1.7 Income and substitution effects

Income and Substitution Effects

Income and substitution effects explain how a price change breaks down into two distinct forces acting on consumer choices. When the price of a good changes, two things happen at once: the good becomes relatively cheaper or more expensive compared to other goods (substitution effect), and the consumer's real purchasing power changes (income effect). Separating these two forces is central to understanding why demand curves slope the way they do and why some goods behave in unexpected ways.

Income vs Substitution Effects

Defining Income and Substitution Effects

The substitution effect captures the change in consumption that results purely from a change in relative prices, holding the consumer's real income (or utility) constant. When good X gets cheaper relative to good Y, consumers have an incentive to substitute toward X, regardless of any change in purchasing power.

The income effect captures the change in consumption that results from the change in real purchasing power caused by the price change, holding relative prices at their new level. A price drop on something you buy regularly is like getting a small raise: your budget stretches further.

Both effects happen simultaneously whenever a price changes. You can't observe them separately in the real world, but you can isolate them analytically using either:

• Hicksian (Hicks) decomposition: holds utility constant to isolate the substitution effect. The compensated budget line is shifted so the consumer can just reach the original indifference curve at the new prices.
• Slutsky decomposition: holds purchasing power constant to isolate the substitution effect. The compensated budget line is shifted so the consumer can just afford the original bundle at the new prices.

The Slutsky approach typically leaves the consumer on a slightly higher indifference curve than the original (since the original bundle is still affordable, the consumer can usually do better by reoptimizing). This means the Slutsky substitution effect is slightly larger, and the Slutsky income effect slightly smaller, than their Hicksian counterparts. But the core logic is identical: decompose the total effect of a price change into a pure relative-price piece and a pure real-income piece.

How the Effects Interact for Different Good Types

The relationship between income and substitution effects depends on the type of good:

• Normal goods: Both effects reinforce each other. A price decrease makes the good relatively cheaper (substitution effect → buy more) and increases real income, which also leads to buying more of a normal good. The demand curve slopes downward unambiguously.
• Inferior goods: The effects work against each other. A price decrease still triggers a positive substitution effect, but the increase in real income leads the consumer to buy less of an inferior good (income effect is negative). As long as the substitution effect dominates, the demand curve still slopes downward, just with a smaller total response than for a comparable normal good.
• Giffen goods: A special, extreme case of inferior goods where the negative income effect actually outweighs the positive substitution effect. A price decrease leads to less consumption, producing an upward-sloping demand curve. This requires the good to take up a large share of the consumer's budget and be strongly inferior. Classic textbook example: staple foods for very poor households (e.g., rice or potatoes consuming most of a subsistence budget).

Impact of Price Changes on Consumer Behavior

Budget Constraint and Graphical Analysis

When the price of good X falls, the budget constraint pivots outward along the X-axis (the intercept on the X-axis increases while the Y-axis intercept stays fixed, assuming income and the price of Y are unchanged). This pivot changes two things:

1. The slope of the budget line (which equals $-\frac{P_X}{P_Y}$) becomes flatter, reflecting the new relative prices.
2. The feasible set expands, meaning the consumer can now reach higher indifference curves.

To decompose the effects graphically (Hicksian method):

1. Start at the original optimum (call it bundle A) where the budget line is tangent to indifference curve $U_1$.
2. Draw the new budget line reflecting the lower $P_X$. Find the new optimum (bundle C) on a higher indifference curve $U_2$.
3. Now draw a compensated budget line: give this line the same slope as the new budget line (reflecting new relative prices) but shift it inward until it is just tangent to the original indifference curve $U_1$. The tangency point is bundle B.
4. The move from A to B is the substitution effect: the consumer reoptimizes at new relative prices while staying on $U_1$.
5. The move from B to C is the income effect: the consumer moves from $U_1$ to $U_2$ at the new price ratio, reflecting the gain in real purchasing power.

This three-bundle diagram (A, B, C) is the standard way intermediate micro courses test your understanding of decomposition. Be comfortable drawing it for both price decreases and price increases.

Factors Influencing the Magnitude of Each Effect

Several factors determine how large each effect is in practice:

• Budget share: Goods that take up a large fraction of income (housing, food for low-income households) produce larger income effects. A 10% drop in rent matters more to your real purchasing power than a 10% drop in the price of chewing gum.
• Availability of close substitutes: More substitutes mean a larger substitution effect. Demand for Coca-Cola is highly substitutable (switch to Pepsi) compared to demand for insulin, which has essentially no substitutes.
• Income elasticity: Luxury goods (income elasticity > 1) have larger income effects than necessities (income elasticity between 0 and 1).
• Consumer preferences: Strong brand loyalty or habit formation can dampen the substitution effect, making consumers less responsive to relative price changes. In terms of indifference curve shape, more convex curves (stronger preference for variety) generate larger substitution effects, while curves closer to perfect complements (L-shaped) generate smaller ones.

Income and Substitution Effects on Demand

Relationship to the Demand Curve

The demand curve you draw in a standard price-quantity diagram reflects the total effect of price changes, which is the sum of income and substitution effects at every price level.

• For normal goods, both effects push consumption in the same direction, so the demand curve slopes downward and can be quite elastic.
• For inferior goods, the opposing income effect partially offsets the substitution effect. The demand curve still slopes downward (in most cases), but the quantity response is smaller than it would be if the good were normal.
• For Giffen goods, the income effect dominates, and the demand curve has an upward-sloping segment over the relevant price range.

This decomposition also connects to two different demand curves you'll encounter:

• Marshallian (ordinary) demand $x(P_X, P_Y, m)$: holds nominal income $m$ constant. Reflects both income and substitution effects. This is the standard demand curve.
• Hicksian (compensated) demand $h(P_X, P_Y, \bar{U})$: holds utility constant at $\bar{U}$. Reflects only the substitution effect. Always slopes downward because the substitution effect always goes opposite to the price change.

The gap between the Marshallian and Hicksian demand curves at any price tells you the size of the income effect for that good. For normal goods, the Marshallian curve is flatter (more elastic) than the Hicksian curve because the income effect reinforces the substitution effect. For inferior goods, the Marshallian curve is steeper.

The Slutsky Equation

The formal link between these effects is the Slutsky equation:

$\frac{\partial x}{\partial P_X} = \frac{\partial h}{\partial P_X} - x \frac{\partial x}{\partial m}$

Reading left to right: the total effect of a price change on Marshallian demand equals the substitution effect (from Hicksian demand) minus the income effect. The income effect term is the quantity consumed ($x$) times the income response ($\frac{\partial x}{\partial m}$). The $x$ multiplier is why budget share matters: the more of the good you consume, the bigger the hit to your real income when its price rises.

Impact on Price Elasticity

Price elasticity of demand is shaped by the relative strength of these two effects:

• A larger substitution effect (many close substitutes, flexible preferences) leads to more elastic demand. Consumers shift away from the good easily.
• A larger income effect amplifies elasticity for normal goods (both effects reinforce) but dampens it for inferior goods (effects oppose).
• Necessities tend to have low price elasticity because both effects are small: few substitutes and low income elasticity.
• Luxuries tend to have high price elasticity because the income effect is large (high income elasticity) and often there are substitutes available.

Applying Income and Substitution Effects to Market Scenarios

Policy Analysis and Design

These effects are essential tools for evaluating real-world policies:

• Taxation: A tax on cigarettes raises the relative price, triggering a substitution effect (smoke less, switch to alternatives) and an income effect (reduced purchasing power). For addictive goods with few substitutes, the substitution effect is small, which is why sin taxes often generate revenue but produce modest behavioral change.
• Subsidies and price controls: A food subsidy lowers the relative price of food, creating a substitution effect toward food and an income effect that frees up budget for all goods. The income effect might cause consumers to shift spending toward non-food goods, which is why in-kind subsidies sometimes have different effects than policymakers expect.
• Welfare program design: Cash transfers create a pure income effect, while targeted vouchers (e.g., housing vouchers) create both income and substitution effects by changing the effective relative price of the subsidized good.

Labor Market Applications

The labor-leisure model is one of the most important applications of income and substitution effects:

• A wage increase makes leisure more expensive relative to consumption (substitution effect → work more), but it also makes the worker richer (income effect → "buy" more leisure, i.e., work less).
• At low wages, the substitution effect typically dominates: higher wages lead to more hours worked.
• At high wages, the income effect can dominate: workers are wealthy enough that they value additional free time more than additional income. This produces the backward-bending labor supply curve.
• Marginal tax rate changes directly affect the net wage, altering the substitution effect in the labor-leisure tradeoff. A higher marginal tax rate reduces the opportunity cost of leisure, which discourages work on the substitution margin, even if the income effect (being poorer due to taxes) pushes toward working more.