Model Answer
0 min readIntroduction
In microeconomics, understanding consumer behavior in response to price changes is crucial for deriving demand curves. The Marshallian demand curve, also known as the ordinary demand curve, illustrates the quantity of a good a consumer is willing and able to purchase at different prices, given their income and the prices of other goods. For normal goods, this relationship is straightforwardly inverse, leading to a downward-sloping curve. However, for an inferior good, the interaction of income and substitution effects creates a more complex scenario. This answer will derive the Marshallian demand curve for an inferior good using these effects within a two-commodity framework and analyze its characteristic slope.
Derivation of Marshallian Demand Curve for an Inferior Good
The derivation of the Marshallian demand curve for an inferior good involves decomposing the total price effect into its income and substitution components. We consider a consumer choosing between two goods, Good X (an inferior good) and Good Y, with a given income and prices. Let's assume the price of Good X (PX) falls, while the price of Good Y (PY) and the consumer's nominal income (I) remain constant. This price change will lead to a new equilibrium for the consumer, which can be analyzed through the following steps:1. Initial Equilibrium
- Initially, the consumer is at equilibrium at point A on indifference curve IC1, tangent to the budget line BL1. At this point, the consumer consumes X1 units of Good X.
2. Price Fall and Total Price Effect
- When the price of Good X falls (PX' < PX), the budget line rotates outwards from BL1 to BL2. The consumer's real income (purchasing power) increases, allowing them to reach a higher indifference curve, say IC2, at a new equilibrium point B.
- The movement from A to B represents the Total Price Effect, which shows the change in the quantity demanded of Good X due to the fall in its price. The quantity demanded of Good X increases from X1 to X3.
3. Decomposition into Substitution and Income Effects
To isolate the substitution and income effects, we employ a hypothetical adjustment to the consumer's income.
a. Substitution Effect
- The Substitution Effect measures the change in quantity demanded due to a change in relative prices, while keeping the consumer's real income or utility constant.
- To achieve this, we hypothetically reduce the consumer's income (or compensate them negatively) so that they can achieve their *original utility level* (IC1) at the *new relative prices*. This is represented by a hypothetical budget line (BL_H), parallel to BL2, tangent to IC1 at point C.
- The movement from A to C shows the substitution effect. Since Good X has become relatively cheaper, the consumer substitutes Good Y for Good X, leading to an increase in the quantity demanded of Good X from X1 to X2. The substitution effect is always negative (i.e., an increase in price leads to a decrease in quantity demanded, and vice-versa) and acts in the opposite direction of the price change.
b. Income Effect
- The Income Effect measures the change in quantity demanded due to the change in real income (purchasing power) resulting from the price change, while keeping relative prices constant.
- This is the movement from the hypothetical equilibrium point C to the final equilibrium point B. At point C, the consumer is at the original utility level but faces new prices. By moving to BL2 (point B), the consumer's income is restored, allowing them to reach a higher utility level (IC2).
- For an inferior good, as real income increases, the quantity demanded of the good tends to decrease. Therefore, the income effect for an inferior good is negative. In our diagram, the movement from C (quantity X2) to B (quantity X3) shows a *decrease* in the consumption of Good X (X3 < X2), meaning the income effect is negative and pushes demand back.
The total price effect (X1 to X3) is the sum of the substitution effect (X1 to X2, positive) and the income effect (X2 to X3, negative). For most inferior goods, the substitution effect is stronger than the negative income effect.
| Effect | Description | Direction for Price Fall (Good X) |
|---|---|---|
| Substitution Effect | Change in quantity demanded due to change in relative prices, keeping utility constant. | Increase in quantity demanded (X1 to X2). Always positive. |
| Income Effect (for Inferior Good) | Change in quantity demanded due to change in real income, keeping relative prices constant. | Decrease in quantity demanded (X2 to X3). Always negative for an inferior good. |
| Total Price Effect | Sum of substitution and income effects. | Net effect on quantity demanded (X1 to X3). |
4. Derivation of the Marshallian Demand Curve
By plotting the price of Good X against the corresponding quantity demanded (initial PX and X1, and new PX' and X3), we can derive the Marshallian demand curve. Since, for most inferior goods, the positive substitution effect (increase X1 to X2) outweighs the negative income effect (decrease X2 to X3), the net effect of a price fall (X1 to X3) is an increase in the quantity demanded. This means the Marshallian demand curve for most inferior goods will be downward sloping.
Is this Demand Curve Always Negatively Sloped?
No, the Marshallian demand curve for an inferior good is not always negatively sloped. While for most inferior goods, the substitution effect dominates the negative income effect, leading to a conventional downward-sloping demand curve, there is a specific and rare exception: Giffen goods.
Explanation:
- Normal Inferior Goods: For typical inferior goods, when the price falls, the positive substitution effect (buying more because it's relatively cheaper) is larger than the negative income effect (buying less because one feels richer). The net outcome is an increase in quantity demanded, maintaining a downward-sloping demand curve.
- Giffen Goods: A Giffen good is a special type of inferior good where the negative income effect is so strong that it outweighs the positive substitution effect. In this unique situation, if the price of the Giffen good falls, the consumer's real income increases, and they drastically reduce their consumption of this inferior good. The reduction due to the income effect is greater than the increase due to the substitution effect.
- Consequently, for a Giffen good, a fall in price leads to a decrease in the quantity demanded, and a rise in price leads to an increase in the quantity demanded. This results in an upward-sloping Marshallian demand curve, which violates the Law of Demand.
Therefore, while all Giffen goods are inferior goods, not all inferior goods are Giffen goods. The demand curve for an inferior good will be negatively sloped unless it is a Giffen good, in which case it will be positively sloped.
Conclusion
The Marshallian demand curve for an inferior good is derived by carefully dissecting the total price effect into the substitution and income effects. A fall in the price of an inferior good leads to a positive substitution effect (increased demand due to relative cheapness) and a negative income effect (decreased demand as real income rises). For the vast majority of inferior goods, the substitution effect is stronger than the negative income effect, resulting in a conventional downward-sloping demand curve. However, in the rare instance of a Giffen good, the negative income effect is so potent that it overcomes the substitution effect, leading to a positively sloped Marshallian demand curve, an exception to the law of demand.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.