A consumer allocates a monthly budget of ₦24,000 between Good X (plotted on the horizontal… — JAMB UTME

A consumer allocates a monthly budget of ₦24,000 between Good $X$ (plotted on the horizontal axis) and Good $Y$ (plotted on the vertical axis). The initial price of Good $X$ ( $P_X$ ) is ₦1,200 per unit and the price of Good $Y$ ( $P_Y$ ) is ₦800 per unit. If the price of Good $Y$ increases by $50\%$ while the consumer's income and the price of Good $X$ remain unchanged, what is the absolute slope of the new budget line?

A
1.50
1.00Answer
C
0.67
D
20.00

Answer

The absolute slope of the new budget line is 1.00.

The absolute slope of a budget line is given by the ratio of the price of the horizontal good to the price of the vertical good (

P_X / P_Y

). After a 50% increase, the price of Good

Y

rises from ₦800 to ₦1,200. Dividing the price of Good

X

(₦1,200) by the updated price of Good

Y

(₦1,200) gives an absolute slope of 1.00.

Step-by-Step Solution

Calculate the updated price of Good

Y

(

P_Y'

)

P_Y' = ₦800 + (0.50 \times ₦800) = ₦1,200

The price of Good

Y

increased by 50%.

State the formula for the absolute slope of the budget line

\text{Slope} = \frac{P_X}{P_Y'}

The slope of a budget line with Good

X

on the horizontal axis and Good

Y

on the vertical axis represents the relative price ratio

P_X / P_Y

Substitute the price values into the slope formula

\text{Slope} = \frac{1,200}{1,200} = 1.00

Dividing the price of Good

X

(₦1,200) by the new price of Good

Y

(₦1,200) yields the updated slope magnitude.

Key Concept

Budget Line Slope and Relative Price Ratio

Estimated Time:1m 30s

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