A person has $ 100 to spend on two goods X and Y whose respective prices are $3 and $5.

Question

A.Draw the budget line.
B.What happens to the original budget line if the budget falls by 25%?
C.What happens to the original budget line if the price of X doubles?
D.What happens to the original budget line if the price of Y falls to $4?

Answer 1

To analyze the budget line and the effects of the changes you've specified, let's start with the budget constraint for the two goods X and Y.

A. Draw the Budget Line

The budget line can be expressed using the equation:

\[ P_x \cdot X + P_y \cdot Y = I \]

Where:

• \( P_x \) is the price of good X ($3)
• \( P_y \) is the price of good Y ($5)
• \( I \) is the income ($100)

So the budget equation becomes:

\[ 3X + 5Y = 100 \]

To find the intercepts:

1. When X = 0: \[ 5Y = 100 \implies Y = \frac{100}{5} = 20 \]

2. When Y = 0: \[ 3X = 100 \implies X = \frac{100}{3} \approx 33.33 \]

Thus, the budget line intercepts are (0, 20) for Y and approximately (33.33, 0) for X. The budget line will be a straight line connecting these two points.

B. Budget Falls by 25%

If the budget falls by 25%, the new budget will be:

\[ I = 100 - (0.25 \cdot 100) = 100 - 25 = 75 \]

The new budget line equation would be:

\[ 3X + 5Y = 75 \]

Intercepts:

1. When X = 0: \[ 5Y = 75 \implies Y = \frac{75}{5} = 15 \]

2. When Y = 0: \[ 3X = 75 \implies X = \frac{75}{3} = 25 \]

The new budget line intercepts are (0, 15) and (25, 0). The budget line shifts inward, indicating less purchasing power.

C. Price of X Doubles

If the price of X doubles, \( P_x = 6 \):

The new budget equation becomes:

\[ 6X + 5Y = 100 \]

Intercepts:

1. When X = 0: \[ 5Y = 100 \implies Y = 20 \]

2. When Y = 0: \[ 6X = 100 \implies X = \frac{100}{6} \approx 16.67 \]

The new budget line intercepts are (0, 20) and approximately (16.67, 0). The budget line pivots inward toward the X-axis, reflecting a reduction in the maximum quantity of X that can be purchased while maintaining the same quantity of Y.

D. Price of Y Falls to $4

If the price of Y falls to $4, the new equation becomes:

\[ 3X + 4Y = 100 \]

Intercepts:

1. When X = 0: \[ 4Y = 100 \implies Y = 25 \]

2. When Y = 0: \[ 3X = 100 \implies X = \frac{100}{3} \approx 33.33 \]

The new budget line intercepts are (0, 25) and approximately (33.33, 0). The budget line pivots outward toward the Y-axis, indicating that the consumer can now afford more of good Y for the same amount spent on X.

Summary of Changes to the Budget Line:

• Original Budget Line: Based on $100 with prices $3 for X and $5 for Y, with intercepts (0, 20) and (33.33, 0).
• 25% Budget Reduction: New budget line intercepts (0, 15) and (25, 0), shifting inward.
• Price of X Doubles: New budget line intercepts (0, 20) and (16.67, 0), pivoting inward toward the X-axis.
• Price of Y Falls to $4: New budget line intercepts (0, 25) and (33.33, 0), pivoting outward toward the Y-axis.