Answer First
Marshallian demand slopes downward because a price increase makes the good relatively more expensive (substitution effect) and reduces the consumer’s purchasing power (income effect). For normal goods, both effects work in the same direction, causing quantity demanded to fall as price rises.
Problem Setup
Marshallian demand solves: \[ \max_{x,y} U(x,y) \quad \text{s.t.} \quad p_x x + p_y y = I. \] Slutsky decomposition: \[ \frac{\partial x}{\partial p_x} = \underbrace{\frac{\partial h}{\partial p_x}}_{\text{substitution effect}} – \underbrace{x \frac{\partial x}{\partial I}}_{\text{income effect}}. \]
Step-by-Step Explanation
1. Substitution effect: the good becomes relatively more expensive
When the price of good X rises, consumers substitute away from X toward relatively cheaper goods. This effect is always negative: \[ \text{SE} < 0. \]
2. Income effect: purchasing power falls
A price increase reduces real income. For normal goods: \[ \text{IE} < 0. \] For inferior goods: \[ \text{IE} > 0. \]
3. For normal goods, both effects reinforce each other
Substitution effect: buy less X. Income effect: buy less X. Thus Marshallian demand slopes downward.
4. For inferior goods, substitution and income effects oppose each other
But the substitution effect dominates for almost all goods, so demand still slopes downward.
5. Giffen goods are the rare exception
If the positive income effect is larger than the negative substitution effect, demand slopes upward. This requires:
- X is strongly inferior,
- X is a large share of the consumer’s budget,
- no close substitutes exist.
These conditions are extremely rare.
Intuition
When a price rises, the good becomes less attractive (substitution effect) and the consumer feels poorer (income effect). Both forces push quantity demanded downward for normal goods.
Common Exam Mistakes
- Thinking the substitution effect can be positive (it cannot).
- Confusing Hicksian and Marshallian demand.
- Forgetting that income effects differ for normal vs. inferior goods.
- Believing Giffen goods are common (they are not).
Final Summary
Marshallian demand slopes downward because substitution and income effects both reduce quantity demanded when price rises. The substitution effect is always negative, and for normal goods the income effect reinforces it, producing the law of demand.
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