A consumer spends their entire monthly budget of \text{₦}2,400 on two commodities, Good X … — JAMB UTME

A consumer spends their entire monthly budget of $\text{₦}2,400$ on two commodities, Good $X$ and Good $Y$ . The market price of Good $Y$ ( $P_y$ ) is $\text{₦}30$ per unit. At utility-maximizing equilibrium under ordinal utility analysis, the consumer purchases $20$ units of Good $X$ and $40$ units of Good $Y$ . What is the magnitude of the Marginal Rate of Substitution of Good $X$ for Good $Y$ ( $MRS_{xy}$ ) at this equilibrium point?

Answer: 2

Answer

The Marginal Rate of Substitution of Good X for Good Y (MRS_xy) at equilibrium is 2.

Under ordinal utility theory, consumer equilibrium occurs at the point of tangency between the budget line and the highest attainable indifference curve. At this point, the slope of the indifference curve (

MRS_{xy}

) equals the absolute slope of the budget line (

\frac{P_x}{P_y}

). First, calculating

P_x

from the budget equation

2400 = 20 P_x + 30(40)

yields

P_x = \text{₦}60

. Then, substituting

P_x

and

P_y

into the equilibrium condition gives

MRS_{xy} = \frac{60}{30} = 2

Step-by-Step Solution

Formulate the budget line equation using total income and expenditures.

2400 = 20 P_x + 30(40)

Total expenditure on both goods must equal total income at budget exhaustion.

Calculate the price of Good X (

P_x

P_x = \text{₦}60

Finding the price of Good X is necessary to establish the price ratio.

Calculate the Marginal Rate of Substitution at consumer equilibrium.

MRS_{xy} = \frac{P_x}{P_y} = \frac{60}{30} = 2

At consumer equilibrium under ordinal utility, the indifference curve is tangent to the budget line, meaning

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

Key Concept

Consumer Equilibrium Condition under Ordinal Utility Analysis

Estimated Time:2m 0s

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