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Difficulty: MediumBudget Line and Budget Constraint

If a consumer's total money income and the price of Good XX (plotted on the horizontal axis) both double while the price of Good YY (plotted on the vertical axis) remains constant, the horizontal intercept of the budget line remains unchanged while the line becomes steeper.

Answer: Answer

Answer

The statement is TRUE.
The horizontal intercept IPX\frac{I}{P_X} remains unchanged because both money income (II) and the price of Good XX (PXP_X) increase by the same proportion (doubling). The absolute slope of the budget line PXPY\frac{P_X}{P_Y} doubles because PXP_X doubles while PYP_Y stays constant, causing the budget line to pivot upward along the vertical axis to 2IPY\frac{2I}{P_Y} and become steeper.

Step-by-Step Solution

1
Determine the initial horizontal intercept and slope of the budget line.
The initial horizontal intercept is IPX\frac{I}{P_X} and the absolute slope is PXPY\frac{P_X}{P_Y}.
This establishes the baseline affordability boundary for Good XX and the relative price ratio.
2
Calculate the new horizontal intercept after income (II) and the price of Good XX (PXP_X) double.
The new horizontal intercept is 2I2PX=IPX\frac{2I}{2P_X} = \frac{I}{P_X}.
Proportionate increases in money income and the price of a good cancel each other out in the horizontal intercept calculation.
3
Calculate the new absolute slope of the budget line after PXP_X doubles while PYP_Y remains unchanged.
The new absolute slope is 2PXPY\frac{2P_X}{P_Y}, which is twice as steep as the original slope PXPY\frac{P_X}{P_Y}.
Good XX has become twice as expensive relative to Good YY, requiring the consumer to give up more units of Good YY for each additional unit of Good XX.

Key Concept

Effects of non-proportionate price and income changes on budget line intercepts and slope
Estimated Time:1m 15s
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Topics

Budget Line and Budget Constraint

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