The magnitude of the slope of the budget line is equal to the or of the good plotted on the __ in terms of the other good.
A) relative price; marginal cost; y-axis
B) relative price; total cost; y-axis
C) relative price; opportunity cost; x-axis
D) price; opportunity cost; x-axis
The correct answer and explanation is :
Correct Answer: C) relative price; opportunity cost; x-axis
Explanation:
In microeconomics, a budget line represents all the combinations of two goods that a consumer can purchase with a given income and at given prices. The slope of the budget line is a key concept because it illustrates how the market allows consumers to trade one good for another.
1. Understanding the Slope of the Budget Line:
Mathematically, the budget line can be written as:
$$
P_x X + P_y Y = I
$$
Where:
- $P_x$ = Price of good X
- $P_y$ = Price of good Y
- $X$ and $Y$ = Quantities of goods X and Y
- $I$ = Income
Solving for $Y$:
$$
Y = \frac{I}{P_y} – \frac{P_x}{P_y}X
$$
In this equation, the slope of the budget line is:
$$
-\frac{P_x}{P_y}
$$
This negative slope shows the rate at which the consumer must give up good Y to get one more unit of good X, which is known as the opportunity cost of X in terms of Y. It also reflects the relative price of X compared to Y.
2. Why “Relative Price” and “Opportunity Cost”?
- The relative price is the price of one good compared to another (here, $\frac{P_x}{P_y}$).
- The opportunity cost of the good on the x-axis is how much of the other good (on the y-axis) must be given up to obtain one more unit of the good on the x-axis.
Therefore, the magnitude (absolute value) of the slope of the budget line equals both the relative price and the opportunity cost of the good on the x-axis.
Conclusion:
Option C is correct because it properly identifies the slope as representing both the relative price and opportunity cost of the good on the x-axis, which is foundational in consumer choice theory.