What happens to the budget set if both the prices as well as the income double? (This question is related to q

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Q. What happens to the budget set if both the prices as well as the income double? (This question is related to question 4.)

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Concept understanding — Budget Line Definition

Let’s start with something you already know from daily life.

You walk into a shop with ₹100 in your pocket. You want to buy some notebooks and some pens. A notebook costs ₹20, a pen costs ₹10. You can’t buy everything you want — you have to choose. If you buy 4 notebooks, that’s ₹80 gone, and you can afford only 2 pens with the remaining ₹20. If you buy 6 pens, that’s ₹60, and you can afford only 2 notebooks. Every possible combination of notebooks and pens that costs exactly ₹100 forms a straight line on a graph. That line is your budget line.

The precise definition

In economics, the budget line (also called the budget constraint) shows all the combinations of two goods that a consumer can buy given their income and the prices of those goods. It is not a suggestion — it is a hard limit. You cannot spend more than your income.

The NCERT Class 11 textbook (Microeconomics, Chapter 2) states it clearly:

P_1 X_1 + P_2 X_2 = M

Where:

$P_1$ = price of good 1
$X_1$ = quantity of good 1
$P_2$ = price of good 2
$X_2$ = quantity of good 2
$M$ = money income of the consumer

The equation says: total expenditure on both goods must exactly equal income. If you spend less, you are not using your full budget. If you spend more, it is impossible.

Why it matters

The budget line is the first real constraint in consumer theory. Before you can talk about what a consumer wants to buy (that comes later, with indifference curves), you must know what they can buy. The budget line separates the feasible from the impossible.

If you plot good 1 on the x-axis and good 2 on the y-axis, the budget line is a downward-sloping straight line. Its slope is $-P_1/P_2$ . That slope has a real meaning: it tells you how many units of good 2 you must give up to get one more unit of good 1. Economists call this the opportunity cost of good 1 in terms of good 2.

Note

The slope is negative because to buy more of one good, you must buy less of the other — your income is fixed.

What happens when things change?

The budget line shifts or rotates when either income or a price changes.

Income changes: If your income rises, the entire line shifts outward (parallel to the original). You can now afford more of both goods. If income falls, it shifts inward.
Price changes: If the price of good 1 falls, the line rotates — the intercept on the x-axis moves right, but the y-intercept stays the same (since the price of good 2 hasn’t changed). The slope becomes flatter. …

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When both prices and income double simultaneously, the budget set remains completely unchanged because the consumer's real purchasing power stays constant.

A budget set represents all the bundles of goods a consumer can afford given her income and the prices she faces. The budget line—the boundary of this set—is defined by the equation $p_1 x_1 + p_2 x_2 = M$ , where $p_1$ and $p_2$ are the prices of goods 1 and 2, $x_1$ and $x_2$ are the quantities, and $M$ is income.

The key insight here is that what matters for a consumer's purchasing power is not the absolute level of prices and income, but their relative magnitudes. If all nominal values scale up or down together, the real opportunities available to the consumer don't change.

Let's see why. Originally, the budget line is:

p_1 x_1 + p_2 x_2 = M

Now suppose both prices and income double. The new budget line becomes:

(2p_1) x_1 + (2p_2) x_2 = 2M

We can factor out the 2 from the left side:

2(p_1 x_1 + p_2 x_2) = 2M

Dividing both sides by 2:

p_1 x_1 + p_2 x_2 = M

This is exactly the original budget line. The equation hasn't changed at all.

What does this mean geometrically? The budget line's slope is $-\frac{p_1}{p_2}$ , which represents the rate at which the market allows you to trade good 1 for good 2. When both prices double, the new slope is $-\frac{2p_1}{2p_2} = -\frac{p_1}{p_2}$ —unchanged. The intercepts also remain the same: the horizontal intercept (maximum of good 1) is $\frac{M}{p_1}$ , which becomes $\frac{2M}{2p_1} = \frac{M}{p_1}$ , and similarly for the vertical intercept. …

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Q.What happens to the budget set if both the prices as well as the income double? (This question is related to question 4.)

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