A consumer allocates a fixed budget between Good X and Good Y. Good X sells for \mathbb{N}… — JAMB UTME

A consumer allocates a fixed budget between Good $X$ and Good $Y$ . Good $X$ sells for $\mathbb{N}40$ per unit, while Good $Y$ sells for $\mathbb{N}15$ per unit. If the consumer obtains $160$ utils of marginal utility from the last unit of Good $X$ , what marginal utility must Good $Y$ yield for the consumer to attain equilibrium?

$60$ utilsAnswer
B
$160$ utils
C
$40$ utils
D
$426.67$ utils

Answer

The marginal utility yielded by Good

Y

must be

60

utils.

Under cardinal utility analysis, a consumer maximizes total satisfaction from a given budget when the marginal utility per monetary unit spent is equal for all commodities consumed (

\frac{MU_X}{P_X} = \frac{MU_Y}{P_Y}

). Given

MU_X = 160

and

P_X = 40

, the marginal utility per Naira spent on Good

X

\frac{160}{40} = 4

. For Good

Y

with price

P_Y = 15

, setting

\frac{MU_Y}{15} = 4

yields

MU_Y = 60

utils.

Step-by-Step Solution

Identify the equilibrium condition under cardinal utility analysis for two goods.

The equi-marginal condition states

\frac{MU_X}{P_X} = \frac{MU_Y}{P_Y}

A rational consumer maximizes satisfaction when the marginal utility per unit of currency spent is equal across all goods.

Calculate the weighted marginal utility per Naira for Good

X

\frac{MU_X}{P_X} = \frac{160}{40} = 4\text{ utils per Naira}.

This yields the satisfaction per Naira spent on Good

X

Solve for the unknown marginal utility of Good

Y

(

MU_Y

\frac{MU_Y}{15} = 4 \implies MU_Y = 4 \times 15 = 60\text{ utils}.

Equating the marginal utility per Naira spent on Good

Y

4

gives the required

MU_Y

Key Concept

Principle of Equi-Marginal Utility

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