Question

In consumer equilibrium analysis, a relative change in the prices of commodities brings about two types of effects on demand i.e. substitution effect and income effect.
Statement (I) : The substitution effect is always positive
Statement (II) : The income effect may be negative
In light of the above statements, choose the most appropriate answer from the options given below:

• A. Both Statement (I) and Statement (II) are true.
• B. Both Statement (I) and Statement (II) are false.
• C. Statement (I) is true but Statement (II) is false.
• D. Statement (I) is false but Statement (II) is true.

Hint:

Remember:
- Substitution Effect = Always works in the opposite direction of the price change (always negative in sign).
- Income Effect = Can be positive (normal goods) or negative (inferior/Giffen goods).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The price effect of a commodity's price change is decomposed into two distinct components: the Substitution Effect (SE) and the Income Effect (IE).
This decomposition is formulated mathematically by the Slutsky Equation:
\[ \frac{\partial x_i}{\partial p_i} = \frac{\partial h_i}{\partial p_i} - x_i \frac{\partial x_i}{\partial m} \] Where the first term on the right represents the Substitution Effect and the second term represents the Income Effect.

Step 2: Detailed Explanation:
Statement (I) states that the substitution effect is always positive.
This statement is false.
The substitution effect of a price change is mathematically proven to be always negative (or non-positive).
Here, "negative" refers to the inverse relationship between the price of a commodity and its quantity demanded.
When the price of a good falls, the consumer always substitutes relatively expensive goods with this cheaper good, causing its demand to rise.
Conversely, when price increases, the substitution effect leads to a decline in demand.
Thus, the sign of the substitution effect derivative is always negative ($\frac{\partial h_i}{\partial p_i} < 0$).
Statement (II) states that the income effect may be negative.
This statement is true.
The income effect measures how consumption changes in response to a change in real purchasing power.
For normal goods, the income effect is positive (higher real income leads to higher demand).
However, for inferior goods (including Giffen goods), the income effect is negative ($\frac{\partial x_i}{\partial m} < 0$).
When the price of an inferior good falls, the increase in real purchasing power actually leads the consumer to buy less of it, preferring superior alternatives.
Therefore, Statement (I) is false and Statement (II) is true.

Step 3: Final Answer:
The correct option is (D).