## Introduction

The indifference curve analysis of consumer choice proposed by John Hicks and Roy Allen (1934) has received a wider applicability in a range of economic theorems. Hicks and Allen later developed, and elaborated, the ‘Slutsky’s theorem’ – the demand theorem initially developed and proposed by Eugen Slutsky – where they applied their indifference curve analysis in an effective manner. At the most simple level Slutsky’s equation brings the effects of price, substitution and income in a mutual relationship reflected in the simple formula of price effect= substitution effect + income effect (Miles 1990).

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## Income Effect and Substitution Effects

According to the Law of Demand a change in the price of goods results in a change in the quantity of demand for those goods. Normally when there is a change in the price of goods it has an opposite or a reverse impact in terms of the quantity demanded by the consumer. In other words changes in the price levels have a negative relationship with the quantity of goods that the consumer is willing and is actually able to purchase. The variations thus caused in the demand levels as a result of the variations in the price levels can largely be decomposed into two effects, namely the income effect and the substitution effect. Both these effects jointly results in the price effect, that is, the inverse relationship between price and demand usually results from both income and substitution effects. Price changes of goods usually lead to changes in the relative price of those goods and the purchasing power of the consumer’s income. Change in relative price is related with substitution effect and change in the purchasing power of the consumer is related to the income effect.

## Definitions

Income Effect:

In a situation where the price of goods remains constant the effect of income may still cause a change in the demand for those goods as a result of the direct impact that levels of income have on the purchasing power of consumers.

At the same time the magnitude of income effect is also expanded in order to analyse the relationship between price changes and income. In other words when the good X experiences a decrease in its price the consumer may continue to purchase the same of quantity and may still have left with some additional money. This additional money is actually a surplus from his budget expenditures and is, in all senses, equated to a rise in his income level or a higher income. Theoretically speaking the purchasing power is positively effected as a result of this higher income which further increases the demand for the same good. The change in the quantity demanded of good X as a result of this ‘as if’ change in income is called Income Effect. That is, any increase or decrease in the price level has a direct impact on the income level.

Substitution effect:

Given that the utility level continues to remain without much variation, substitution effect is the change in the demand for a particular good in relation to the change in its price. Substitution effect is directly associated with the relative prices of other products of the same good in the market.

To draw further from the previous instance of good X, changes in the price of good Y results in changes in the relative price of good X as compared to the good Y: When there is decrease in the price of good X, the price of X is lowered with respect to the price of Y. And the consumer will be able and willing to purchase more of X than before as the opportunity cost of X is lower. Likewise, the increase in the price of X results in the less purchase of good X. This extra or less amount of good X purchased by the consumer because of the fall or rise respectively in price of good X is called the ‘Substitution effect’.

The sum total of these isolated changes, changes caused by the effects of income and substitution, is precisely what is referred to as the total change. In other words the total change in the quantity demanded due to price change is equivalent to these sum of changes.

## Instantiations

To instantiate the above mentioned definitions further let us look at these examples. Firstly, the law of demand suggests that the relationship between the price and demand of a particular commodity is inverse and negative. For example, when the price of apple goes up its demand in the market falls. For this fall in demand, two important components work simultaneously. First, when there is increase in the price of apple, the consumer who has budgeted to purchase apple has a lower purchasing power. Hence, though the actual budget of the consumer has remained without much variation, the price increase of apple has lowered his purchasing capacity and thus diminished his income. This relationship between the price levels and the purchasing power of the consumer is what is meant by income effect. The income effect is more vivid and direct.

Secondly, when the price of apple increases, with given purchasing power, the amount of mango that the consumer has to sacrifice in order to acquire one apple increases. That is, apple is relatively less expensive. The relative price of apple is the number of mangoes that must be sacrificed to purchase apple. If the price of an apple is \$1.00 and mango costs \$2.00, then one apple is equal to ½ mango. The relative price of an apple is equal to ½ mangoes. Similarly, the relative price of mango is equal to 2 apples.

If the dollar price of an apple increases to \$2.00, the consumer has to sacrifice 1 mango to acquire each apple (that is, apple is relatively more expensive), but the consumer need only give up 1 Apple to purchase a Mango. With this substitution effect, the consumer will switch between Apple and Mango by keeping her overall satisfaction unchanged.

## Algebraic Illustration of Income and Substitution Effects

In algebraic form, the price effect can be shown as:

âˆ†Qd/âˆ†P = [âˆ†Qd/âˆ†P] Substitution effect + [âˆ†Qd/âˆ†P]Income effect, where,

âˆ†Qd is change in quantity demanded and âˆ†P is change in price.

When the income effect alone is considered, it is written as [âˆ†Qd/âˆ†P] income effect = [âˆ†Qd/âˆ†I] *[âˆ†I/âˆ†P] where âˆ†I is change in income. The income effect is the product of two terms, [âˆ†Qd/âˆ†I] and [âˆ†I/âˆ†P] in which [âˆ†Qd/âˆ†I] measure the change in quantity demanded due to change in income while the term [âˆ†I/âˆ†P] indicates the change in income or purchasing power due to change in price. And each unit of price increase leads to the decrease of purchasing power in the same amount. That is, [âˆ†I/âˆ†P] = -Qd. By substituting this into the original equation, price effect can be written as

âˆ†Qd/âˆ†P = [âˆ†Qd/âˆ†P] Substitution effect – âˆ†Qd *[âˆ†I/âˆ†P].

In this formula, the substitution effect is always negative. That is, an increase in price always results in the substitution of the particular good for which price increases by the other good. On the other hand, price effect is positive in the case of normal goods. When there is increase/ decrease in income it leads to an increase/ decrease in quantity demanded. That is, for normal goods, âˆ†Qd/âˆ†I >0.

For normal goods, price effect due to the joint action of the income and substitution effects leads to a negative effect.

## Graphical Representation of Income and Substitution Effects

The decomposition of price effect into income and substitution effects is clearly represented graphically with the help of indifference curve analysis.

Source: Dewett and Verma (2008) and Koutsoyiannis A. (1979)

In the original indifference curve IC1, the consumer maximizes the utility at an equilibrium point E where budget line of AB touches the indifference curve, IC1. At that point, the marginal rate of substitution of good x equals its relative price. When there is increase in price, the consumer has to shift the equilibrium to another indifference curve IC2. The new equilibrium point is E2 where more units of Y (from 60 to 80 units) and less units of X (from 30 to 10 units) are consumed. The budget line in this context is AB’.

The movement from the point E to E2 represents the total effect of the price change.

Then the decomposition of price effect into substitution effect and income effect can be seen in the diagram. As the consumer always wants to stay on the higher indifference curve, a new budget line CD is drawn parallel to AB’. Under this the consumer is assumed to be able to remain in the same higher IC1 with a new relative price. In an attempt to remain in the same indifference curve with a different relative price, the consumer moves from E to E’. This movement is the substitution effect. In terms of goods, the consumer purchases 10 units lesser of good X and 20 more units of good Y. In other words, the consumer purchases more of good Y of which relative price is less than that of X.

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For examining income effect, it is assumed that the substitution effect has already happened. In the diagram, a new budget line AB’ is drawn when the purchasing power of the consumer falls due to the increase in price of good X. The relative price remains constant at this point, E2. With the fall in purchasing power, the consumer will have less of goods. In the diagram the income effect is shown as the movement from the equilibrium point E’ to E2.

## The case of Inferior Goods and Luxuries (where the income effect reacts in the opposite direction)

In the case of normal good, as we have seen in the previous sections, the income effect is negatively related to the price change. The inverse relationship between price and demand as stated in the Law of Demand is true in the case of a normal good. At the same time the relationship between income and demand for normal goods is positive. When there is increase in the income of consumer, the quantity demanded will rise as the purchasing power of the consumer increases.

But these situations do not hold in the case of exceptional goods. If a good is termed as inferior, when the income of a consumer rises, she simply reduces its consumption and consumes goods which are more superior have got relatively more status. Hence, the income and demand are negatively related in the case of inferior goods and the income effect and price change are also similarly negatively related. That is, price increases, the purchasing power of the consumer decreases and the quantity demanded will be decreased.

Whether the good is normal or inferior, the substitution effect is always negative.

When we take the case of luxurious goods, price effect and quantity demanded goes in the same direction unlike in the case of normal goods. The rise in the price of luxurious good never curtails its demand. Instead, the price and demand are positively related.

Regardless of the nature of goods, whether normal, inferior or luxuries, the total effect of price changes on the quantity demanded can be separated as income effect and substitution effect. As a result of the substitution effect, the consumer takes the advantage of relative price level and tries to keep in the same satisfactory level (as shown in the graphical representation). In consequence of the income effect, the purchasing power and budget of the consumer is altered. The nature (whether positive or negative) and strength of these effects jointly determine the price effect. And from the nature of these effects, the nature of the goods or property of the goods (whether inferior, normal or luxuries) are decided.