An indifference curve is convex to the origin because the marginal rate of substitution (M… — JAMB UTME

An indifference curve is convex to the origin because the marginal rate of substitution ( $MRS_{xy}$ ) increases as a consumer substitutes commodity $X$ for commodity $Y$ along the curve.

Answer: Answer

Answer

The statement is False. Indifference curves are convex to the origin due to a diminishing marginal rate of substitution (

MRS_{xy}

), not an increasing one.

The statement is false because standard indifference curves are convex to the origin due to the Principle of Diminishing Marginal Rate of Substitution. As a consumer substitutes good

X

for good

Y

, they are willing to give up successively fewer units of good

Y

for each additional unit of good

X

Step-by-Step Solution

Identify the relationship between the slope of an indifference curve and the Marginal Rate of Substitution (

MRS_{xy}

)

The slope of an indifference curve at any point represents the marginal rate of substitution (

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

Convexity to the origin describes how this slope changes as a consumer moves down the curve from left to right.

Analyze how

MRS_{xy}

changes along a convex indifference curve

As the consumer acquires more units of

X

and fewer units of

Y

, the marginal utility of

X

(

MU_x

) falls while the marginal utility of

Y

(

MU_y

) rises, causing the ratio

\frac{MU_x}{MU_y}

to decrease (diminish).

This behavior follows the law of diminishing marginal utility under ordinal utility analysis.

Evaluate the validity of the statement

Because

MRS_{xy}

diminishes (decreases) rather than increases along the curve, the statement is false.

An increasing

MRS_{xy}

would produce a concave indifference curve to the origin.

Key Concept

Diminishing Marginal Rate of Substitution and Indifference Curve Convexity

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