# Substitution and Income Effect, Topics in Demand and Supply Analysis, CFA Level I, Economics

Blog article 4, Substitution and Income Effect, Topics in Demand and Supply Analysis, CFA Level 1 Economics

We consider the household optimum in a two-goods world.If the price of the first good rises, then the budget line turns inwards on the x1 axis. We can then distinguish between

– Overall effect,
– Substitution effect and
– Income effect

where the overall effect is the sum of the substitution and income effect.

The old household optimum lies at point A, the tangent point of the old utility curve U0 and the old budget line B0.

To the overall effect. If the price of the first good increases, the budget line turns inwards on the x1 axis, namely from B0 to B1. We get a new tangential point at B01, namely point C (by the way, we know that there will be another intermediate point B, so we speak of point C here already).

First, the movement from point A to point C is the so-called overall effect, which expresses a decrease in demand for the first good, which has become more expensive, and (here) shows an increase in demand for the second good. We see that the overall effect points to the left as a result of the price increase. The first good is thus an ordinary good, because price and quantity in demand move in different directions.

The overall effect can now be broken down into the so-called substitution effect and the so-called income effect.

In the case of the substitution effect, the relatively more expensive good (here the first good) is substituted, i.e. replaced, by the relatively cheaper good (i.e. the second good).

LAMBERT RULE:
The substitution effect always points in the opposite direction to the price movement. In other words: price and quantity move into opposite directions. So if the first price rises, the substitution effect points to the left on the x1 axis. If the first price falls, the substitution effect on the x1-axis points to the right.

Finally, the income effect. First of all, it can be observed that because of the increased price of the first good, one can buy less (!) in real terms. If this (real) reduction in income is to remain unconsidered at first, the new budget line B1 must be shifted fictitiously to the right until B1 is tangent to the old utility indifference curve U0. We get the fictitious budget line B01 (which lies parallel to B1, i.e. expresses the same price ratio as B1). The intermediate budget line B01 is tangent to the old indifference curve U0 at point B.

We now look at points A, B and C. The movement from point A to B is called substitution effect, the movement of B to point C is called income effect. They sum up to the overall effect, which is the movement from A to C.

The income effect here shows from B to C on the x1 axis to the left. As a consequence of the decreased real income (because the price of the first good had risen) the demand for good 1 decreases. The first good is therefore a normal good, because real income and demanded quantity move in the same direction.

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