Understanding the Relation Between Compensated and Uncompensated Demand Curves
Introduction to Compensated and Uncompensated Demand Curves
In economic theory, the relation between compensated (also known as Hicksian) and uncompensated (Marshallian) demand curves is crucial for understanding consumer behavior. This article delves into the intricate relationship between these curves, focusing on the implications of utility maximization and the role of income and substitution effects.The Core Relation Between Compensated and Uncompensated Demand Curves
At any given level of utility, the compensated and uncompensated demand curves must be equal. This implies that any change in the compensated demand is influenced by the income effect, leading to an adjustment in the optimal expenditure on goods due to a change in price.Mathematical Representation and Implications
To illustrate, consider the following identity:ΔQc ΔQu ΔExpenditure
Where: ΔQc: Change in compensated demand ΔQu: Change in uncompensated demand ΔExpenditure: Change in optimal expenditure on goods due to price change This equation highlights the necessity to account for both the substitution and income effects in understanding consumer choices.Uncompensated Demand Curve: A Primer
The uncompensated demand curve, also known as the Marshallian demand curve, simply asks: If the price of good X rises by 20%, how much will the quantity demanded change, holding everything else constant?Example: Chips and Limca
Let's consider a concrete example. Imagine you buy 4 packs of chips (C) and 4 bottles of Limca (L) when the price of chips is 20/pack and the price of Limca is 30/bottle, exhausting your budget of 200 bucks. At this point, the price ratio (Pc/Pl) is 2/3. The total utility from these purchases is such that the utility from chips divided by the price of chips equals the utility from Limca divided by the price of Limca. This ensures that you are maximizing utility from your expenditure:C/80 L/120
C 2L/3
However, if the price of chips rises to 40, you can now only buy 2 packs for 80 bucks, reducing utility by nearly 50. To maintain your initial total utility (T), you would need to either: Adjust the basket to consume the same quantity of chips, increasing the expenditure on chips to 160. Or, if the substitution effect outweighs the income effect, you might buy fewer chips but a greater quantity of Limca.Compensated Demand Curve: Incorporating Income and Substitution Effects
The compensated demand curve, on the other hand, seeks to separate the substitution and income effects. It asks: Given a change in the price of good X, how much of the change in consumption is caused by the substitution effect (change in relative prices) and how much by the income effect (change in purchasing power)?Example Explained
Returning to the initial example, if you calculate that the uncompensated demand change is -10 when the price of chips rises by 20%, the compensated demand curve would help you determine how much of this 10 reduction in demand is due to the substitution effect and how much due to the income effect.Consumption Decision:
Substitution Effect: The change in relative prices of the consumption basket (Price of X / Price of Y). Income Effect: The change in purchasing power due to the price change. For example, if the new price of chips is 40, and you can now only afford 2 packs, the decrease in utility might be partially offset by increasing the expenditure on chips to maintain the same level of utility. The compensated demand curve would show how much of this change in consumption is due to a shift in prices versus a change in purchasing power.