A consumer's preferences for Good X (on the horizontal axis) and Good Y (on the vertical a… — JAMB UTME

A consumer's preferences for Good $X$ (on the horizontal axis) and Good $Y$ (on the vertical axis) yield an indifference curve where the consumer is willing to give up $6$ units of $Y$ to acquire $1$ additional unit of $X$ at consumption bundle $A$ . As the consumer moves to bundle $B$ by consuming more $X$ , the rate of substitution drops to $3$ units of $Y$ for $1$ additional unit of $X$ . Which of the following statements correctly explains the economic rationale behind this behavior and its geometric implication for the curve?

A
The marginal rate of substitution remains constant throughout, causing the indifference curve to be a downward-sloping straight line.
The marginal rate of substitution diminishes because the marginal utility of Good $X$ falls relative to Good $Y$ , making the indifference curve convex to the origin.Cevap
C
Total utility reaches its maximum at bundle $B$ where marginal utility becomes zero, causing the indifference curve to become concave to the origin.
D
The consumer's total budget constraint shrinks as more of Good $X$ is consumed, causing the curve to shift inward toward the origin.

Cevap

The marginal rate of substitution diminishes because the marginal utility of Good X falls relative to Good Y, making the indifference curve convex to the origin.

As a consumer moves down an indifference curve by consuming more of Good X in place of Good Y, the marginal utility of Good X decreases while that of Good Y increases. Since the Marginal Rate of Substitution (

MRS_{xy}

) equals the ratio of marginal utilities (

\frac{MU_x}{MU_y}

MRS_{xy}

decreases along the curve. Geometrically, this diminishing rate causes the slope of the curve to become flatter from left to right, making the indifference curve convex to the origin.

Adım Adım Çözüm

Analyze the change in substitution rates between bundle A and bundle B

The consumer sacrifices fewer units of Good Y (decreasing from 6 to 3) for each extra unit of Good X.

This reduction demonstrates a diminishing Marginal Rate of Substitution (

MRS_{xy}

) along the curve.

Relate the Marginal Rate of Substitution to Marginal Utility ratios

The Marginal Rate of Substitution is expressed as

MRS_{xy} = \frac{MU_x}{MU_y}

. As more of Good X is consumed,

MU_x

declines relative to

MU_y

The principle of diminishing marginal utility dictates that acquiring more units of a specific commodity reduces its relative additional satisfaction.

Deduce the geometric shape of the curve

A progressively decreasing absolute slope (

MRS_{xy}

) from left to right establishes that the curve bends inward.

Diminishing marginal rate of substitution is the exact theoretical foundation for the convexity of an indifference curve to the origin.

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Diminishing Marginal Rate of Substitution and Convexity of Indifference Curves

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