A consumer purchasing two goods, X and Y, attains equilibrium when the marginal utility of… — JAMB UTME

A consumer purchasing two goods, $X$ and $Y$ , attains equilibrium when the marginal utility of Good $X$ ( $MU_x$ ) is $40$ utils and its price ( $P_x$ ) is $\text{₦}10$ . If the price of Good $Y$ ( $P_y$ ) is $\text{₦}5$ , what is the marginal utility of Good $Y$ ( $MU_y$ ) in utils at consumer equilibrium?

Answer: 20 utils / 20 / 20utils

Answer

The marginal utility of Good

Y

at consumer equilibrium is 20 utils.

Under cardinal utility analysis, consumer equilibrium for two commodities is achieved when the ratio of marginal utility to price is equal for both commodities (

\frac{MU_x}{P_x} = \frac{MU_y}{P_y}

). Substituting

MU_x = 40

P_x = 10

, and

P_y = 5

gives

\frac{40}{10} = \frac{MU_y}{5}

, which simplifies to

4 = \frac{MU_y}{5}

. Solving for

MU_y

gives

20

utils.

Step-by-Step Solution

State the equimarginal condition for consumer equilibrium when consuming two goods.

\frac{MU_x}{P_x} = \frac{MU_y}{P_y}

According to cardinal utility analysis, a consumer maximizes utility when the marginal utility per monetary unit spent is equal across all commodities.

Substitute the given values (

MU_x = 40

P_x = 10

P_y = 5

) into the formula.

\frac{40}{10} = \frac{MU_y}{5}

Substituting the known parameters sets up an algebraic equation for the unknown marginal utility of Good

Y

Solve the equation for

MU_y

4 = \frac{MU_y}{5} \implies MU_y = 4 \times 5 = 20\text{ utils}

Multiplying the marginal utility per naira spent (4 utils/naira) by the price of Good

Y

(₦5) gives the marginal utility of Good

Y

Key Concept

Equimarginal Principle of Consumer Equilibrium

Estimated Time:1m 30s

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