We now proceed to derive from indifference curve analysis a law of demand which should state in general terms the relationship between price and quantity demanded of a good. In other words, we will try to derive a general demand theorem which describes the direction in which quantity demanded of the good will change as a result of a change in price of a good.

In order to understand the way in which price-demand relationship is established in indifference curve analysis, consider Fig. 8.38. Given the price of two goods and his income represented by the budget line BL1, 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 BL1.

The consumer will now be in equilibrium at a point on the new budget line BL1. If the equilibrium position on BL2 lies to the right of Q such as at R in Fig. 8.38, it will mean that the consumer buys more quantity of good X than at Q. And, if the equilibrium position on BL2, lies to the left of Q such as at H in Fig. 8.38, it will show that the consumer buys less of good X than at Q. Now, it can be proved that the new equilibrium point on BL2 will usually lie to the right of Q, meaning thereby that the quantity demanded of the good X will increase as its price falls.

As seen above, the direction and magnitude of the change in quantity demanded as a result of the fall in price of a good will depend upon the direction and strength of income effect on the one hand and substitution effect on the other. If the income effect is positive, as is normally the case, it will work towards increasing the quantity demanded of good X when its price falls. The substitution effect which is always negative 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, both the income effect (when positive) and negative substi­tution effect will so act as to increase 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. This case is illustrated in Fig. 8.38 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 BL2 to the level indicated by BL2 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 good will vary inversely with its price when 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 the 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 the 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 the price of the 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 the 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.

Here 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 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 incorrect 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, 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 the price of the good falls, a good amount of the 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 the 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 the price of the inferior bread falls, people will purchase less than before. This is because the fall in the price of the bread on which they spend a very large portion of their income causes such a large increase in their purchasing power that, bread is an inferior good there and accounts for a bulk of their budget expenditure will create a large negative income effect. They will therefore reduce the consumption of bread when its price falls since large negative income effect outweighs the substitution effect.

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;