Movies are $10 a ticket, and DVD rentals are $5 a DVD. With movies on the vertical axis, the magnitude of the slope of the budget line is
A) 1/2.
B) 2.
C) 5.
D) 10.
The correct answer and explanation is :
Correct Answer: B) 2
Explanation:
This question is based on the concept of a budget line, a fundamental idea in microeconomics that shows all the combinations of two goods a consumer can afford given their income and the prices of the goods.
Let’s assume the consumer has a fixed budget, say \$100, to spend on movies and DVD rentals.
- Price of one movie ticket = \$10
- Price of one DVD rental = \$5
Let:
- $M$ = number of movies
- $D$ = number of DVDs
Then the budget constraint can be written as:
$$
10M + 5D = 100
$$
We can rewrite this in the form of a linear equation to find the slope:
$$
M = \frac{100}{10} – \frac{5}{10}D \Rightarrow M = 10 – 0.5D
$$
This equation is in the format:
$$
M = \text{intercept} – (\text{slope}) \times D
$$
So, the slope of the budget line is –0.5. However, since the question asks for the magnitude of the slope, we ignore the negative sign and focus on the absolute value, which is:
$$
|\text{slope}| = 0.5
$$
But here’s the trick: the question specifies that movies are on the vertical axis and DVDs on the horizontal axis.
So:
- Vertical axis = movies (M)
- Horizontal axis = DVDs (D)
The slope of the budget line is calculated as:
$$
\text{Slope} = \frac{\text{Price of horizontal axis good}}{\text{Price of vertical axis good}} = \frac{5}{10} = 0.5
$$
BUT since the formula for slope is rise over run, and you’re plotting movies (Y-axis) over DVDs (X-axis), the correct expression of the slope is:
$$
\text{Slope} = -\frac{Price of movies}{Price of DVDs} = -\frac{10}{5} = -2
$$
Therefore, the magnitude of the slope is 2.