The table below presents a consumer's indifference schedule showing various combinations o… — JAMB UTME

The table below presents a consumer's indifference schedule showing various combinations of Good $X$ and Good $Y$ that yield the same level of satisfaction:

Combination	Good $X$ (units)	Good $Y$ (units)
I	1	18
II	2	12
III	3	7
IV	4	3
V	5	1

What is the Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) as the consumer transitions from combination II to combination III, and which property of indifference curves is confirmed by the overall progression across all combinations?

$MRS_{xy} = 5$ ; it confirms that indifference curves are convex to the origin due to a diminishing marginal rate of substitution.Cevap
B
$MRS_{xy} = 5$ ; it confirms that indifference curves are concave to the origin due to an increasing marginal rate of substitution.
C
$MRS_{xy} = 7$ ; it confirms that indifference curves slope downward with a constant marginal rate of substitution.
D
$MRS_{xy} = 12$ ; it confirms that higher indifference curves represent higher levels of total utility.

Cevap

MRS_{xy} = 5

; it confirms that indifference curves are convex to the origin due to a diminishing marginal rate of substitution.

Moving from combination II

(2X, 12Y)

to combination III

(3X, 7Y)

requires sacrificing

5

units of Good

Y

to gain

1

unit of Good

X

, giving an

MRS_{xy}

5

. Across the entire schedule, the rate of sacrifice decreases (

6 \rightarrow 5 \rightarrow 4 \rightarrow 2

). This law of diminishing marginal rate of substitution is the fundamental reason standard indifference curves are convex to the origin.

Adım Adım Çözüm

Calculate the Marginal Rate of Substitution (

MRS_{xy}

) between combination II and combination III.

\Delta X = 3 - 2 = 1

unit;

\Delta Y = 12 - 7 = 5

units.

MRS_{xy} = \left| \frac{\Delta Y}{\Delta X} \right| = \frac{5}{1} = 5

The Marginal Rate of Substitution measures the amount of Good

Y

a consumer is willing to give up to obtain an additional unit of Good

X

while keeping total utility constant.

Analyze the pattern of

MRS_{xy}

across all consecutive combinations in the schedule.

From I to II:

MRS_{xy} = \frac{18 - 12}{1} = 6

. From II to III:

MRS_{xy} = \frac{12 - 7}{1} = 5

. From III to IV:

MRS_{xy} = \frac{7 - 3}{1} = 4

. From IV to V:

MRS_{xy} = \frac{3 - 1}{1} = 2

Tracking the full schedule reveals whether the willingness to substitute is increasing, constant, or diminishing.

Relate the diminishing trend of

MRS_{xy}

to the geometric property of indifference curves.

The progression

6 \rightarrow 5 \rightarrow 4 \rightarrow 2

shows a diminishing

MRS_{xy}

, which geometrically ensures that the indifference curve is convex to the origin.

As a consumer acquires more of Good

X

, its marginal utility relative to Good

Y

falls, leading to a flatter slope (diminishing rate of substitution) moving left to right.

Anahtar Kavram

Marginal Rate of Substitution (

MRS_{xy}

) and Convexity of Indifference Curves

Tahmini Süre:1m 30s

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