In consumer utility theory, as a consumer moves downward from left to right along a standa… — JAMB UTME

In consumer utility theory, as a consumer moves downward from left to right along a standard, origin-convex indifference curve for two commodities, $X$ and $Y$ , how does the Marginal Rate of Substitution ( $MRS_{xy}$ ) behave?

It diminishes continuously as more units of $X$ are substituted for $Y$ .Cevap
B
It remains constant across all combination points on the curve.
C
It increases steadily as the quantity of $X$ consumed rises.
D
It falls to zero at the point where total utility from both goods is maximized.

Cevap

The Marginal Rate of Substitution (

MRS_{xy}

) diminishes continuously as more units of

X

are substituted for

Y

The correct answer accounts for the principle of diminishing marginal rate of substitution. As a consumer increases consumption of Good

X

, its marginal utility (

MU_x

) decreases relative to that of Good

Y

(

MU_y

). Consequently, the consumer yields smaller amounts of

Y

for each extra unit of

X

, making

MRS_{xy}

diminish and conferring a convex shape to the indifference curve.

Adım Adım Çözüm

Define Marginal Rate of Substitution (

MRS_{xy}

)

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

MRS_{xy}

measures the rate at which a consumer is willing to give up Good

Y

to obtain one additional unit of Good

X

while keeping total utility constant.

Analyze the impact of moving downward along the curve

As consumption of

X

increases,

MU_x

falls (due to diminishing marginal utility), while

MU_y

rises as

Y

becomes scarcer to the consumer.

The principle of diminishing marginal utility dictates that as a good becomes more abundant, its marginal valuation declines.

Determine the curvature property resulting from this behavior

The slope of the curve (

MRS_{xy}

) flattens, making the curve convex to the origin.

A diminishing ratio of

\frac{MU_x}{MU_y}

directly accounts for the origin-convex shape of standard indifference curves.

Anahtar Kavram

Diminishing Marginal Rate of Substitution and Indifference Curve Convexity

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