The Income and Substitution Effects

When the price of pizza was $10, the consumer bought 6 pizzas for a total pizza spending of $60. When the price of pizza falls to $5, the consumer can buy 6 pizzas for $30, so the drop in the price of pizza gives the consumer an additional $30 to spend. With greater income, the consumer may choose to spend more money on pizza and more money on gas. More generally, a fall in the price of a good means the consumer’s income goes further than before, so a fall in price is in some ways similar to an increase in income.

A price change is more than a change in income, however. Imagine that the price of pizza falls from $10 to $5, which, as we said, gives the consumer an extra $30 to spend. Feeling richer, the consumer heads to the market to buy more pizza and gasoline, but on the way a pickpocket takes the extra $30. Without the extra income, should the consumer still change his consumption bundle? Yes. The price of pizza has fallen relative to the price of gas and the consumer should take advantage of this change in relative prices by consuming more pizza. Of course, if the consumer has been pick-pocketed on the way to market, the only way he can consume more pizza is by consuming less gasoline. Even so, the consumer will be better off by substituting pizza for gasoline in response to the change in relative prices. Remember, the optimal consumption rule says that to maximize utility, we need , but if the consumer was maximizing utility before the price change, then after the PPizza falls, it must be that , and this tells us that after PPizza falls, the consumer should buy more pizza and less gas.

Thus, a change in price causes consumers to change their consumption bundle for two reasons, the income effect and the relative price, or substitution effect. In Figure 25.11, we show how to decompose the total effect of a price change into the income and substitution effects. The fall in the price of pizza causes the consumer to shift from buying 6 pizzas at the old optimum to buying 9 pizzas at the new optimum. This is the total effect of the price change. To decompose the total effect, we take the new budget constraint, which reflects the new relative prices, and we shift it back toward the origin until it is tangent to the old indifference curve at point H. The shifting back of the budget constraint is like the pickpocket we describe earlier—we reduce the consumer’s income until the consumer has the same utility level (is on the same indifference curve) as before the price change.*

Income and Substitution Effects To decompose the total effect of a price change into the income and substitution effects, shift the new budget constrant back until it is just tangent to the old indifference curve (at H).
The substitution effect is given by change in consumption along the old indifference curve from the “Old optimum” to point H. The income effect is given by the change in consumption from point H to the “New optimum.”

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The substitution effect is the change in consumption caused by a change in relative prices holding the consumer’s utility level constant.

We can now define the substitution and income effects more precisely. The substitution effect is the change in consumption caused by a change in relative prices holding the consumer’s utility level constant. Thus, in Figure 25.11, the substitution effect is the change in consumption from “Old optimum” to point H. The income effect is the change in consumption caused by the change in purchasing power from a price change. Thus, in Figure 25.11, the income effect is given by the movement from H to “New optimum.”

The income effect is the change in consumption caused by the change in purchasing power from a price change.