A consumer allocates a total income of ₦6,000 exclusively to purchase good X and good Y. G… — JAMB UTME

A consumer allocates a total income of ₦6,000 exclusively to purchase good $X$ and good $Y$ . Good $X$ is plotted on the horizontal axis and costs ₦600 per unit, while good $Y$ is plotted on the vertical axis and costs ₦300 per unit. What is the absolute value of the slope of this consumer's budget line?

$2.0$ Answer
B
$0.5$
C
$10.0$
D
$20.0$

Answer

The magnitude of the slope of the budget line is

2.0

The slope of a budget line when good

X

is on the horizontal axis and good

Y

is on the vertical axis equals

-\frac{P_X}{P_Y}

. Taking the absolute value gives

\frac{600}{300} = 2.0

, which reflects the opportunity cost of purchasing one additional unit of good

X

in terms of good

Y

Step-by-Step Solution

Identify the given economic parameters from the problem statement.

Total Income (

I

) = ₦6,000; Price of Good

X

(

P_X

) = ₦600; Price of Good

Y

(

P_Y

) = ₦300.

Establishing the price and budget parameters is required to set up the budget equation.

State the standard formula for the slope of the budget line.

Slope =

-\frac{P_X}{P_Y}

, so the absolute value of the slope is

\frac{P_X}{P_Y}

The slope of the budget constraint measures the market opportunity cost of good

X

in terms of good

Y

foregone.

Substitute the prices of good

X

and good

Y

into the ratio.

Absolute Slope =

\frac{600}{300} = 2.0

Dividing the price of the horizontal-axis good by the price of the vertical-axis good provides the relative price ratio.

Key Concept

Budget Line Slope and Relative Price Ratio

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