Derive the “Price Effect” of a price fall. Disintegrate the price effect into substitution effect and income effect.

The Price Effect represents the total change in the quantity demanded of a good resulting from a change in its own price, assuming all other factors, such as consumer income, tastes, and the prices of other goods, remain constant. It is the fundamental concept underlying the Law of Demand, which posits an inverse relationship between price and quantity demanded for most goods. When the price of a good falls, consumers typically respond by purchasing more of that good, and vice versa. This observed change in consumption, however, is a composite of two distinct underlying effects: the substitution effect and the income effect.

Understanding the Price Effect and its decomposition is crucial in microeconomic theory because a change in price alters consumer behavior in two fundamental ways simultaneously. Firstly, it changes the relative attractiveness of the good compared to its substitutes, making it either cheaper or more expensive. Secondly, it alters the consumer’s real purchasing power; a fall in price effectively makes the consumer richer in real terms, as they can now afford more with the same nominal income. By disentangling these two forces, economists gain a more profound insight into the intricate mechanisms driving consumer choice and the shape of demand curves.

• The Price Effect: A Comprehensive Analysis of a Price Fall
  • Disintegrating the Price Effect: Substitution and Income Effects
• The Substitution Effect
  • Hicksian Substitution Effect (Compensated Variation)
  • Slutsky Substitution Effect (Cost Difference)
• The Income Effect
  • Graphical Derivation of the Income Effect
  • Direction of the Income Effect
• Combining the Effects: The Price Effect Reconstructed
  • Illustrative Summary

¶The Price Effect: A Comprehensive Analysis of a Price Fall

The Price Effect captures the combined influence of a price change on the quantity of a good demanded. When the price of a good (say, Good X) falls, the consumer’s budget constraint pivots outwards, expanding their consumption possibilities. Initially, the consumer is in equilibrium, maximizing utility subject to their budget constraint. This equilibrium is represented by the tangency point of the initial budget line (BL1) with the highest attainable indifference curve (IC1). At this point, the marginal rate of substitution (MRS) between the two goods equals the ratio of their prices.

Graphically, if the price of Good X falls, while the price of Good Y and the consumer’s income remain constant, the budget line will pivot outwards from its Y-intercept, becoming flatter. The new budget line (BL2) represents the expanded opportunity set. The consumer will then move to a new equilibrium point (E2), where the new budget line (BL2) is tangent to a higher indifference curve (IC2). The total change in the quantity demanded of Good X (from X1 to X2) as a result of this price fall is the Price Effect. This movement from the initial equilibrium (E1) to the new equilibrium (E2) encapsulates both the change in relative prices and the change in real purchasing power.

¶Disintegrating the Price Effect: Substitution and Income Effects

To understand the separate impacts of changes in relative prices and real income, the Price Effect is meticulously broken down into the Substitution Effect and the Income Effect. This decomposition allows economists to isolate the pure effect of a change in relative prices from the effect of a change in purchasing power.

¶The Substitution Effect

The Substitution Effect measures the change in the quantity demanded of a good due solely to a change in its relative price, holding the consumer’s level of real income or utility constant. When the price of Good X falls, it becomes relatively cheaper compared to Good Y. Consumers are incentivized to substitute away from the relatively more expensive Good Y and towards the now relatively cheaper Good X. This effect always works in the opposite direction of the price change: if the price falls, the substitution effect leads to an increase in quantity demanded; if the price rises, it leads to a decrease.

There are two primary approaches to isolating the substitution effect: the Hicksian approach (compensated variation) and the Slutsky approach (cost difference). Both yield conceptually similar results but differ in how they define “constant real income.”

¶Hicksian Substitution Effect (Compensated Variation)

Graphical Derivation (Hicksian):

1. Initial Equilibrium (E1): Start with the consumer in equilibrium at point E1, where the initial budget line (BL1) is tangent to indifference curve IC1, consuming X1 units of Good X.
2. Price Fall and New Budget Line (BL2): The price of Good X falls, causing the budget line to pivot outwards to BL2. The consumer moves to a new equilibrium at E2 on a higher indifference curve IC2, consuming X2 units of Good X. The total change (X2 - X1) is the Price Effect.
3. Constructing the Hypothetical Budget Line (BLh): To isolate the substitution effect, we imagine taking away enough income from the consumer so that they can just afford to remain on the original indifference curve (IC1) at the new, lower relative prices. This is done by drawing a hypothetical budget line (BLh) that is:
   • Parallel to the new budget line (BL2), reflecting the new relative prices.
   • Tangent to the original indifference curve (IC1).
4. Hicksian Substitution Effect: The tangency point of BLh with IC1 is E_Hicks. The movement from E1 to E_Hicks represents the Hicksian substitution effect (X_Hicks - X1). This movement occurs along the same indifference curve, indicating a pure substitution of the relatively cheaper good for the relatively more expensive one, with no change in overall utility.

¶Slutsky Substitution Effect (Cost Difference)

Graphical Derivation (Slutsky):

1. Initial Equilibrium (E1): As before, the consumer is at E1 on BL1, consuming X1 units of Good X.
2. Price Fall and New Budget Line (BL2): The price of Good X falls, leading to BL2 and the new equilibrium E2, consuming X2 units.
3. Constructing the Hypothetical Budget Line (BLs): To isolate the substitution effect, we draw a hypothetical budget line (BLs) that is:
   • Parallel to the new budget line (BL2), reflecting the new relative prices.
   • Passes through the original consumption bundle (E1). This means the consumer is given just enough hypothetical income to purchase the original bundle at the new prices.
4. Slutsky Substitution Effect: The consumer, facing the new relative prices represented by BLs and having sufficient income to buy the original bundle, will then choose a new optimal bundle where BLs is tangent to the highest possible indifference curve (IC_Slutsky). Let this tangency point be E_Slutsky. The movement from E1 to E_Slutsky represents the Slutsky substitution effect (X_Slutsky - X1). Note that E_Slutsky will generally be on a higher indifference curve than IC1, as the consumer can achieve higher utility by rearranging their consumption after being able to afford the original bundle at cheaper prices.

Comparison of Hicksian and Slutsky: Both methods correctly capture the direction of the substitution effect (always opposite to the price change). The Hicksian method is theoretically cleaner as it holds utility constant, providing a measure of how much income would need to be compensated to maintain the same utility level. The Slutsky method is often considered more practical as it is based on observable consumption bundles and changes in purchasing power. For normal goods, the Slutsky substitution effect is generally larger than the Hicksian substitution effect because the Slutsky method allows the consumer to reach a higher indifference curve, implying a greater incentive to substitute.

¶The Income Effect

The Income Effect measures the change in the quantity demanded of a good due to the change in the consumer’s real income (purchasing power) resulting from the price change, holding relative prices constant. When the price of Good X falls, the consumer’s fixed nominal income can now buy more of Good X (or more of other goods), effectively increasing their real income or purchasing power. This change in real income will then influence the quantity demanded, depending on whether the good is normal, inferior, or Giffen.

¶Graphical Derivation of the Income Effect

The income effect is the remaining part of the Price Effect after the substitution effect has been accounted for.

Following the Hicksian Approach:

1. Hicksian Substitution Effect: We found E_Hicks (X_Hicks) on IC1, representing the substitution effect (X_Hicks - X1).
2. Income Effect: The movement from the hypothetical point E_Hicks on IC1 to the final actual equilibrium E2 on IC2 represents the income effect. This movement is a parallel shift from the hypothetical budget line (BLh) to the actual new budget line (BL2). This parallel shift signifies that relative prices are held constant (as both lines have the same slope), and only real income is changing (from the level corresponding to BLh to the higher level corresponding to BL2). The change in quantity demanded from X_Hicks to X2 is the Hicksian income effect.

Following the Slutsky Approach:

1. Slutsky Substitution Effect: We found E_Slutsky (X_Slutsky) on IC_Slutsky, representing the substitution effect (X_Slutsky - X1).
2. Income Effect: The movement from the hypothetical point E_Slutsky on IC_Slutsky to the final actual equilibrium E2 on IC2 represents the income effect. This movement is a parallel shift from the hypothetical budget line (BLs) to the actual new budget line (BL2). The change in quantity demanded from X_Slutsky to X2 is the Slutsky income effect.

¶Direction of the Income Effect

The direction of the income effect depends on the nature of the good:

• Normal Goods: For normal goods, an increase in real income leads to an increase in the quantity demanded. Therefore, when the price of a normal good falls (increasing real income), the income effect will be positive, leading to an increase in the quantity demanded.
• Inferior Goods: For inferior goods, an increase in real income leads to a decrease in the quantity demanded. When the price of an inferior good falls (increasing real income), the income effect will be negative, leading to a decrease in the quantity demanded.
• Giffen Goods: Giffen goods are a rare and special type of inferior good where the negative income effect is so strong that it outweighs the positive substitution effect. Consequently, when the price of a Giffen good falls, the quantity demanded actually decreases, violating the Law of Demand. This is a theoretical possibility but rarely observed in practice.

¶Combining the Effects: The Price Effect Reconstructed

The total Price Effect is the sum of the Substitution Effect and the Income Effect:

Price Effect = Substitution Effect + Income Effect

Let’s illustrate this for a price fall in Good X:

1. For Normal Goods:

   • Substitution Effect: When Px falls, Good X becomes relatively cheaper, so consumers substitute towards X. (X_Hicks - X1 > 0 or X_Slutsky - X1 > 0). This effect always increases demand for a price fall.
   • Income Effect: When Px falls, real income increases. Since X is a normal good, increased real income leads to increased demand for X. (X2 - X_Hicks > 0 or X2 - X_Slutsky > 0). This effect also increases demand for a price fall.
   • Total Price Effect: Both effects work in the same direction, reinforcing each other. The total quantity demanded of X increases significantly when its price falls. This confirms the downward-sloping demand curve for normal goods.

2. For Inferior Goods (Non-Giffen):

   • Substitution Effect: When Px falls, Good X becomes relatively cheaper, so consumers substitute towards X. This increases demand for X. (X_Hicks - X1 > 0 or X_Slutsky - X1 > 0).
   • Income Effect: When Px falls, real income increases. Since X is an inferior good, increased real income leads to decreased demand for X. (X2 - X_Hicks < 0 or X2 - X_Slutsky < 0).
   • Total Price Effect: The substitution effect (which increases demand) and the income effect (which decreases demand) work in opposite directions. However, for a typical inferior good that is not Giffen, the substitution effect is stronger than the income effect. Therefore, the net Price Effect is still an increase in quantity demanded (X2 > X1), meaning the demand curve is still downward sloping, but typically less steep than for a normal good.

3. For Giffen Goods:

   • Substitution Effect: When Px falls, Good X becomes relatively cheaper, so consumers substitute towards X. This increases demand for X. (X_Hicks - X1 > 0 or X_Slutsky - X1 > 0).
   • Income Effect: When Px falls, real income increases. Since X is a Giffen good (an extreme type of inferior good), the decrease in demand due to the income effect is so large that it outweighs the increase in demand due to the substitution effect. (X2 - X_Hicks is a large negative value, such that |X2 - X_Hicks| > |X_Hicks - X1|).
   • Total Price Effect: The net Price Effect is a decrease in quantity demanded (X2 < X1) when the price falls. This implies an upward-sloping demand curve, which is a rare exception to the Law of Demand. Giffen goods are theoretical curiosities, often associated with staple foods consumed by very poor households, where the income effect of a price change on that staple is disproportionately large.

¶Illustrative Summary

The decomposition of the Price Effect into the Substitution Effect and the Income Effect is a cornerstone of consumer theory. It provides a sophisticated framework for analyzing how consumers react to price changes by separating the impact of altered relative prices from the impact of changed purchasing power. This distinction is vital for a nuanced understanding of market demand, the welfare implications of price changes, and the design of effective economic policies, demonstrating that the observed total effect is often a complex interplay of these two fundamental behavioral responses.