In ordinal utility analysis, a rational consumer maximizes satisfaction subject to a budge… — JAMB UTME

In ordinal utility analysis, a rational consumer maximizes satisfaction subject to a budget constraint at the point of tangency between an indifference curve and the budget line. At this equilibrium point, the Marginal Rate of Substitution ( $MRS_{xy}$ ) must be equal to which of the following?

The price ratio of the two commodities ( $\frac{P_x}{P_y}$ )Answer
B
The ratio of the total utilities of the two commodities ( $\frac{TU_x}{TU_y}$ )
C
A constant slope along a straight-line indifference curve
D
The combined sum of the market prices ( $P_x + P_y$ )

Answer

The price ratio of the two commodities (

\frac{P_x}{P_y}

)

In ordinal utility theory, consumer equilibrium is achieved when the consumer maximizes utility given their budget constraint. Graphically, this happens at the point where the highest attainable indifference curve is tangent to the budget line, meaning the slope of the indifference curve (

MRS_{xy}

) equals the price ratio of the two goods (

\frac{P_x}{P_y}

Step-by-Step Solution

Identify the graphical condition for consumer equilibrium in ordinal utility theory.

Equilibrium occurs at the point of tangency between the budget line and the highest reachable indifference curve.

At the point of tangency, the slope of the indifference curve matches the slope of the budget line.

Equate the mathematical definitions for the slopes.

The slope of the indifference curve is

MRS_{xy}

and the slope of the budget line is

\frac{P_x}{P_y}

, yielding

MRS_{xy} = \frac{P_x}{P_y}

This condition ensures the rate at which the consumer is willing to trade good

X

for good

Y

equals the rate at which the market allows them to trade.

Key Concept

Consumer Equilibrium under Ordinal Utility

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