What is price effect? How can it be decomposed into income effect and substitution effect?

The price effect is the total change in the consumer's equilibrium, and hence in the quantity demanded of a good, when the price of that good changes while income and the price of the other good stay constant; by the Hicksian method it can be broken into a substitution effect and an income effect.

1. Meaning of price effect: it is the total effect of an own-price change on the quantity demanded, moving the consumer to a higher indifference curve (price fall) or a lower one (price rise).
2. Price Consumption Curve (PCC): joining the successive equilibrium points as price changes gives the PCC.
3. Sign of the effect: the price effect is negative for a normal good (price down → demand up) and positive for a Giffen good (price down → demand down).
4. Derivation of demand: from the price–quantity pairs on the PCC, the demand curve is derived.
5. Why decompose: a price change simultaneously alters relative prices and real income, so the total effect is a mixture that Hicks separates out.
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, with X rising from X₁ to X₂.
7. Compensated budget line: Hicks draws an imaginary line CD parallel to the new line AB₁ but tangent to the original indifference curve IC₁, removing the real-income gain (the compensating variation).
8. Substitution effect: the move from E₁ to E₃ along IC₁ (X₁ → X₃) is the pure effect of the relative-price change, always increasing purchases of the now-cheaper good.
9. Feature of the substitution effect: the consumer stays on the same indifference curve, so satisfaction is unchanged and only the composition of the bundle shifts.
10. Income effect: the move from E₃ on IC₁ to E₂ on IC₂ (X₃ → X₂) is caused by the gain in real income from the price fall.
11. Sign of the income effect: it is positive for normal goods (reinforcing the substitution effect) and negative for inferior goods (opposing it).
12. Combining: Price effect (X₁X₂) = Substitution effect (X₁X₃) + Income effect (X₃X₂).
13. Normal good: both effects work in the same direction, giving a strong downward-sloping demand curve.
14. Inferior and Giffen goods: for inferior goods the negative income effect partly offsets the substitution effect; for a Giffen good it outweighs it, producing an upward-sloping demand curve.
15. Conclusion of the method: decomposition shows why the demand curve normally slopes downward and pinpoints the exceptional Giffen case.

Thus, the price effect is the combined result of a substitution effect and an income effect, and separating the two explains the slope of the demand curve for normal, inferior and Giffen goods.