Notes on Substitution Effect and Income Effect

Notes on Substitution effect and income effect

1)Motivation

Whenever there is a change in price of one of the goods, this causes changes in the quantity demanded for all the goods. This raises the question: why did quantity demanded for all the goods change when only price has changed. The reason is that a price change causes two changes.

• First, there is a change in the relative price of the goods. This will force the consumers to substitute the relatively cheaper goods for the relatively more expensive goods.
• Second, there would be a change in the general purchasing power or relative income because the consumers can now afford more (less for increase in price) goods in general.

When we observe the change in optimal consumption decision, we only see the final outcome; we cannot observe the change caused by relative price change and change caused by relative income change. So we decompose the effect of price change in to substation effect and income effect.

Price effect = substitution effect + income effect

Also, the effect of a change in price varies depending on whether the goods in question are normal goods or inferior goods.

2)Normal Goods and Inferior Goods

If the consumption of a good increases with income, it is a normal good. If the consumption goes down, it is an inferior goods. For normal goods, the income expansion curve is upward sloping. For inferior goods, the Income expansion path is backward bending.

3)Substitution and income effect for Normal goods

• We will have two goods leisure (L) and C, both are normal goods. Price of L, which is real wage w, increases.
• Because of the price increase, consumer would like substitute the relatively more expensive good L for the cheaper good C. This substitution of one goods for the other is known as the substitution effect (SE). The SE always moves opposite to the price movement. Hence, the SE for normal goods is always negative. So, for SE, consumption of leisure(L) goes down
• Also because of the price increase there is an increase in the relative income of the consumer in the sense that he can now afford more of both goods. Also, an increase in real really increases the income of the consumer. This change in the general purchasing power is known as Income (relative) effect (IE). The IE always moves in the same direction to the price movement for Normal Goods. Hence, for normal goods, IE is always positive.So, for IE, consumption of both C and L goes up
• Price effect(PE) = SE(-) + IE(+) = (+) or (-)

So, whether the decline in the price of L will lead to an increase in the consumption of L will depend on the relative strength of SE and IE.

• If IE > SE, PE is positive, L goes down
• If IE < SE, PE is negative, L goes up

4)Substitution and income effect for Inferior goods

• For inferior goods, SE is still negative but now IE is always negative as well.
• Price effect(PE) = SE(-) + IE(-) = (-)

Therefore, an increase in real wage will always lead to a decline of L when L is an inferior good.

Figure 4.8 Increase in the Real Wage Rate: Income and Substitution Effects

Graphically we see that:

• For an increase in the price of L (real wage), consumption of leisure goes down because of SE, (from F to O).
• Because of IE which is positive for normal good L, consumption of leisure increases(O to H)
• In this case, SE =IE. Hence the consumption of L is the same before and after the increase in real wage.