If all prices rise by 5 percent and money income remains constant

If all prices rise by 5 percent and money income remains constant, the new budget line will have

A) a steeper slope.

B) a flatter slope.

C) a positive slope.

D) the same slope.

The correct answer and explanation is :

The correct answer is D) the same slope.

Explanation:

In economics, the budget line 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 is determined by the ratio of the prices of the two goods, specifically the negative of the ratio of the price of one good to the price of the other. This slope reflects the opportunity cost of choosing one good over the other.

In this question, the assumption is that all prices rise by 5 percent, but money income remains constant. Let’s break this down step by step.

1. Initial Budget Line:
   Suppose the consumer is considering two goods, Good X and Good Y. The initial budget constraint can be expressed as: $$
   M = P_X \cdot X + P_Y \cdot Y
   $$ where:

• $M$ is the money income,
• $P_X$ is the price of Good X,
• $P_Y$ is the price of Good Y,
• $X$ and $Y$ are the quantities of Good X and Good Y consumed, respectively. The slope of the budget line is: $$
  \text{slope of the budget line} = – \frac{P_X}{P_Y}
  $$ This indicates the trade-off between Good X and Good Y in terms of their prices.

1. Price Increase:
   If all prices rise by 5 percent, the new prices will be:

• $P_X’ = 1.05 \cdot P_X$
• $P_Y’ = 1.05 \cdot P_Y$ The new budget constraint becomes: $$
  M = P_X’ \cdot X + P_Y’ \cdot Y = 1.05 \cdot P_X \cdot X + 1.05 \cdot P_Y \cdot Y
  $$

1. New Budget Line:
   The new budget line will still have the same general form as the original budget line, but the prices have increased. The new slope of the budget line will be: $$
   \text{slope of the budget line} = – \frac{P_X’}{P_Y’} = – \frac{1.05 \cdot P_X}{1.05 \cdot P_Y} = – \frac{P_X}{P_Y}
   $$ This shows that the slope of the budget line remains unchanged because the prices of both goods increased by the same percentage (5 percent). The relative prices, and thus the opportunity cost, remain the same.
2. Conclusion:
   Since both prices increase by the same proportion, the slope of the budget line does not change. The consumer can still trade off the same amount of one good for the other at the same rate. Therefore, the new budget line will have the same slope as the original budget line.

Thus, the correct answer is D) the same slope.