Q.How does the budget line change if the price of good 2 decreases by a rupee but the price of good 1 and the consumer's income remain unchanged? (This question is related to question 4.)

The budget line represents all combinations of two goods that a consumer can afford given their income and the prices of the goods. Its equation is given by:

If the price of good 2 ($P_2$) decreases while the price of good 1 ($P_1$) and the consumer's income ($M$) remain unchanged, the following occurs:

1. X-intercept: The maximum quantity of good 1 that can be purchased is $M/P_1$. Since $M$ and $P_1$ are constant, the X-intercept of the budget line remains unchanged.
2. Y-intercept: The maximum quantity of good 2 that can be purchased is $M/P_2$. Since $M$ is constant and $P_2$ decreases, the value of $M/P_2$ increases. This means the Y-intercept shifts outwards, indicating the consumer can now afford more of good 2. …

The budget line represents all possible combinations of two goods that a consumer can afford given their income and the market prices of those goods. It illustrates the consumer's consumption possibilities. The equation of a budget line is given by:

This equation states that the total expenditure on good 1 ($P_1 x_1$) plus the total expenditure on good 2 ($P_2 x_2$) must be equal to the consumer's income ($M$).

To understand how the budget line changes, it is helpful to consider its intercepts and its slope. If we plot good 1 on the horizontal axis and good 2 on the vertical axis:

• The horizontal intercept (maximum quantity of good 1 affordable if all income is spent on good 1) is $M/P_1$.
• The vertical intercept (maximum quantity of good 2 affordable if all income is spent on good 2) is $M/P_2$.
• The slope of the budget line is $-P_1/P_2$, which represents the rate at which the consumer must give up units of good 2 to obtain one additional unit of good 1, given their income and market prices. It is the market rate of substitution between the two goods.

Now, let's analyze the specific change: the price of good 2 decreases by a rupee, while the price of good 1 and the consumer's income remain unchanged.

Let the initial prices be $P_1$ and $P_2$, and income be $M$.

The new price of good 2 is $P_2' = P_2 - 1$.

The price of good 1 remains $P_1$.

The income remains $M$.

We examine the impact on the intercepts and the slope:

1. Change in the horizontal intercept ($M/P_1$):

   Since the consumer's income ($M$) and the price of good 1 ($P_1$) both remain unchanged, the horizontal intercept $M/P_1$ will not change. This means the point where the budget line touches the good 1 axis stays fixed.

2. Change in the vertical intercept ($M/P_2$): …