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Difficulty: EasyBudget Line and Budget Constraint

If the price of good XX falls while the consumer's income and the price of good YY remain unchanged, the budget line rotates outward along the XX-axis and becomes less steep.

Answer: Answer

Answer

The statement is True. A reduction in the price of good XX increases the horizontal intercept (IPx\frac{I}{P_x}) while keeping the vertical intercept (IPy\frac{I}{P_y}) fixed, causing the budget line to rotate outward along the XX-axis and decrease in slope (PxPy\frac{P_x}{P_y}), which makes it flatter.
A fall in the price of good XX increases the maximum purchasable quantity of good XX (IPx\frac{I}{P_x}), moving the horizontal axis intercept outward while the vertical axis intercept (IPy\frac{I}{P_y}) stays stationary. Since the slope magnitude is the price ratio PxPy\frac{P_x}{P_y}, a smaller PxP_x yields a smaller slope, making the budget line flatter.

Step-by-Step Solution

1
Identify the formulas for the budget line intercepts and slope.
Horizontal intercept = IPx\frac{I}{P_x}, Vertical intercept = IPy\frac{I}{P_y}, Absolute slope = PxPy\frac{P_x}{P_y}.
These equations define how income and prices determine the position and steepness of the budget line.
2
Analyze the impact of a decrease in PxP_x on the intercepts.
The horizontal intercept IPx\frac{I}{P_x} increases, while the vertical intercept IPy\frac{I}{P_y} remains unchanged.
Because income (II) and the price of good YY (PyP_y) are constant, only the maximum purchasable amount of good XX changes.
3
Evaluate the change in the slope of the budget line.
The absolute slope PxPy\frac{P_x}{P_y} decreases, indicating that the budget line becomes less steep (flatter).
A lower price for good XX reduces the opportunity cost of good XX in terms of good YY.

Key Concept

Impact of Price Changes on Budget Line Rotation and Slope
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Topics

Budget Line and Budget Constraint

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