## Difference between “Income Elasticity of Demand” and “Cross Elasticity of Demand”

Income elasticity of demand may be defined as the ratio of the proportionate change in the quantity demanded of a commodity to a proportionate change in the income of the consumer. Thus, income elasticity of demand, ey of any commodity is

Where,

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q stands for the quantity demanded.

y stands for the income of the consumer.

?q stands for the change in the quantity demanded

?y stands for the change in income of the consumer.

For example, income of the consumer increases from Rs. 500 to Rs. 600, resulting in an increase in the quantity demanded from 10 units to 15 units. Then,

For most of the goods, income elasticity of demand will be positive, as with increase in the level of income, people tend to spend more on the goods. Such goods are called normal goods. But, people divide their increased income among various goods differently.

On some goods, they will spend a larger proportion of their increase in income (large value of e) and on other goods, they may spend a smaller proportion (small value of ey). According to Engel, the percentage of income spent on food and other necessities by the poor is more. It declines as income rises.

This is known as Engel’s law, which can be used as a measure of welfare and the development stage of the economy. Hence, numerically, values of ey may differ considerably. (Case of negative income elasticity has been discussed in the next section). However, the
weighted sum of income elasticity of demand for various goods must add up to one. (Proved in Problem 12).

Determinants:

Income elasticity of demand depends on the time period, because consumption patterns adjust with a time tag to changes in income. For non durable goods, short run income elasticity is lesser than long run income elasticity. Opposite is the case for durable goods. It also depends on the nature of the commodity.

Importance:

Income elasticity of demand is useful in classification of goods into luxuries, necessities and inferior goods. Producers should invest in industry with high income elasticities except during recession. The concept of elasticity of demand is also useful in forecasting demand for commodities over time. With this production strategies can be developed to meet the demand requirements.

Some Important Income Elasticity:

We have seen that in the price elasticity of demand, elasticity equal to one was very important as it made the division between elastic and inelastic demands. But, in the case of income elasticity of demand, there is no unique dividing line. It is not easy to say at once as to what are the most important values of income elasticity.

However, the following income elasticities of demand seem to be interesting, which show that an understanding of the income elasticity of demand useful both for business firms as well as the Government.

First, zero income elasticity is of great significance. It implies that demand for commodity does not change with the change in income. In this case, consumer does not spend anything on the commodity out of the increase in his level of income.

Consequently, consumer’s expenditure on the commodity under consideration does not increase with the increase in his income. Zero income elasticity in this way becomes a dividing line. On one side of this line are the goods, whose income elasticity is positive. With the increase in income, more quantity of such goods is bought.

This is the case with most of the goods (normal goods). On the other side of this line are the goods whose income elasticity is negative. It means that with the increase in the income, consumer spends less on these goods. In other words, increase in income leads to a fall in the quantity purchased of these goods.

How much fall in the quantity purchased will be, depends upon the numerical value of the income elasticity. These goods are called inferior goods, because, with the increase in the income, consumer does not like to consume these goods. Instead, he purchases some better goods whose income elasticity is positive.

Second important value of income elasticity of demand is one. In this case, demand for a good rises in proportion to rise in income. This means that consumer continues to spend the same proportion of his income on the good under consideration, as he was spending before the rise in income. Engle curve starting from origin (OA in Fig 2.19) has income elasticity of demand equal to one. Here,

If the elasticity of demand is greater than one, it means that he spends a larger proportion of the increase in income on the good than he was spending before the rise in income. And if the income elasticity of demand is less than one, it means that he spends a smaller proportion of the increase in income than he was spending before the increase in income.

One can think that if after the increase in income, consumer spends a larger proportion on a good (ey > 1), it should be a superior good or a luxury. On the other hand, if proportion of the consumer’s income spent on a good falls (ey < 1), it is a necessity or an inferior good.

In first case, demand for commodity rises more than in proportion to a rise in income, while in the second case demand for commodity rises less than in proportion to a rise in income, resulting in concave and convex shaped Engel curves respectively.

Income elasticity exceeding one implies that the sales of the product will rise more rapidly than economic growth. Likewise, income elasticity lowers than one implies that the sales of the product will rise, but, slower than the economic growth. If the economy is growing at 5% and income elasticity of demand is 0.2, a firm in the industry can expect annual sales rise of 5% x 0.2 = 1%.

Similarly, if income elasticity is 2, firms can expect sales to grow at the rate of 5% x 2= 10% annually. In the former case, the product of the firm lags economic growth, while, in the latter case, the product leads to economic growth.

Firm with product having high income elasticities have good growth opportunities in the expanding economy. This poses a serious problem for the policy makers of most of the developing economies plagued by this disease. Whether the product will lag or lead economic growth can be known from the value of elasticity of demand of the product.

Similarly, in times of recession, decline in the sales of the firm will be slower or faster than the decline in economic activity, depending on whether income elasticity is less than one or exceeds one in the two cases respectively. Firms whose products have low income elasticities neither gain much, if the economy neither expands nor lose much, if the economy retards.

On the other hand, firms having product with high income elasticities indicate susceptibility to fluctuations in economic activities. Thus, the knowledge of income elasticities is useful in forecasting the effects of changes in economic activity on demand and hence in planning the product mix by the business firms.

Now, it can be concluded that income elasticity of demand is different for different goods Luxuries like cars, jeweller’, precious stones, etc. have high elasticity. While necessities like vanaspati ghee, soap, salt, matches, etc. have low elasticity. By and large, income elasticity is higher for durable goods than for non-durable goods.

However, for a same good, value of elasticity coefficient may be different at different levels of income. Fig. 2.19 shows the relationship between income and consumption. As the income increases level of consumption rises showing a positive income elasticity of demand.

The maximum consumption demand is at OB level of income. Consumption becomes constant in the income range OB to OC, showing zero income elasticity. Beyond OC, income elasticity of demand becomes negative, i.e., a further increase in income causes a fall in consumption demand.

Cross Elasticity of Demand:

Sometimes two goods are related in such a way that the change in the price of one good causes a change in the quantity of the other good. The degree of responsiveness in the demand for one good to the change in the price of the other good (substitute or complement) is called the cross elasticity of demand.

It is measured as the ratio of percentage change in amount demanded of one commodity to the percentage change in price of other commodity. Let the quantity demanded of commodity ‘X’ depends upon the price of commodity ‘Y’ Cross elasticity of demand (ec) between ‘X’ and ‘Y’ is:

If the price of coffee rises from Rs. 100 per kg. to Rs. 125 per kg. and consequently demand for tea increases from 10 kg. to 15 kg, the cross elasticity of demand between tea and coffee will be

Cross elasticity of demand is positive for substitutes and negative for complements. The magnitude of the value shows the extent of closeness of the relationship between the two commodities. The higher is the value of the cross elasticity, the stronger will be the degree of substitutability or complementarily of the two goods.

In extreme case, when the two goods are perfect complements, the cross elasticity of demand between them is minus infinity. Similarly, for perfect substitutes, cross elasticity of demand is plus infinity. If the two goods have no relation between them, the cross elasticity of demand is zero.

Determinant:

The main determinant of cross elasticity of demand is the nature of the commodities relative to their uses. The cross elasticity is high, when the two commodities satisfying the same need equally well and vice-versa.

Importance:

The knowledge of cross elasticity is important for business firms operating in markets with different brands competing with each other. Such information helps them to find the effects of change in price of one brand on the others supplied by the competitors. If the cross elasticity of demand between two rival products ‘A’ and ‘B’ is 2, the firm of product ‘A’ can expect 20 percent rise in demand for its product with every 10 per cent rise in the price of product ‘B’.

Thus, cross elasticities play a vital role under monopolistic competition and oligopoly in taking price, output and product decisions, so as to avoid potential loss from rivals’ strategies. Further, by keeping the cross elasticities between its product and other similar ones, firm can prove that substitutes are close and buyers have effective choice. This will protect it from anti-trust laws.

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