A consumer allocates a monthly income of \text{₦}12,000 between Good X and Good Y. The mar… — JAMB UTME

A consumer allocates a monthly income of $\text{₦}12,000$ between Good $X$ and Good $Y$ . The market price of Good $Y$ is $\text{₦}400$ per unit. At consumer equilibrium under ordinal utility analysis, the consumer purchases $15$ units of Good $Y$ . If the Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) at this equilibrium point is $1.5$ , how many units of Good $X$ does the consumer purchase?

Answer: 10 units

Answer

10 units

Under ordinal utility theory, consumer equilibrium occurs at the point of tangency between the highest attainable indifference curve and the budget line, satisfying

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

. Given

MRS_{xy} = 1.5

and

P_y = \text{₦}400

, the price of Good

X

P_x = 1.5 \times 400 = \text{₦}600

. Spending

15

units of

Y

\text{₦}400

consumes

\text{₦}6,000

of the total

\text{₦}12,000

budget, leaving

\text{₦}6,000

for Good

X

. Dividing

\text{₦}6,000

P_x = \text{₦}600

yields exactly

10

units of Good

X

Step-by-Step Solution

Calculate the total expenditure on Good Y

₦6,000

Multiply the equilibrium quantity of Y (15 units) by the unit price of Y (₦400).

Determine the remaining budget allocated to Good X

₦6,000

Subtract total expenditure on Y from the overall income (₦12,000 - ₦6,000).

Calculate the unit price of Good X using the ordinal equilibrium condition

₦600

At consumer equilibrium under ordinal utility, the slope of the indifference curve equals the slope of the budget line (

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

). Thus,

1.5 = \frac{P_x}{400} \Rightarrow P_x = 600

Calculate the quantity of Good X purchased

10 units

Divide the expenditure on Good X (₦6,000) by the price of Good X (₦600).

Key Concept

Consumer Equilibrium under Ordinal Utility

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