### 8.9 Income- and substitution- effects

The changes in consumption resulting from a change in the price of a good can be divided into two effects: the substitution effect and the income effect. The substitution effect results from the change in the price ratio, the income effect from the induced change of the purchasing power of the household. To illustrate this, we assume a price decline for Good 1 :

Substitution effects:
If the price of Good 1 falls, the consumer can afford more of Good 1 for one unit of Good 2 than before. At the optimum point, this exchange ratio (= market price ratio) corresponds to the marginal rate of substitution, i.e. the ratio in which the goods can be exchanged without changing the benefit. Now, if the price of Good 1 relative to Good 2 falls, the household can save money without changing its benefit by shifting consumption from Good 2 to Good 1 . This is due to the fact that the benefit-neutral exchange ratio (marginal rate of substitution = slope of the tangent of the benefit-indifference curve) is now greater than the price ratio (slope of the new budget line). This shift in consumption towards Good 1 takes place until the marginal rate of substitution corresponds to the price ratio (point A).
In the graphic, the substitution effect is shown by the pink arrows. Point A lies on the old indifference curve where the MRS equals the price ratio. The tangent, also drawn in pink, shows that the slope corresponds to the slope of the new budget line.
For Good 1 , the substitution effect is positive if the price of Good 1 . And it is negative for Good 2 .
For the above analysis, we assume that none of the goods is a SEC:Giffengueter ist.
Income effect:
In point A, the household consumes only part of its disposable income. It can achieve a higher indifference curve by exhausting its budget. To do so, it consumes equally more of both goods until the new optimum is reached.
The income effect is positive for both goods if the price of a good falls, and if none of the goods is an inferior good. The brown arrows represent the income effect.
Overall effect:
The overall effect on Good 1 of a price reduction of Good 1 is positive because both individual effects are positive. (If Good 1 were a Giffen good, the income effect would be negative, since Giffen goods are always also inferior goods). The overall effect on Good 2 of a price reduction of Good 1 can be both positive and negative. This depends on the relative strength of the substitution effect (negative) and income effect (positive). In the example above we have used a Cobb-Douglas utility function. For these utility functions, the total effect is always zero, since the income effect and the substitution effect cancel each other out.

(c) by Christian Bauer
Prof. Dr. Christian Bauer
Chair of monetary economics
Trier University
D-54296 Trier
Tel.: +49 (0)651/201-2743
E-mail: Bauer@uni-trier.de
URL: https://www.cbauer.de