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Difficulty: MediumBudget Line and Budget Constraint

A consumer allocates a fixed monetary budget exclusively between Good XX (plotted on the horizontal axis) and Good YY (plotted on the vertical axis). If the market price of Good XX decreases while the consumer's income and the price of Good YY remain unchanged, which of the following describes the resulting structural change to the budget line?

  1. The budget line pivots outward along the horizontal axis, becoming flatter.Answer
  2. B
    The budget line shifts parallel to the right away from the origin.
  3. C
    The budget line pivots inward along the vertical axis, becoming steeper.
  4. D
    The slope of the budget line increases because Good XX is now more expensive relative to Good YY.

Answer

The budget line pivots outward along the horizontal axis, becoming flatter.
The horizontal intercept of a budget line is given by I/PXI/P_X and the vertical intercept by I/PYI/P_Y. When the price of Good XX drops while income and the price of Good YY remain constant, the maximum quantity of Good XX affordable increases, pushing the horizontal intercept outward. Since the vertical intercept does not move, the budget line pivots around the vertical intercept and its absolute slope (PX/PYP_X/P_Y) decreases, making the line flatter.

Step-by-Step Solution

1
Identify the equation and intercepts of the budget line
The budget equation is PXX+PYY=IP_X X + P_Y Y = I. The horizontal intercept is I/PXI/P_X, the vertical intercept is I/PYI/P_Y, and the absolute slope is PX/PYP_X/P_Y.
Intercepts define the maximum quantities affordable of each good when spending all income on that single good.
2
Analyze the impact of a decrease in PXP_X
As PXP_X decreases to PX′P_X', the horizontal intercept I/PX′I/P_X' increases (moves further right). The vertical intercept I/PYI/P_Y remains unchanged.
Income II and PYP_Y are constant, so the consumer can purchase more units of Good XX but the maximum amount of Good YY remains fixed.
3
Determine the change in slope
The magnitude of the slope decreases from PX/PYP_X/P_Y to PX′/PYP_X'/P_Y, meaning the budget line becomes flatter.
The slope measures the opportunity cost of Good XX. A cheaper Good XX requires giving up fewer units of Good YY per unit of Good XX acquired.

Key Concept

Budget Line Rotation and Relative Price Changes
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Topics

Budget Line and Budget Constraint

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