A consumer adjusting their bundle of goods moves along an indifference curve, giving up 4 … — JAMB UTME

A consumer adjusting their bundle of goods moves along an indifference curve, giving up $4$ units of Good $Y$ to obtain $2$ additional units of Good $X$ without changing their total level of satisfaction. What is the Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) over this range?

$2.0$ Answer
B
$0.5$
C
$6.0$
D
$1.0$

Answer

The Marginal Rate of Substitution (

MRS_{xy}

) is equal to

2.0

The Marginal Rate of Substitution of

X

for

Y

(

MRS_{xy}

) measures the units of Good

Y

a consumer must sacrifice to gain one additional unit of Good

X

while keeping total utility constant. Here, sacrificing

4

units of

Y

for

2

units of

X

gives an average rate of

\frac{4}{2} = 2.0

Step-by-Step Solution

Identify the change in quantity of Good

Y

(

\Delta Y

) and Good

X

(

\Delta X

)

\Delta Y = -4

(reduction of 4 units of

Y

) and

\Delta X = +2

(gain of 2 units of

X

)

The consumer gives up

Y

in exchange for

X

to remain on the same indifference curve.

Apply the Marginal Rate of Substitution formula

MRS_{xy} = -\frac{\Delta Y}{\Delta X} = -\left(\frac{-4}{2}\right) = 2.0

The magnitude of the slope of the indifference curve represents the rate at which

Y

is substituted for

X

Key Concept

Marginal Rate of Substitution (MRS) along an Indifference Curve

Estimated Time:1m 0s

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