The magnitude of the slope of the budget line measures the
A) opportunity cost of the good on the horizontal axis in terms of the good on the vertical axis.
B) opportunity cost of the good on the vertical axis in terms of the good on the horizontal axis.
C) price elasticity of demand.
D) price elasticity of supply.
The correct answer and explanation is :
Correct Answer: A) opportunity cost of the good on the horizontal axis in terms of the good on the vertical axis.
Explanation:
In microeconomics, the budget line (or budget constraint) represents all the combinations of two goods that a consumer can purchase given their income and the prices of those goods. The slope of the budget line plays a key role in understanding trade-offs and opportunity costs.
Let’s denote:
- $P_x$ = price of the good on the horizontal axis (Good X),
- $P_y$ = price of the good on the vertical axis (Good Y),
- $I$ = income of the consumer.
The budget line equation is:
$$
P_x X + P_y Y = I
$$
To express the budget line in terms of Y (vertical axis), solve for $Y$:
$$
Y = \frac{I}{P_y} – \frac{P_x}{P_y}X
$$
The slope of the budget line is:
$$
-\frac{P_x}{P_y}
$$
This negative slope indicates the trade-off between the two goods. Specifically, the magnitude of the slope ($\frac{P_x}{P_y}$) shows how many units of the good on the vertical axis (Good Y) a consumer must give up to obtain one more unit of the good on the horizontal axis (Good X). In simpler terms, the slope quantifies the opportunity cost of consuming more of Good X in terms of how much of Good Y must be sacrificed.
Therefore, the magnitude of the slope tells us the opportunity cost of the good on the horizontal axis (Good X) in terms of the good on the vertical axis (Good Y).
Choices C and D, referring to price elasticity, are unrelated here because elasticity measures responsiveness to price changes, not budget constraints.
Choice B is incorrect because it reverses the direction of the opportunity cost being measured by the slope.
Conclusion: The correct interpretation of the slope of the budget line is that it measures the opportunity cost of the good on the horizontal axis in terms of the good on the vertical axis, making Option A the correct answer.