Along an indifference curve that is concave to the origin, the Marginal Rate of Substituti… — JAMB UTME

Along an indifference curve that is concave to the origin, the Marginal Rate of Substitution ( $MRS_{xy}$ ) increases as a consumer substitutes Good $X$ for Good $Y$ , indicating that the consumer is willing to give up progressively larger amounts of Good $Y$ to acquire each additional unit of Good $X$ .

Answer: Answer

Answer

The statement is True.

The statement is correct because concavity to the origin mathematically implies an increasing absolute slope along the indifference curve as consumption of Good

X

increases. Consequently,

MRS_{xy}

increases rather than diminishes, requiring larger sacrifices of Good

Y

for additional units of Good

X

Step-by-Step Solution

Define the Marginal Rate of Substitution (

MRS_{xy}

) in terms of indifference curve geometry.

The

MRS_{xy}

is represented by the absolute value of the slope of the indifference curve at any point, calculated as

MRS_{xy} = -\frac{\Delta Y}{\Delta X} = \frac{MU_x}{MU_y}

Establishing the link between curve slope and

MRS_{xy}

is essential for analyzing indifference curve curvature.

Analyze how slope changes along a curve that is concave to the origin.

As a consumer moves down along a concave curve (increasing consumption of Good

X

and decreasing consumption of Good

Y

), the curve grows progressively steeper.

Increased steepness from left to right means that the magnitude of

\frac{\Delta Y}{\Delta X}

gets larger.

Relate the changing slope to consumer trade-offs and

MRS_{xy}

Because the curve gets steeper,

MRS_{xy}

increases. This confirms that the consumer must give up larger quantities of Good

Y

for each additional unit of Good

X

This validates that the statement correctly describes the behavioral implications of a concave indifference curve.

Key Concept

Indifference Curve Curvature and Marginal Rate of Substitution

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