Explain the optimal choice of consumer with the help of a diagram.

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Q. Explain the optimal choice of consumer with the help of a diagram.

Karnataka PUCKarnataka 2nd PUC Commerce Board 2022Subjective· 6mImportance★★★★★

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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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Optimal choice is where the budget line is tangent to the highest reachable indifference curve: MRS = price ratio (Px/Py).

The consumer's problem is to get the maximum satisfaction from a limited income, given the prices of two goods. Two tools are used: the budget line (all combinations of the two goods the consumer can just afford with his income) and the indifference map (curves of equal satisfaction, higher curves meaning more satisfaction).

Optimal choice condition: The consumer is in equilibrium at the point where the budget line just touches (is tangent to) the highest indifference curve he can reach.

Diagram in words: With good X on the horizontal axis and good Y on the vertical axis, draw the downward-sloping budget line AB. Superimpose the indifference map. The budget line will be tangent to one indifference curve, say IC₂, at a point E. Curves above IC₂ (like IC₃) are unattainable — they lie beyond the budget line. Curves below (like IC₁) are attainable but give less satisfaction. So E on IC₂ is the best the consumer can do.

Conditions of equilibrium:

First-order (necessary): at E the slope of the indifference curve equals the slope of the budget line, i.e. the Marginal Rate of Substitution equals the price ratio: MRS = Px/Py.
Second-order (sufficient): the indifference curve must be convex to the origin at the point of tangency (diminishing MRS). …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set ANNUAL1 mark
$Q. Write the equation of budget line.$
›Reveal solutionSolution

Budget line equation: Px·x + Py·y = M.

If a consumer has income M, and buys x units of Good X at price Px per unit and y units of Good Y at price Py per unit, the TOTAL expenditure is Px·x + Py·y. The budget line represents every combination where this total expenditure exactly equals the full income: Px·x + Py·y = M. Rearranging to the familiar straight-line (y = mx + c) form: y = (M/Py) − (Px/Py)·x — a straight line with Y-intercept M/Py (the quantity of Y obtainable if the ENTIRE income is spent on …

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CBSE 2025Set MARCH1 markMCQ
$Q. The inequality P1x1 + P2x2 \leq M shows :$
(a) Budget line equation
(b) Budget constraint
(c) Demand function
(d) Supply function
›Reveal solutionSolution

P1x1 + P2x2 ≤ M represents the budget constraint — option (b).

…

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CBSE 2025Set ANNUAL1 markMCQ
$Q. Equation of budget line is - (A) M = P1x2 + P2x1 (B) M = P1x2 \div P2x1 (C) M = P1x1 \div P2x2 (D) M = P1x1 + P2x2$
›Reveal solutionSolution

The budget line equation is M = P1x1 + P2x2 (total spending equals income), so (D) is correct.

In the RBSE/CBSE Class-12 theory-of-consumer-behaviour chapter, the budget line shows every bundle of two goods the consumer can afford when the entire money income is spent. If the consumer buys x1 units of good 1 at price P1 and x2 units of good 2 at price P2, then the amount spent on the two goods together must equal income M:

P1x1 + P2x2 = M

…

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CBSE 2025Set ANNUAL1 markMCQ
$Q. If the price of a pen is Rs. 20, then one rupee will be worth-$
(a) 1 pen
(b) 20 pen
(c) 0.5 pen
(d) 0.05 pen
(a) 1 pen
(b) 20 pen
(c) 0.5 pen
(d) 0.05 pen
›Reveal solutionSolution

₹1 worth of a good = 1 ÷ price of the good = 1/20 = 0.05 pen.

If the price of one pen is ₹20, this means ₹20 buys exactly 1 pen. So ₹1 buys 1/20th of a pen, i.e., 0.05 pen. This is simply the reciprocal relationship between the price of a good (in money per unit) and the 'real' (goods) value of money (units of the good per rupee): Real value …

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CBSE 2024Set ANNUAL1 mark
$Q. Very short answer:$
(ix) Where on the budget line will the optimum bundle be located?
›Reveal solutionSolution

The optimum bundle is on the budget line, where the budget line touches (is tangent to) the highest possible indifference curve.

A rational consumer spends the entire income, so the chosen bundle must lie on the budget line (not inside it). Among all bundles on the budget line, the consumer picks the one giving maximum satisfaction, which is the point where the budget line is tangent to the highest attainable indifference curve. At this point the slope of the budget line (price ratio) equals the slope of t …

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CBSE 2024Set ANNUAL1 markMCQ
$Q. Price ratio PX/PY indicates the slope of ______.$
(a) budget line
(b) budget set
(c) price line
(d)
(a) and
(c) both
›Reveal solutionSolution

The price ratio Px/Py is the slope of the budget line — option (a).

The budget line (price line) represents all combinations of two goods X and Y that a consumer can buy by spending her entire income M at given prices Px and Py. Its equation is Px·X + Py·Y = M. Rearranged, Y = M/Py − (Px/Py)·X, so the slope of the budget line is −Px/Py; in absolute terms the slope equals the price ratio Px/Py. Thi …

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CBSE 2023Set ANNUAL1 markMCQ
$Q. The slope of the budget line is -$
(a) –P2/P1
(b) –P1/P2
(c) P1/P2
(d) P2/P1
›Reveal solutionSolution

The slope of the budget line is −P1/P2 — option (b).

The budget line is P1·X1 + P2·X2 = M, where good 1 is measured on the horizontal axis. Solving for X2 gives X2 = M/P2 − (P1/P2)·X1, so the slope (ΔX2/ΔX1) is −P1/P2. It is negative because to buy more of one go …

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CBSE 2020Set MARCH1 markMCQ
$Q. Which of the following represents budget line equation ?$
(a) P1X1 + P2X2 = M
(b) P1X1 + P2X2 < M
(c) P1X1 + P2X2 > M
(d) None of these
›Reveal solutionSolution

The budget line equation is P1X1 + P2X2 = M.

…

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Q.Explain the optimal choice of consumer with the help of a diagram.

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