Indifference curve analysis with its technique of looking upon the price effect as a combination of income effect and substitution effect explains relationship between price and quantity demanded in a better and more analytical way.

A distinct advantage of viewing the price effect as a sum of income effect and substitution effect is that through it the nature of response of quantity purchased to a change in the price of a good can be better and easily explained.

In case of most of the goods, the income effect and substitution effect work in the same direction. But, in some cases, they may pull in different directions. The direction of substitution effect is quite certain. A fall in the relative price of a good always leads to the increase in quantity demanded of the good. In other words, substitution effect always induces the consumer to buy more of the cheaper good.

But the direction of income effect is not so certain. With a rise in income, the individual will generally buy more of a good. But with the rise in income the individual will buy less of a good if it happens to be an inferior good for him since he will use better or superior substitutes in place of the inferior good when his income rises. Thus the income effect may be either positive or negative. For normal goods, the income effect is positive.

Therefore, when price of a normal good falls and results in increase in the purchasing power, income effect will act in the same direction as the substitution effect, that is, both will work towards increasing the quantity demanded of the good whose price has fallen. For the inferior good in which case income effect is negative, income effect of the price change will work in opposite direction to the substitution effect.

The net effect of the price change will then depend upon the relative strengths of the two effects. To sum up, price effect is composed of income effect and substitution effect and further that the direction in which quantity demanded will change as a result of the change in price will depend upon the direction and strength of the income effect on the one hand and strength of the substitution effect on the other.

Price Demand Relationship: Normal Goods:

In order to understand the way in which price-demand relationship is established in indifference curve analysis, consider Fig 8.43. Given the price of two goods and his income represented by the budget line PL1, the consumer will be in equilibrium at Q on indifference curve IC1. Let us suppose that price of X falls, price of Y and his money income remaining unchanged so that budget line now shifts to PL2.

The consumer will now be in equilibrium at a point on the new budget line PL2. If the equilibrium position on PL2 lies to the right of Q such as at R in Fig. 8.43, it will mean that the consumer buys more quantity of good X than at Q. Now, it can be proved that in case of normal goods the new equilibrium point on budget line PL2 thereby that the quantity demanded of the good X will increase as its price falls.

The direction and magnitude of the change in quantity demanded as a result of fall in price of a good depend upon the direction and strength of income effect on the one hand and substitution effect on the other. As for normal goods, the income effect is positive, it will work towards increasing the quantity demanded of good X when its price falls. The substitution effect which is always negative and operates so as to raise the quantity demanded of the good if its price falls and reduces the quantity demanded of the good if its price rises.

Thus, in case of normal goods both the income effect (when positive) and negative substitution effect work in the same direction and cause increase in the quantity purchased of good X whose price has fallen with the result that the new equilibrium point will lie to the right of the original equilibrium point Q such as point R in Fig. 8.43 above. Substitution effect causes MK increase in quantity demanded. Income effect which is positive here also leads to the increase in quantity demand by KN. Each effect therefore reinforces the other.

As a result, the total effect of a fall in price of X from the level indicated by PL1 to the level indicated by PL2 is the rise in quantity demanded of good X from OM to ON, that is, quantity demanded increases by MN which is equal to MK + KN. To sum up, the income effect and substitution effect in case of normal goods work in the same direction and will lead to the increase in quantity demanded of the good whose price has fallen. In other words, quantity purchased of a normal good will vary inversely with its price as in its case income effect is positive.

#### Price-Demand Relationship: Inferior Goods:

In case of inferior goods the income effect will work in opposite direction to the substitution effect. When price of an inferior good falls, its negative income effect will tend to reduce the quantity purchased, while the substitution effect will tend to increase the quantity purchased. But normally it happens that negative income effect of change in price is not large enough to outweigh the substitution effect.

This is so because a consumer spends a very small proportion of his income on a single commodity and when price of a commodity falls, a very little income is released. In other words, income effect even when negative is generally too weak to outweigh the substitution effect.

It follows therefore that as a result of fall in price of a good the .substitution effect which always induces the consumer to buy more of the good whose price has fallen will usually outweigh the negative income effect. Thus even in most cases of inferior goods the net result of the fall in price will be increase in its quantity demanded. It is thus clear that in a majority of inferior goods quantities demanded of the good will vary inversely with price and the Marshallian law of demand will hold good.

The price-demand relationship in case of inferior goods having weaker income effect is illustrated in Figure 8.45. It will be seen from Fig. 8.45 that the fall in price of good X makes the consumer to shift from equilibrium at Q to a new equilibrium at R. As a result, quantity purchased of good X increases from OM to OT. But the income effect is negative and is equal to HT.

If income effect alone was working, it would have caused the consumer to buy HT less of good X. But substitution effect is universally present and always induces the consumer to buy more of the relatively cheaper good. In Fig. 8.45 substitution effect is equal to MH and is greater than negative income effect HT.

Therefore, the net effect of the fall in price of good X is the increase in quantity demanded by MT. Hence we conclude that in case of inferior goods, quantity demanded varies inversely with price when negative income effect is weaker than the substitution effect. In other words, even in case of inferior goods having weaker income effect, the demand curve will be downward sloping.

Price-Demand Relationship: Giffen Goods or Giffen Paradox:

There is a third possibility. This is that there may be some inferior goods for which the negative income effect is strong or large enough to outweigh the substitution effect. In this case, quantity purchased of the good will fall as its price falls and quantity purchased of the good will rise as its price rises. In other words, in this case quantity purchased or demanded will vary directly with price.

Now, the income effect can be substantial only when the consumer is spending a very large proportion of his income on the good in question so that when price of the good falls, a good amount of income is released. If that good happens to be inferior good, the income effect will be negative as well as strong and may outweigh the substitution effect so that with the fall in price, the consumer will buy less of the good.

Such an inferior good in which case the consumer reduces its consumption when its price falls and increases its consumption when its price rises is called a Giffen good named after the British statistician, Sir Robert Giffen, who in the mid- nineteenth century is said to have claimed that when price of cheap common foodstuff like bread went up the people bought and consumed more bread.

A rise in the price of bread caused such a large decline in the purchasing power of the poor people that they were forced to cut down the consumption of meat and other more expensive food. Since bread even when its price was higher than before was still the cheapest food article, people consumed more of it and not less when its price went up. Similarly, when price of an inferior good, on which people spend a large proportion of their income, falls people will purchase less than before.

This is because the fall in price of an inferior good on which they spend a very large portion of their income causes such a large increase in their purchasing power that creates a large negative income effect. They will therefore reduce the consumption of that good when its price falls since large negative income effect outweighs the substitution effect.

The price-demand relationship in case of a Giffen good is illustrated in Fig. 8.46. With a certain given price-income situation depicted by the budget line PL1, the consumer is initially in equilibrium at Q on indifference curve IC1. With a fall in price of the good, the consumer shifts to point R on indifference curve IC2. It will be seen From Fig. 8.46 that with the fall in price and, as a result, the shift of the budget line from PL1 to PL2 the consumer reduces his consumption of the good X from OM to ON.

This is the net effect of the negative income effect which is here equal to HN which induces the consumer to buy less of good X and the substitution effect which is equal MH which induces the consumer to buy more of the good. Since the negative income effect HN is greater than the substitution effect MH, the net effect is the fall in quantity purchased of good X by MN with the fall in its price. Thus, the quantity demanded of a Giffen good varies directly with price. Therefore, if a demand curve showing price-demand relationship of a Giffen good is drawn, it will slope upward.

Thus, the quantity demanded of a Giffen good varies directly with price. For a good to be a Giffen good, the following three conditions are necessary:

(1) The good must be inferior good with a large negative income effect;

(2) The substitution effect must be small; and

(3) The proportion of income spent upon the inferior good must be very large.

Three Demand Theorems Based on Indifference Curve Analysis:

It follows from above that, indifference curve analysis enables us to derive a more general law of demand in the following composite form, consisting of three demand theorems to which the Marshallian law of demand constitutes a special case:

(a) The quantity demanded of a good varies inversely with price when the income effect is positive or nil.

(b) The quantity demanded of a good varies inversely with price when the income effect for the good is negative but is weaker than the substitution effect.

(c) The quantity demanded of a good varies directly with price when the income effect for the good is negative and this negative income effect of a change in price is larger than the substitution effect.

In the case, (a) and (b) the Marshallian law of demand holds good and we get a downward sloping demand curve. The case (a) applies to normal goods in which income effect and substitution effect work in the same direction. The case (b) applies to inferior goods which are not Giffen goods. When the third case occurs, we get a Giffen good of positively sloping demand curve. Marshallian law of demand does not hold true in the third case.Marshall mentioned a Giffen good case as an exception to his law of demand.

Thus the indifference curve analysis is superior to Marshallian analysis in that it yields a more general law of demand which covers the Giffen-good case. The explanation for the occurrence of a Giffen good is that in its case the negative income effect outweighs the substitution effect. Since Marshall ignored the income effect of the change in price, he could not provide a satisfactory explanation for the reaction of the consumer to a change in price of a Giffen good.

However, it may be pointed out that it is very hard to satisfy theabove mentioned third conditions for the occurrence of the Giffen good, namely, the consumer must be spending a very large proportion of his income on an inferior good. Therefore, although Giffen good case is theoretically possible the chance of its occurrence in the actual world is almost negligible.

This is because consumption of the people is generally diversified so that people spend a small proportion of their income on a single commodity with the result that price-induced income effect even when negative is generally small and cannot therefore outweigh the substitution effect. Marshall believed that quantity demanded could vary directly with price, and,asmentioned above. Sir Robert Giffen is said to have actually observed this phenomenon.