve with mush methodical way.
Postulations

  1. There is transitivity in customer’s inclinations
  2. He prefers combination of more articles to less in any condition
  3. His likings have not been changed
  4. There is consistency in his market performance
  5. There are two commodities R and S. Based on the above hypothesis, customer chooses a specific combination of the two articles for one of the two causes, one of the chosen combinations is favoured to all other combinations or the one which is not chosen lies outside his budget line. Let us now see the first picture representation.

            If the customer divulges his inclination for Combination C on his first budget line AB, all other points on and below the line AB proves inferior zone. On the other hand points above and / or to the right of C in the vicinity ECD are favoured to C as they have more of article R and / or S. Thus the shaded vicinity ECD above C is called Preferred Zone.

            Still more there are combinations of the articles in the vicinity below ECD and above the line AB to the left and right of C that are not ordered by the customer. They are ECA and DCB and are called Ignorance zone for the cause that the customer’s inclinations are not recognised in them.

            It follows that the indifference curve must pass through C and lie below the vicinity ECD and above the budget line AB. It must be negatively inclined and convex to the origin from the point C, as it will be in the upper and lower zones of ignorance. Now let us discuss about the second sketch.

            To uncover out the exact location of the indifference curve let us first assume that the price of article S drops so that the customer’s new budget line is JK which cuts the main line AB at point P below point C. Now the customer will choose one of the combinations P or any other combination on the PK fragment on the like JK. All other points on JP fragment of this line to the left of P would be conflicting with his choice for the cause that they lie in the inferior to C. Thus the triangle PKB is sliced off from the lower ignorance zone.

            By modelling such budget lines below point C and applying the same causing, the whole the portion below C in the lower ignorance zone can be eradicated. Likewise we can slice off points to the left of C in the upper ignorance zone of this sketch. In case the price of R increases in the new budget line VM passes through the original point C which shows the same real income as at point C.

            Consider that the customer chooses a new point, say H on the budget line VM. Thus he divulges his inclination for H to C, both being on the same budget line. But all combinations in the vicinity FHG to the right and above H are favoured to H for the cause that this vicinity denotes combinations which have more of one of the articles than the combination H.

            In other words H is favoured to C and FHG is favoured to H. Thus by ranking the combinations in the vicinity GAHT as favoured to C, we have eradicated some of the upper ignorance zone. By repeating this procedure, we narrow down the ignorance zone and eventually locate the indifference curve which is denoted in the next figure. Here is the third picture’s description.

                                           

            The form of the indifference curve is revealed in this picture. It shows the curve I to be convex to the origin at Point C for the cause that it passes through the lower and upper ignorance zones.

            To provide auxiliary evidences, first we consider AB as the straight line indifference curve. The line AB cannot be an indifference curve for the cause that the choice of C divulges all other points on AB to be inferior to C and the customer cannot be at the same time indifferent between point C and any other point AB.

            Second, it cannot be a curve like I2 as revealed in the picture intersecting the line AB at point C for the cause that all points below C have been divulged inferior to C and the customer is indifferent to them.

            Third, the indifference curve cannot be concave through C like the curve I1, for the cause that the upper and lower portions of this curve are in the inferior zone and all points have been divulged inferior to C. Hence, the indifference curve can only be convex to the origin, as curve I in this picture.

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