Note on Decomposition of Price Effect Into Income and Substitution Effect

• Note
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Meaning

A change in demand for a commodity, say X, due to change in the price of the same commodity (i.e. X) is called price effect. The price effect describes the phenomenon on the consumer’s purchases for a commodity (say X good) when its price changes, given consumer's tastes & preferences, his income and the price of good Y remains constant. It shows the total effect on consumer's demand for a commodity due to the change in the price of the same commodity, other things being equal. The total price effect consists of two direct effects of price change on consumer's choice i.e. (i) Income effect and (ii) Substitution effect.

Substitution effect arises due to the change in the relative price of a commodity. It happens due to the absolute change in the price of the same commodity. When the price of one commodity increases (or decreases), it becomes relatively dearer (or cheaper) than the other. The consumers have an inherent tendency to substitute cheaper goods for relatively dearer ones. This is called substitution effect. A change in the relative prices of goods makes a rational consumer substitute a relatively cheaper commodity for the dearer one. Such effect of the change in relative prices of goods is described as the substitution effect. Under this effect, the consumer will tend to buy more of a good, the price of which has fallen and less of the good price of which has remained unchanged or has increased as he would reallocate his expenditure in favor of the relatively cheaper good and substitute for the dearer one.

It was assumed that the income level of the consumer remains constant or unchanged in the consumer's equilibrium analysis, given the prices of two goods X and Y. If the income level of the consumer changes (i.e. either increases or decreases), then there is the effect in the purchase decision, given the prices of the two good, and tastes & preferences of the consumer. This effect on the demand or purchasing decision is known as income effect. Income effect shows the total effect on demand for goods due to the change in income of the consumer, other things being equal.

Thus, total price effect is composed of income and substitution effect. There are two methods of decomposing total price effect into income and substitution effects. They are as:

• Hicksian approach
• Slutchky approach

Decomposition of price effect into income and substitution effects with a fall in price of normal goods under Hicksian approach

In the figure, suppose that consumer is initially in equilibrium position at E1 on the indifference curve IC1 where initial budget line AB is tangent to indifference curve IC1. Here, the consumer buys (or purchase) OQ1 units of X good and ON1 units of Y good. Now, suppose the price of X falls or decline other things being equal (i.e. the price of Y and level of income of the consumer remains unchanged or constant), the initial budget line AB shifts rightward to AC due to the increase in purchasing power of consumer for X good. The new budget line (AC) is tangent to IC2 at the point E2 and the consumer reaches a new equilibrium. The new equilibrium shows that the consumers purchase (or buys) OQ2 units of X good and reduces N1N2 units of Y good. This process of adjustment on the consumption X and Y is called total price effect.

Now the problem is how to split the price effect of X good (i.e. Q1Q2) into the income and substitution effects since price effect (PE) is composed of income effect (IE) and substitution effect (SE) i.e. PE = IE + SE. If we measure any of these effects (IE or SE), we can easily find the others. Hicks suggested a convenient and direct way measure first the income effect.

According to Hicks, the consumer can be bought to the initial indifference curve IC1, by imposing taxes (such as an increase in income tax), in according with the new budget line. In other words, when the government increases income tax, the consumer's real disposable income decreases and budget line shifts leftwards as a parallel of AC to EF. The new budget line EF is tangent to the initial indifference curve IC1 at the point E3. The point E3 represents the consumer's equilibrium at new price budget line (or price ratio) of X and Y, after the elimination of the real income effect. The equilibrium point E3 shows that the consumers purchase OQ3 units of X good and ON3 units of Y good. Here, he reduces his demand for X good by Q2Q3 units. The change in quantity demanded of X results from a decrease in consumer's real income due to increase in income tax. Hence, Q2Q3 is the income effect.

When the consumer is in initial purchasing power from the cutting down of increased purchasing power or real income due to fall in the price of X, he compares the relative price of X with Y. It results that X good is relatively cheaper than Y good. The change in relative prices will induce the consumer to rearrange the purchases of X and Y. Here, he substitutes Q1Q3 units of X for N1N3 units of Y. It is shown by the equilibrium point E3. This process in substitution effect. In short,

PE = SE + IE

or, Q1Q2 = Q1Q3 + Q2Q3

Superiority of ordinal approach over cardinal approach

1. Cardinal approach does not explain the effects of consumer's demand due to change in the price of the commodity, income of the consumer and relative prices of two goods, i.e. price effect, income effect and substitution effect respectively whereas ordinal approach does it.
2. Cardinal approach does not explain Giffen paradox or effects on consumer's demand for inferior good due to change in income whereas ordinal approach explains the phenomenon with the help of negative income effect.
3. Cardinal approach explains the principle of consumer's surplus by setting the assumption of cardinal measurement of utility, which is unrealistic, whereas ordinal approach this principle by setting the assumption of ordinal measurement of utility which is realistic

Reference

Koutosoyianis, A (1979), Modern Microeconomics, London Macmillan

• A change in demand for a commodity, say X, due to change in the price of the same commodity (i.e. X) is called price effect.
• The total price effect consists of two direct effects of price change on consumer's choice i.e. (i) income effect and (ii) Substitution effect.
• When the price of one commodity increases (or decreases), it becomes relatively dearer (or cheaper) than the other. The consumers have an inherent tendency to substitute cheaper goods for relatively dearer ones. This is called substitution effect.
• If the income level of the consumer changes, then there is the effect in the purchase decision, given the prices of the two good, and tastes & preferences of the consumer. This effect on the demand or purchasing decision is known as income effect.
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