Substitution Effect

The substitution effect is the change in the quantity of a good that a consumer buys because its price has changed relative to other goods, with the consumer's purchasing power held constant. When something becomes more expensive compared with its alternatives, people buy less of it and more of the alternatives; when it becomes cheaper, they switch toward it. The substitution effect always works in the opposite direction to the price change.

It is one of two parts into which economists split the response to a price change. The other is the income effect: a price rise also makes the buyer poorer in real terms, which changes demand for everything. Together they make up the total effect seen in the market, and they explain why most demand curves slope downward. The decomposition is a standard tool of microeconomics and sits behind the measurement of elasticity.

Suppose the price of beef rises sharply while chicken stays the same. Even if someone handed you exactly enough extra money to keep buying your usual shopping, you would probably buy a bit less beef and a bit more chicken, simply because chicken is now the better deal. That switch is the substitution effect.

Without the extra money, you would also feel a little poorer, and might cut back on other things too. That second response is the income effect. Separating the two helps economists predict how people will react to taxes, wage changes and price shocks.

For most goods, called normal goods, both effects point the same way: a price rise makes the good relatively dearer and makes the buyer poorer, so demand falls on both counts. For inferior goods, which people buy less of as their income rises, the income effect pushes in the opposite direction. In the rare case of Giffen goods, the income effect is strong enough to outweigh the substitution effect, so demand rises with price. Veblen goods are different: their demand rises with price because the high price itself confers status, not because of the income effect.

The Russian economist Eugen Slutsky set out the decomposition in 1915. John Hicks and Roy Allen developed it further in 1934, and Hicks presented it in Value and Capital (1939). Hicks shared the 1972 Nobel Memorial Prize in Economic Sciences with Kenneth Arrow for work on general equilibrium and welfare theory. The two versions differ in how "constant purchasing power" is defined: Slutsky keeps the original bundle affordable, while Hicks keeps the consumer's level of satisfaction, or utility, unchanged.

The Slutsky equation splits the effect of a price change on demand into its two parts:

• $x_i$ is the quantity of good $i$ demanded and $p_i$ is its price.
• $h_i$ is compensated (Hicksian) demand, the quantity bought if income is adjusted to keep the consumer as well off as before.
• $m$ is the consumer's money income.
• The first term on the right is the substitution effect, which is never positive; the second is the income effect.

Worked example: a commuter buys 10 coffees a week at $4. The price rises to $5. To keep the original bundle affordable, she would need $10 \times 1 = 10$ dollars more a week. If, with that compensation, she would buy 8 coffees, the substitution effect is $-2$. Without compensation she actually buys 7, so the income effect is a further $-1$, and the total effect is $-3$ coffees a week.

• Labor supply. A higher wage makes leisure more costly in terms of income given up, so the substitution effect encourages more work, while the income effect allows more leisure. Which dominates shapes the response to tax changes and is central to labor economics and debates about the Laffer curve.
• Saving. Higher interest rates make future consumption cheaper relative to spending today, encouraging saving, though income effects can offset this for savers who already hold wealth.
• Taxes and subsidies. Taxes change relative prices and so cause substitution, which is the source of their efficiency cost. A Pigouvian tax or a carbon tax deliberately uses substitution to steer behavior.
• Competition and market definition. If customers would readily switch to another product after a small price rise, competition authorities treat the two as in the same market; strong substitution limits monopoly power.

Price indexes with a fixed basket of goods ignore the fact that consumers substitute away from items whose prices rise fastest, so they tend to overstate the rise in the cost of living. The 1996 Boskin Commission estimated that the US Consumer Price Index overstated inflation by about 1.1 percentage points a year, with substitution among the causes. In response, the Bureau of Labor Statistics changed its methods and in 2002 began publishing a chained CPI, which updates the basket as spending shifts. Since 2018 US federal income tax brackets have been indexed to the chained CPI. Statistical agencies also use hedonic adjustment to deal with changes in quality, a related but separate problem.

The substitution effect assumes people respond to relative prices in a consistent way. Behavioral economics shows that habits, defaults and framing can slow or distort that response, and switching often takes time, which is why long-run responses to price changes are usually larger than short-run ones.

• OpenStax Principles of Economics: How Changes in Income and Prices Affect Consumption Choices
• The Nobel Prize: Economic Sciences 1972 (Hicks and Arrow)