The objectives of this lecture are :

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1 SPARATION OF INCO FFCT AND SUBSTITUTION FFCT TH HKSIAN THOD In the last episode or in the first episode we had discussed about the Sluskian method. In this episode we are going to discuss about the Hicksian method. The objectives of this lecture are : 1. To understand the Hicksian method of Separation of Income ffect and Substitution ffect of a price change and 2. To learn how income effect is used to classify goods into superior goods, normal goods, neutral goods, inferior goods and Giffen goods. HKS S THOD 1 GOOD Y O Q Q 2 N Q 1 N 2 N 1 X Now in this diagram, that you see on this screen, according to this method in order to keep real income constant, the consumer s money income should be reduced so much, that he is forced to go to the original indifference curve. In this diagram, we have reduced the consumer s money income by 1 and drawn a new income price line 1 N 2. The new price line 1 N 2 is tangential to the initial indifference curve at the point 2. Thus, according to the second method, the consumer s real income is constant at 2 and not at point as was in the case of Slutsky s method. At the point 2 the quantity demanded is OQ 2. Before the price of X fell, the quantity demanded was OQ. Thus, the net increase is QQ 2 after cancelling out of the income effect. This increase, is due to the substitution effect. Now if we give the consumer back what we have taken away from him earlier, he will move back to 1, revealing to us the income effect. He will move back to 2 He will move back to 1 which means to say that Q 2 Q 1 increase in

2 demand is due to the income effect. The total Increase QQ 1 consequent to the fall in the price of X can be accounted for thus: QQ 2, which is the substitution effect and Q 2 Q! which is the income effect. It is thus clear that, for a given fall in the price of X, the substitution effect is greater according to Slutsky than according to Hicks. The Hicksian method is more scientific than Slutsky s method as pointed out earlier. In the Hicksian method, under the substitution effect, the consumer moves along the same indifference curve, though he rearranges his purchase of the two commodities. He is not allowed to move to a higher indifference curve, which is not the case in the Slutskian method, where, he is able to move to a higher indifference curve, and thereby become better off than before. In Hicks method, the consumer becomes neither better off nor worse off as a result of the compensating variation in income. According to Hicks method the consumer remains on the same indifference curve though he moves from point Q to Q 2, Hicks method therefore confirms more to the accepted interpretation of compensating variation in income than Slutsky s method. It would therefore be conducive to better understanding if we separate the income effect and the substitution effects of price change with the application of the Hicksian method. This means that when Hicks applies the compensating variation in income, he is not trying to bring the consumer back to the original combination as Slutsky does, but he is trying to bring back the consumer to the original level of satisfaction. i.e., the new budget line after application of the compensating variation in income, the new budget line is tangential to the initial indifference cure at 2and thereby it pins the consumer to that point and he will not be able to move to a higher indifference curve and thus, the income effect is cancelled out fully. Where as, in the Slutskian method, the income effect was not cancelled out fully and this was why the consumer was able to move to a situation which makes him better off. Some people have made differences between these two applications, the Slutskian application of change in income and the Hicksian application of change in income. While the Hicksian method is known as Compensating Variation in Income, the Slutskian method is known as Cost Difference, and this is how some sort of a difference arises between the Sluskian and Hicksian methods, but we have seen that scientifically, the Hicksian method is superior... Classification of Goods: Now let us move to the next aspect. How does this Income effect help us in classifying goods? One important thing that we should remember about these two effects is that, the substitution effect is always positive for a fall in the price; because, here in this case when the price falls, demand changes/demand increases and therefore there is a positive change in demand. Substitution effect will always be positive because a cheaper commodity is always substituted for the costlier commodity. As a consequence, the quantity demanded of a commodity whose price has fallen, must always increase because it is bound to be substituted for the commodity whose price has risen. Though the Substitution effect is always positive, the same thing cannot be said of the Income effect.

3 The income effect may be positive, negative or zero according to the nature of the commodity under consideration. In the case of a superior or neutral commodity, the income effect is bound to be positive. If however the commodity happens to be an inferior or sub-normal one, the income effect is bound to be negative. When the negativeness of the income effect more than cancels out the positiveness of the substitution effect, it implies that the quantity demanded of such a commodity, other things remaining constant or same, decreases with the increase in the consumer s income and vice versa, and such a good is called a Giffen good. In the case of other commodities whose quantity demanded does not respond to the changes in the consumer s income one way or the other, the income effect will be zero. Such commodities are termed as Neutral commodities. Let us try to understand these things with the help of some diagrams: From the diagram that you see on the screen, it can be seen that initially, when the price is at P, the quantity demanded is OQ, and when the price has fallen, then the consumer moves to 1 on the indifference curve 1, and the quantity purchased is OQ 1. This change in demand due to a change in price is known as the price effect; i.e., QQ 1 is the price effect. Now, if we apply the compensating variation in income as suggested by Hicks, and we take away some of the income of the consumer to bring him back to the original level of satisfaction, In the diagram, you can see that initially the consumer was buying OQ quantity of the good, and when the price fell, he moved to indifference curve 1 which specifies OQ 1 as the quantity and he is at equilibrium at 1. The change in demanded which has taken place due to the fall in price is QQ 1. QQ 1 Is known as the price effect. Now let us apply the Hicksian compensating variation in income and bring back the consumer to the original level of satisfaction. It implies that, when you are taking away money from the consumer, the budget line N 1 slides downwards until it reaches N 2, which is tangential to the initial indifference curve, and the consumer is at equilibrium at 2, showing that the demand now, after canceling out the income effect, the remaining demand is OQ 2 and the change in demand is QQ 2. This change in demand QQ 2, which is derived after canceling out the income effect, is obviously the substitution effect. When we give back the amount that we had taken from the consumer, then the consumer moves back from 2 to 1. This is the income effect. So we can clearly see that when the consumer is moving from 2 to 1, the quantity is increasing and so the income effect is positive in this case. We had learned that substitution effect is always positive when the price falls, but the income effect may be positive, negative or zero. In this case income effect is positive. Now in the next diagram, we have a situation where income effect is negative.

4 INCO FFCT IS POSITIV IN TH CAS OF A NORAL OR SUPRIOR GOOD HKS THOD IN TH CAS OF NORAL GOOD 1 GOOD Y O Q Q 2 N Q 1 N 2 N 1 X INCO FFCT IS NGATIV IN TH CAS OF A SUBNORAL OR INFRIOR GOOD HKS THOD GOOD Y 2 O Q Q 1 Q 2 N N 2 N 1 X

5 INCO FFCT IS GRATR THAN SUBSTITUTION FFCT - IN TH CAS OF A GIFFN GOOD (Which Is A Special Case Of an Inferior Good) 1 HKS THOD 1 GOOD Y 1 2 O Q 1 Q Q 2 N N 2 N 1 X INCO FFCT IS ZRO IN TH CAS OF NUTRAL GOOD HKS THOD GOOD Y 2 O Q Q 2 N N 2 N 1 X

6 As you can see, when the price has fallen, the consumer moves from to 1 and this is known as the price effect. Price effect constitutes Income effect plus Substitution effect. But when compensating variation in income is applied, the budget line slides from N 1 to 1 N 2, which is tangential to the initial indifference curve at 2, and you can see that the substitution effect is greater. We can see that the substitution effect is now 2 or QQ 2 in terms of quantity. This is the substitution effect. Now when you give back the amount that you took from the consumer, he will move from 2 to 1 and that constitutes the income effect. We can see that there is a reduction in the quantity from OQ 2 to OQ 1. Therefore, income effect is negative in this case. The total change in demand will only be to the extent of QQ 1. Here, we have seen a case where income effect is negative but it does not cancel out the whole of the substitution effect. The income effect may be negative to such an effect that it cancel out the substitution effect, it may more than cancel out the substitution effect also. So let us look at these cases in the next diagrammes In the diagram that you see now on your screen, you can clearly see that the negative ness of the income effect is greater than the positiveness of the substitution effect and therefore more than cancels out the substitution effect, and therefore, when the price has fallen, the demand has reduced. Let us look at this diagram in more detail. Initially, the consumer was at point on Indifference curve and the quantity that he purchased was OQ. When the price fell, the quantity decreased and the consumer moved from to 1.which lies on indifference curve 1. Thereby, the quantity purchased now is OQ 1. In other words, the price fall has lead to a reduction in demand, rather than leading to an increase in demand. Now let us look at the components of this price effect. When we apply the compensating variation of income to the consumer, the budget line N 1, slides downwards parallely because you have taken away money to the position of 1 N 2, which is tangential to the initial indifference curve, thereby bringing back the consumer to the original level of satisfaction. In other words, the consumer after the application of the compensating variation in income, has shifted from 1 to 2. Now the substitution effect is QQ 2. Substitution effect will always be positive as we have seen. So QQ 2 is the substitution effect. Now, when you give back the money that you have taken from the consumer, to him He will move back to 2, and this constitutes the income effect. Here, we can see that the income effect, more than cancels out the positiveness of the substitution effect and thereby, on the whole, demand falls rather than increasing due to a fall in the price. Such a good is known as a Giffen good Now, Giffen good is an extreme case of an inferior good. Inferior goods are goods that have a negative income effect. The negative ness of the income effect may be smaller than the positiveness of the substitution effect, it may be equal to the positiveness of the substitution effect, it may be also as in this case be greater than the positiveness of the substitution effect and such a case of inferior good is a special case of an inferior good and it is know as a Giffen good. Summary: In this lesson, we have tried to understand the Hicksian method of Separation of Income ffect and Substitution ffect of a price change and also to learn how income effect is used to classify goods into superior goods or normal goods, neutral goods, inferior goods and Giffen goods. We have learnt that, while separating the income effect and the

7 substitution effects of a price change, Hicks applies the Compensating Variation in Income in such a manner that the consumer is brought down to the original or initial level of satisfaction. With regard to classification of goods, we have learnt that the income effect is used for this purpose. A fall in price may lead to a positive income effect or a negative income effect or an income effect that is equal to zero. Such goods that experience a positive income effect is positive, due to a fall in price are known as normal goods or superior goods. Goods that experience a negative Income effect are known as sub-normal or inferior goods. In this case, we had learnt that three possible situation can arise; the negativeness of the Income effect may be weaker than the positiveness of the substitution effect. In this case, demand will increase even though it is an inferior good. The negativeness of the Income effect may just be equal to the positiveness of the substitution effect and in this case demand will not change due to a fall or change in price. Another situation that can arise in the case of some goods is that Income effect is zero and here also demand will rise due to a fall in price such goods are called Neutral goods. The last case that can arise is that the negativeness of the Income effect, more than outweighs the positiveness of the substitution effect due to a fall in price and here the demand will fall rather increase due to a fall in price and such goods are called Giffen goods and these are a special type of inferior goods. Questions: 1. How does Hicks attempt to separate the Income effect and Substitution effect of a change in price? 2. How is Hicks method different to Slutsky s method? 3. How is the income effect used in classifying goods into superior, inferior neutral and Giffen goods?. References: 1. icro conomics by Pendik and Rubenfeld 2. icro conomics by.l. Seth