A consumer allocates a fixed income between Good X and Good Y. At their current consumptio… — JAMB UTME

A consumer allocates a fixed income between Good $X$ and Good $Y$ . At their current consumption combination, the Marginal Rate of Substitution of $X$ for $Y$ ( $MRS_{xy}$ ) is $3$ , while the market price of Good $X$ ( $P_x$ ) is $\text{₦}150$ and the market price of Good $Y$ ( $P_y$ ) is $\text{₦}30$ . Assuming strictly convex indifference curves, what adjustment should the consumer make to attain consumer equilibrium under ordinal utility analysis?

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 as total utility is already maximized

Answer

The consumer should decrease consumption of Good

X

and increase consumption of Good

Y

Under ordinal utility analysis, consumer equilibrium is attained where the indifference curve is tangent to the budget line, satisfying

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

. Given

P_x = \text{₦}150

and

P_y = \text{₦}30

, the price ratio is

5

. Since the current

MRS_{xy}

3

, the marginal rate of substitution is less than the market price ratio (

3 < 5

). To increase

MRS_{xy}

toward equilibrium, the consumer must decrease consumption of Good

X

and increase consumption of Good

Y

, moving to a higher indifference curve tangency point.

Step-by-Step Solution

Calculate the price ratio of the two goods (

P_x / P_y

P_x / P_y = \frac{150}{30} = 5

The price ratio represents the slope of the budget line (the market rate of exchange between Good

X

and Good

Y

Compare the Marginal Rate of Substitution (

MRS_{xy}

) to the price ratio (

P_x / P_y

MRS_{xy} = 3 < P_x / P_y = 5

Consumer equilibrium under ordinal utility requires

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

at the point of tangency between the indifference curve and the budget line.

Determine the necessary change in consumption to restore equilibrium.

Since

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

, the consumer values Good

X

less than the market price demands. To raise

MRS_{xy}

5

, the consumer must reduce consumption of Good

X

and increase consumption of Good

Y

along the budget line, relying on the principle of diminishing marginal rate of substitution.

Moving up and to the left along an indifference curve increases the slope (

MRS_{xy}

) until it equals the slope of the budget line.

Key Concept

Consumer Equilibrium under Ordinal Utility (

MRS_{xy} = P_x / P_y

)

Estimated Time:2m 0s

Question

Answer

Step-by-Step Solution

Key Concept

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