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Difficulty: HardBudget Line and Budget Constraint

A consumer allocates a total monetary budget of ₦18,000 to purchase Good XX (plotted on the horizontal axis) and Good YY (plotted on the vertical axis). At current market prices, the consumer can afford a maximum of 60 units of Good XX or 45 units of Good YY. If the price of Good XX decreases by 25%25\% while the price of Good YY and total money income remain constant, what is the absolute value of the slope of the new budget line?

  1. 0.5625Answer
  2. B
    0.7500
  3. C
    1.7778
  4. D
    0.4219

Answer

The absolute value of the slope of the new budget line is 0.5625.
The initial unit prices derived from maximum affordable quantities are Px = ₦300 and Py = ₦400. Decreasing Px by 25% gives a new price Px' = ₦225. Because the slope of the budget line on a standard coordinate system (Good X on the horizontal axis) equals -Px / Py, its magnitude is 225 / 400 = 0.5625.

Step-by-Step Solution

1
Calculate initial unit prices of Good X and Good Y from budget intercepts
Px = ₦18,000 / 60 = ₦300; Py = ₦18,000 / 45 = ₦400
The maximum quantity of each good attainable with full budget equals Income divided by unit price.
2
Determine the updated price of Good X after a 25% price decrease
Px' = ₦300 × (1 - 0.25) = ₦225
A 25% price fall reduces the nominal price per unit of Good X by ₦75.
3
Compute the slope of the new budget line
Absolute slope = Px' / Py = 225 / 400 = 0.5625
The absolute slope of a budget line with Good X on the horizontal axis represents relative prices (Px / Py).

Key Concept

Budget Line Slope and Price Changes
Estimated Time:2m 0s
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Topics

Budget Line and Budget Constraint

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