The magnitude of the slope of the budget line is determined by
A) the marginal rate of substitution.
B) the level of income.
C) the consumer’s preferences for the goods.
D) relative prices.
The correct answer and explanation is :
The correct answer is:
D) relative prices.
Explanation:
The budget line represents all the possible combinations of two goods that a consumer can afford given their income and the prices of the goods. The slope of the budget line is an important economic concept that reflects the opportunity cost of consuming one good in terms of the other. The magnitude of the slope is determined by the relative prices of the two goods being considered.
To elaborate, the budget line equation is generally expressed as:
$$
P_x \cdot X + P_y \cdot Y = I
$$
Where:
- $P_x$ is the price of good $X$,
- $P_y$ is the price of good $Y$,
- $X$ and $Y$ are quantities of goods $X$ and $Y$, respectively,
- $I$ is the income of the consumer.
From this equation, the slope of the budget line can be derived as:
$$
\text{Slope of Budget Line} = -\frac{P_x}{P_y}
$$
This shows that the slope of the budget line is directly related to the ratio of the prices of the two goods. The absolute value of this slope tells us the rate at which the consumer must give up one good to consume more of the other, which is equivalent to the opportunity cost of one good in terms of the other.
Now, let’s look at the incorrect answers:
- A) the marginal rate of substitution: While the marginal rate of substitution (MRS) is an important concept in consumer theory, it relates to the consumer’s preferences and how they are willing to trade one good for another. The MRS is not the factor determining the slope of the budget line; it represents the consumer’s trade-offs along the indifference curve, not the budget constraint.
- B) the level of income: The level of income determines the position of the budget line (its outward or inward shift) but does not affect its slope. The slope is governed by the relative prices of the goods, not income.
- C) the consumer’s preferences for the goods: Preferences affect the consumer’s choice along the budget line but do not affect the slope of the budget line itself. The slope reflects the prices of the goods, not how much the consumer likes them.
Thus, the correct factor determining the magnitude of the slope of the budget line is relative prices of the goods.