Under the ordinal utility approach, a consumer optimizes satisfaction subject to a budget … — JAMB UTME

Under the ordinal utility approach, a consumer optimizes satisfaction subject to a budget constraint when purchasing two commodities, Good $X$ and Good $Y$ . Which condition must hold true at this point of consumer equilibrium?

The Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) is equal to the price ratio of the two goods ( $\frac{P_x}{P_y}$ ), and the indifference curve is convex to the origin.Answer
B
The Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) remains constant at all points along the indifference curve.
C
The Total Utility derived from Good $X$ equals the Total Utility derived from Good $Y$ at the point of maximum expenditure.
D
The Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) is equal to the inverse price ratio ( $\frac{P_y}{P_x}$ ).

Answer

Consumer equilibrium is attained where the Marginal Rate of Substitution of Good

X

for Good

Y

(

MRS_{xy}

) equals the ratio of their prices (

\frac{P_x}{P_y}

), and the indifference curve is convex to the origin.

The statement specifying that

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

and that the indifference curve is convex to the origin is correct because consumer equilibrium in ordinal utility analysis requires the indifference curve to be tangent to the budget line at a point where the marginal rate of substitution is diminishing.

Step-by-Step Solution

Identify the slope of the indifference curve and budget line

Slope of Indifference Curve =

-MRS_{xy}

; Slope of Budget Line =

-\frac{P_x}{P_y}

The indifference curve represents consumer preferences, while the budget line represents consumer expenditure capacity.

Apply the tangency condition for utility maximization under ordinal analysis

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

At the point of equilibrium, the rate at which the consumer is willing to substitute Good

X

for Good

Y

equals the rate at which the market allows substitution.

Verify the second-order condition for equilibrium

The indifference curve must be strictly convex to the origin.

Convexity ensures a stable equilibrium point where the marginal rate of substitution is diminishing.

Key Concept

Consumer Equilibrium under Ordinal Utility

Estimated Time:1m 0s

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