The magnitude of the slope of the budget line is the ratio of
A) a price to its quantity.
B) a quantity to its price.
C) two prices.
D) two marginal rates of substitution.
The correct answer and explanation is :
Correct Answer: C) two prices.
Explanation:
The budget line in economics is a graphical representation that shows all the combinations of two goods a consumer can purchase with a given income, given the prices of the two goods. The slope of the budget line is particularly important because it reflects the rate at which one good can be traded for another while staying within budget.
Mathematically, the budget constraint is written as:
$$
P_x \cdot X + P_y \cdot Y = I
$$
Where:
- $P_x$ = price of good X
- $P_y$ = price of good Y
- $X$, $Y$ = quantities of goods X and Y
- $I$ = consumer’s income
To find the slope of the budget line, solve for $Y$:
$$
Y = \frac{I}{P_y} – \frac{P_x}{P_y} \cdot X
$$
The slope here is $-\frac{P_x}{P_y}$, and the magnitude of this slope is:
$$
\left| \frac{P_x}{P_y} \right|
$$
This represents how many units of good Y a consumer must give up to afford one more unit of good X, without exceeding the budget. So, the slope is the ratio of the price of good X to the price of good Y.
This ratio is not about quantities (which rules out choices A and B), nor does it relate to marginal rates of substitution (MRS), which refer to consumer preferences rather than budget constraints—so choice D is also incorrect.
Thus, the slope of the budget line reflects the opportunity cost of one good in terms of another, purely in terms of prices, not preferences or quantities.
In conclusion:
The magnitude of the slope of the budget line is the ratio of two prices, specifically the price of the good on the horizontal axis to the price of the good on the vertical axis, which is why Option C is correct.