Explain the price effect for normal substitutes. How can it be decomposed into income and substitution effects? Explain.

The price effect (or total effect) is the change in the consumer's equilibrium when the price of one good changes, income and the other price held constant; for a normal good the total effect can be split into a substitution effect and an income effect by the Hicksian method.

1. Meaning of the price effect: it measures how the quantity demanded of a good changes when its own price changes, tracing the consumer's move to a new indifference curve.
2. Price Consumption Curve (PCC): joining the successive equilibrium points as price falls gives the PCC, from which the demand curve is derived.
3. Case of substitutes: when goods X and Y are substitutes and X becomes cheaper, the consumer buys more X and less Y, since X now replaces Y in consumption.
4. Direction for a normal good: the price effect is negative for a normal good — a fall in price raises quantity demanded — giving a downward-sloping demand curve.

Decomposition into substitution and income effects (Hicksian approach):

5. The idea: the total price effect combines two forces — the change in relative prices (substitution) and the change in real income (income) — which Hicks separates using a compensated budget line.
6. Total effect shown: when X's price falls, the budget line swings from AB to AB₁ and the consumer moves from E₁ to E₂, so quantity of X rises from X₁ to X₂ (the total price effect).
7. Compensating variation: Hicks draws an imaginary budget line CD parallel to the new line AB₁ but tangent to the original indifference curve IC₁, removing just enough income to cancel the real-income gain.
8. Substitution effect: the movement from E₁ to E₃ along the same indifference curve IC₁ (X₁ → X₃) is the pure substitution effect — the switch caused purely by X becoming relatively cheaper.
9. Nature of the substitution effect: it is always in the opposite direction to the price change (cheaper good bought more), and the consumer stays on the same IC at a different point.
10. Income effect: restoring the withdrawn income moves the consumer from E₃ on IC₁ to E₂ on the higher IC₂ (X₃ → X₂) — this is the income effect of the price fall.
11. Nature of the income effect: since the good is normal, the real-income gain further raises demand, so the income effect reinforces the substitution effect.
12. Adding them: Price effect (X₁X₂) = Substitution effect (X₁X₃) + Income effect (X₃X₂).
13. For substitutes specifically: the substitution effect strongly pulls consumption toward the cheaper good X and away from its substitute Y.
14. Deriving demand: at price P₁ demand is X₁ and at the lower price P₂ demand is X₂; joining these points gives a downward-sloping demand curve, confirming X is a normal good.
15. Example: as tea gets cheaper relative to coffee, the consumer switches toward tea (substitution effect) and, feeling better off, buys still more tea (income effect).

Thus, for a normal good the total price effect is the sum of a substitution effect and a reinforcing income effect, and for substitutes the substitution effect is what drives the consumer toward the good whose price has fallen.