If a consumer spends a fixed money income exclusively on Good X (plotted on the horizontal… — JAMB UTME

If a consumer spends a fixed money income exclusively on Good $X$ (plotted on the horizontal axis) and Good $Y$ (plotted on the vertical axis), a simultaneous per-unit tax on Good $X$ and per-unit subsidy on Good $Y$ will cause the budget line to pivot inward along the horizontal axis, pivot outward along the vertical axis, and become steeper.

Answer: Answer

Answer

The statement is True. Increasing the price of the horizontal good while decreasing the price of the vertical good reduces the horizontal intercept, expands the vertical intercept, and increases the magnitude of the slope (

P_X / P_Y

), making the budget line steeper.

The statement is correct because taxing Good

X

raises

P_X

while subsidizing Good

Y

lowers

P_Y

. The absolute slope of the budget line equals

P_X / P_Y

. A higher numerator (

P_X

) and a lower denominator (

P_Y

) increase the value of

P_X / P_Y

, resulting in a steeper budget line anchored to a smaller horizontal intercept and a larger vertical intercept.

Step-by-Step Solution

Analyze the impact on the horizontal intercept (

I / P_X

Taxing Good

X

increases

P_X

, which decreases

I / P_X

and pivots the horizontal intercept inward toward the origin.

The horizontal intercept represents total income divided by the price of Good

X

Analyze the impact on the vertical intercept (

I / P_Y

Subsidizing Good

Y

decreases

P_Y

, which increases

I / P_Y

and pivots the vertical intercept outward away from the origin.

The vertical intercept represents total income divided by the price of Good

Y

Determine the change in the budget line slope magnitude (

P_X / P_Y

With

P_X

rising and

P_Y

falling, the price ratio

P_X / P_Y

increases, causing the budget line to become steeper.

The slope of the budget line measures the rate at which Good

Y

must be given up for Good

X

in the market.

Key Concept

Budget Line Rotation and Slope Dynamics

Estimated Time:1m 15s

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