The Income Effect | Econ Academy

The income effect captures the second force at play when a price changes: the change in purchasing power. When $P_{X}$ falls, your nominal income hasn’t changed, but your real income has increased — you can reach a higher indifference curve. The income effect measures how consumption changes as the consumer moves from the compensated bundle $B$ (on $I C_{1}$ , at the new prices) to the new optimum $C$ (on the higher $I C_{2}$ ).

Graphically, the income effect is the parallel shift from the helper line tangent to $I C_{1}$ at $B$ outward to the actual new budget line $B L_{2}$ tangent to $I C_{2}$ at $C$ . The two lines are parallel (same price ratio), so the move from $B$ to $C$ is a pure income change — identical to what would happen if you gave the consumer a cash transfer at the new prices.

Interactive — The Income Effect: From B to C

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Total effect first, then decompose: the income effect falls out as what’s left over after taking out the substitution effect.

The whole income-effect leg is a parallel shift of the budget line. Same slope (same price ratio), more income. For a normal good both effects push the same way; for an inferior good the income leg points backward against the substitution leg — which is the setup that makes Giffen behaviour theoretically possible.

Key Term

Income Effect and the Slutsky Equation

For normal goods: Income effect is positive (same direction as substitution effect). Higher real income $\to$ buy more $X$ .

For inferior goods: Income effect is negative (opposite to substitution effect). Higher real income $\to$ buy less $X$ .

Slutsky equation: $\frac{\partial X ^{*}}{\partial P _{X}} = \frac{\partial X ^{h}}{\partial P _{X}} - X^{*} \frac{\partial X ^{*}}{\partial I}$

Slutsky equation: the total price effect decomposes into substitution and income effects

The Slutsky equation is the formal decomposition. Notice the income effect term has a minus sign and is multiplied by $X^{*}$ — the quantity consumed. This means the income effect is larger when the consumer spends a large share of their budget on the good. For a staple food that absorbs most of a poor household’s budget, the income effect of a price change can be enormous. This is exactly the setup that makes Giffen goods possible.

Worked Example

Good X is an inferior good. A consumer currently buys 15 units. When $P_{X}$ falls by 2 dollars, the substitution effect increases demand by 4 units. The income effect of a 1 dollar increase in income reduces demand by 0.1 units. What is the total change in demand?

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Why is the income effect multiplied by $X^{*}$ in the Slutsky equation?

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Apply income effect analysis:

For a normal good, when its price falls, the income effect:

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