A consumer allocating a fixed income between Good X and Good Y faces market prices of P_x … — JAMB UTME

A consumer allocating a fixed income between Good $X$ and Good $Y$ faces market prices of $P_x = \text{₦}60$ and $P_y = \text{₦}15$ . At their current consumption bundle, the Marginal Rate of Substitution ( $MRS_{xy}$ ) is $3$ . Assuming standard indifference curves that are strictly convex to the origin, how should the consumer adjust their purchases to attain equilibrium?

Decrease consumption of Good $X$ and increase consumption of Good $Y$ Answer
B
Increase consumption of Good $X$ and decrease consumption of Good $Y$
C
Increase consumption of both Good $X$ and Good $Y$ simultaneously
D
Maintain the current consumption bundle without modification

Answer

The consumer should decrease consumption of Good

X

and increase consumption of Good

Y

In ordinal utility analysis, consumer equilibrium is reached at the point where the indifference curve is tangent to the budget line, satisfying the condition

MRS_{xy} = \frac{P_x}{P_y}

. Given

P_x = \text{₦}60

and

P_y = \text{₦}15

, the market price ratio is

\frac{60}{15} = 4

. Since the current

MRS_{xy}

3

, which is less than

4

, the consumer values Good

X

less than the market does at the margin. To raise

MRS_{xy}

to match the market ratio of

4

, the consumer must decrease consumption of Good

X

and increase consumption of Good

Y

along the budget constraint.

Step-by-Step Solution

Calculate the market price ratio of Good

X

to Good

Y

\frac{P_x}{P_y} = \frac{60}{15} = 4.

The price ratio determines the slope of the budget line.

Compare the current Marginal Rate of Substitution (

MRS_{xy}

) to the price ratio.

MRS_{xy} = 3 < \frac{P_x}{P_y} = 4.

Equilibrium under ordinal utility requires

MRS_{xy} = \frac{P_x}{P_y}

at the point of tangency.

Determine the necessary adjustment to restore equilibrium along a convex indifference curve.

Reduce Good

X

and increase Good

Y

to increase

MRS_{xy}

from

3

4

Due to the diminishing rate of marginal substitution, reducing consumption of

X

increases

MU_x

and increasing consumption of

Y

decreases

MU_y

, which raises

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

toward

4

Key Concept

Consumer Equilibrium under Ordinal Utility

Estimated Time:2m 0s

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