The Substitution Effect

When the price of good $X$ falls, two things happen at once: the relative price changes, and the consumer’s purchasing power increases. The substitution effect isolates the first force — the pure impact of the relative price change, holding the consumer’s utility (satisfaction) constant. It answers the question: “If we kept you on the same indifference curve but gave you the new price ratio, how would your consumption change?”

To isolate the substitution effect graphically, we use the following construction: after $P_X$ falls, draw a line with the new price ratio and slide it inward until it just touches the original indifference curve $I{C}_1$. The tangency point is the compensated bundle $B$, sitting on $I{C}_1$ itself. The horizontal move from $A$ to $B$ is the substitution effect: a pure relative-price reshuffle at the same level of satisfaction.

The whole trick is in step 3. The dashed line has the new slope but is slid in until it kisses the original indifference curve. So satisfaction stays fixed on $I{C}_1$ and only relative prices have changed — the move $A\to B$ is pure substitution.

Why is the substitution effect always negative? Intuitively, if $X$ gets cheaper relative to $Y$, any rational consumer will tilt their consumption toward $X$ and away from $Y$, even if their overall satisfaction hasn’t changed. Geometrically, when you rotate the budget line around the indifference curve (keeping the consumer on the same IC), the tangency always moves in the direction of the cheaper good. There’s no scenario where you’d substitute away from a good that just became relatively cheaper — that would mean the indifference curve isn’t convex.