Model Answer
0 min readIntroduction
The Marshallian approach to demand theory, developed by Alfred Marshall, is a foundational concept in microeconomics that explains consumer behavior based on utility maximization subject to a budget constraint. Unlike the Hicksian approach which keeps utility constant, Marshallian demand, also known as uncompensated demand, holds money income constant when analyzing price changes. A key assumption in Marshallian analysis is the diminishing marginal utility of goods and, crucially for this problem, the constant marginal utility of money. This framework allows for a direct relationship between price, income, and quantity demanded, forming the basis of the downward-sloping demand curve.
Understanding Marshallian Demand and the Equimarginal Principle
The Marshallian demand theory posits that a consumer aims to maximize their total utility from consuming various goods, subject to their given income and market prices. The equilibrium condition for utility maximization is based on the law of equimarginal utility, which states that a consumer allocates their income such that the ratio of the marginal utility to the price is equal for all goods consumed, and also equal to the marginal utility of money.
Mathematically, for a consumer consuming goods X and Y, the equilibrium condition is:
MUx / Px = MUy / Py = MUm
Where:
MUxandMUyare the marginal utilities of goods X and Y, respectively.PxandPyare the prices of goods X and Y, respectively.MUmis the marginal utility of money, assumed to be constant in the Marshallian approach.
Demonstrating No Change in Quantity Demanded
Let's consider the scenario where all prices and the consumer's income increase in the same proportion. Suppose prices (Px, Py) and income (I) all increase by a factor 'k' (where k > 1). The new prices will be k * Px and k * Py, and the new income will be k * I.
The original budget constraint for the consumer is:
Px * Qx + Py * Qy = I
After the proportional increase, the new budget constraint becomes:
(k * Px) * Qx + (k * Py) * Qy = k * I
We can factor out 'k' from the left side of the new budget constraint:
k * (Px * Qx + Py * Qy) = k * I
Dividing both sides by 'k' (since k > 0):
Px * Qx + Py * Qy = I
This shows that the new budget constraint is identical to the original budget constraint. Geometrically, a proportional increase in all prices and income means the budget line shifts outwards in a parallel fashion, but its slope (-Px/Py) remains unchanged because the ratio of prices is constant (-k*Px / k*Py = -Px/Py). Since the budget line remains effectively the same in terms of purchasing power and relative prices, the consumer faces the exact same set of attainable bundles as before.
Furthermore, let's re-examine the equimarginal utility condition:
Original condition: MUx / Px = MUy / Py = MUm
New condition: MUx / (k * Px) = MUy / (k * Py) = MUm'
Since the marginal utility of money (MUm) is assumed to be constant in Marshallian analysis, and the relative prices (Px/Py) remain unchanged, the consumer will strive to maintain the same equality of marginal utility to price ratios. Because their real purchasing power has not changed, the combination of goods (Qx, Qy) that maximizes utility will remain the same. The consumer can afford the same quantities of goods as before, and the relative attractiveness of those goods (in terms of utility per dollar) has not changed.
Therefore, when prices and income increase in the same proportion, the consumer's real income remains constant, relative prices do not change, and the optimal consumption bundle, and thus the quantity demanded for each commodity, remains unchanged in the Marshallian approach.
Conclusion
In conclusion, the Marshallian approach demonstrates that a proportional increase in all prices and the consumer's money income leaves the quantity demanded for a commodity unchanged. This outcome stems from two critical aspects: first, the consumer's real income or purchasing power remains constant, and second, the relative prices of goods do not alter. The budget constraint, when scaled proportionally for both prices and income, reverts to its original form, indicating no change in the feasible set of consumption bundles. This principle highlights the importance of real income and relative prices, rather than nominal values, in determining consumer demand under the Marshallian framework.
Answer Length
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