A consumer allocates a total income of ₦15,000 exclusively to buy Good X and Good Y. The p… — JAMB UTME

A consumer allocates a total income of ₦ $15,000$ exclusively to buy Good $X$ and Good $Y$ . The price of Good $X$ ( $P_X$ ) is ₦ $1,500$ per unit, and the price of Good $Y$ ( $P_Y$ ) is ₦ $1,000$ per unit. If the consumer buys $6$ units of Good $X$ , what is the maximum number of units of Good $Y$ that can be purchased?

Answer: 6 units

Answer

The maximum number of units of Good

Y

the consumer can purchase is

6

units.

Using the budget equation

I = P_X Q_X + P_Y Q_Y

, substituting the given values yields

15,000 = (1,500 \times 6) + (1,000 \times Q_Y)

. Simplifying gives

15,000 = 9,000 + 1,000 Q_Y

, so

1,000 Q_Y = 6,000

, resulting in

Q_Y = 6

units.

Step-by-Step Solution

Calculate expenditure on Good

X

Expenditure on

X = 6 \times 1,500 = 9,000

Total spending on Good

X

is quantity multiplied by unit price.

Determine remaining budget for Good

Y

Remaining budget =

15,000 - 9,000 = 6,000

Subtracting expenditure on Good

X

from total income leaves the available budget for Good

Y

Calculate maximum quantity of Good

Y

Quantity of Good

Y = 6,000 / 1,000 = 6

Dividing the remaining budget by the unit price of Good

Y

yields the maximum affordable quantity of Good

Y

Key Concept

Budget Constraint and Linear Budget Equation

Question

Answer

Step-by-Step Solution

Key Concept

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