Managerial economics guide 2

Price effect, substitution effect and income effect

Consider an individual with income m. She can choose between bundles of two goods, X₁ and X₂, whose prices are p₁ and p₂ respectively. We start from an initial optimal position or initial bundle.

Optimal point using Lagrange method

Using the Lagrange method, we know the optimal point is the tangent point between the highest possible indifference curve and the budget line. X*₁ X*₂ is the bundle of goods which is demanded with price p₁ and p₂.

Budget line and price changes

The budget line is constructed by real incomes. If the price of X₁ increases, the budget line is constructed by the new real incomes. We'll find the new optimal point, the new demanded bundle at the tangency between the highest possible indifference curve and the budget line, and we may call this X̂₁. X̂₁ is the bundle of goods which is demanded with a new price p'&sub>1 and the old price p₂.

Overall price effect

What we define as the overall price effect is simply the difference between X₁ and X̂₁, so the movement between these two points is induced by the increase in price. Because one good has to become relatively more expensive after the increase in price, the other one becomes relatively less expensive.

Substitution and income effects

In order to maximize one’s satisfaction, one would like to substitute one good with the other to reach a new efficient point. But we also have to take into account that due to the increase in price of good X₁, there’s been an effective decrease in real income.

When we talk about the substitution effect, we concentrate on the purely substitution effect, which means that we have to offset the income effect. We can do this by making up a virtual budget line; this budget line will have the same slope as the new budget line because the consumer must react to the new price. This budget line also crosses the old bundle so that with these new prices, the consumer might also purchase X₁.

This way, we can give the consumer a compensation in purchase power for the loss in real income suffered due to the increase in price. The tangency point between the highest possible indifference curve and the new virtual budget line is the bundle that this consumer would buy, given compensation, with which they can get at least the same utility as before but at the new price.

X̂₁ is the quantity of the two goods that this consumer would buy with compensation.