Relationship between “Price Elasticity”, “Income Elasticity” and “Substitution Elasticity”

Price elasticity of demand depends upon the income elasticity and substitution elasticity in the same manner in which price effect depends upon the income effect and substitution effect discussed in Chapter 5 on Ordinal Utility Approach.

The relationship between the three elasticities can be expressed in the form of a mathematical formula as follows:

e_p =k_x e_y +(l- k_x)e_s

Where

e_p is the price elasticity of demand

e_y is income elasticity of demand

e_s is elasticity of substitution

k_x is proportion of the income of the consumer spent on good ‘X’

This equation expressing the relationship between the three elasticities holds good in all the situations. If we know any two elasticities, we can always calculate the third elasticity, if the proportion of money income spent on the commodity is also given.

image source: 8e57487048d92f1d4381-b1cf9e400bde416ba8b02c6592a8690c.r16.cf2.rackcdn.com

The first part (k_x e_y) of this equation shows that increase in the demand for a commodity depends firstly upon the income effect of a fall in the price of the good. This in turn depends upon the proportion of income spent on the good, because this determines the amount of income previously spent on good ‘X’ is available for spending, as this good has now become cheaper.

Given e_y , greater the proportion of income spent on good ‘X’, the greater the income saved by the fall in its price, which is now available for purchasing more units of ‘X’ and other good(s). Secondly, the increase in the demand for a commodity depends upon the numerical value of its income elasticity of demand.

The income elasticity of demand determines what part of income (k) saved by the fall in the price of good ‘X’ will be spent on this good and what part will be spent on other good(s). The first part of the equation, thus, shows the influence of the income effect on price elasticity of demand.

The second part (1 – k ) e_s of the equation shows that price elasticity of demand depends firstly upon the extent to which it is possible to substitute good ‘X’ for, say, good ‘Y’ (substitution effect of a fall in the price of the good), because good ‘X’ has now become cheaper. In other words, it depends upon the elasticity of substitution. It also depends upon the amount of good ‘Y’ that the consumer was buying before the fall in the price of good ‘X’.

The extent to which one can switch over from good ‘Y’ to good ‘X’ depends upon the amount of good ‘Y’ that he was buying before the fall in the price of good ‘X’. If one was not buying good ‘Y’ before, one cannot substitute good ‘X’ for it.

The expression (1 – k ) in the equation shows the proportion of income which is not spent on good ‘X’. This proportion determines the limits within which substitution of good ‘X’ for good ‘Y’ is possible.

We may conclude that price elasticity of demand for a particular commodity is determined by the (i) proportion of income spent on the commodity, (ii) income elasticity of demand, (iii) proportion of income spent on other good(s) and (iv) elasticity of substitution.

Price elasticity can be calculated, if we know the first three factors. Income elasticity of demand and elasticity of substitution help us in understanding, why the price elasticity of a particular good is high or low. The income elasticity of demand for a necessity like salt is low and a consumer spends a very low proportion on it.

The elasticity of substitution between salt and other goods is also low due to unavailability of its substitutes. On account of this reason, salt has low price elasticity. On the contrary, price elasticity of demand for luxury goods like VCRs, cars, etc. is high on account of high income and substitution effects. The consumers also spend a large portion of their income on such goods. Hence, these goods have high price elasticity.