If all prices fall by 5 percent and money income remains constant, the new budget line will have
A) a positive slope.
B) the same slope.
C) a steeper slope.
D) a flatter slope.
The correct answer and explanation is :
The correct answer is D) a flatter slope.
Explanation:
In economics, the budget line represents the combinations of two goods that a consumer can afford to purchase given their income and the prices of those goods. The slope of the budget line reflects the rate at which the consumer can trade one good for the other, which is determined by the relative prices of the goods. The equation for the budget line is:
$$
P_x \cdot X + P_y \cdot Y = M
$$
Where:
- $P_x$ and $P_y$ are the prices of goods X and Y, respectively,
- $X$ and $Y$ are the quantities of goods X and Y, respectively,
- $M$ is the consumer’s income.
The slope of the budget line is given by the negative of the price ratio, i.e.,
$$
\text{slope} = -\frac{P_x}{P_y}
$$
Now, let’s consider the scenario where all prices fall by 5 percent, but the consumer’s income remains constant. If the prices of both goods drop by 5%, then both $P_x$ and $P_y$ will decrease by 5%. This would make the ratio of the prices $\frac{P_x}{P_y}$ smaller. Since the slope of the budget line is determined by this price ratio, the slope will become less steep (flatter).
Effect on the budget line:
- When the prices of both goods decrease, the consumer is able to afford more of both goods for the same income. Thus, the consumer’s purchasing power increases, which shifts the budget line outward. However, because both prices have fallen by the same percentage, the relative price between the two goods remains unchanged.
- The new budget line will have the same horizontal intercept (the amount of good X the consumer can afford if they buy only X), but the vertical intercept (the amount of good Y the consumer can afford if they buy only Y) will be higher.
- The key change is in the slope: the budget line becomes flatter because the ratio of prices $\frac{P_x}{P_y}$ is smaller, reflecting the reduced opportunity cost of consuming one good relative to the other.
In conclusion, when prices of both goods fall by the same percentage, the budget line will become flatter, meaning the correct answer is D) a flatter slope.