The consumer's budget: budget set, budget line and its shifts

Detail

1. The set-up: income, prices and a bundle

• NCERT uses a consumer with two goods: bananas (good 1) and mangoes (good 2).
• x₁ = quantity of bananas. x₂ = quantity of mangoes.
• p₁ = price of a banana. p₂ = price of a mango.

• M = her money income.

• A bundle (x₁, x₂) is one combination of the two goods, e.g. (2, 3) = 2 bananas and 3 mangoes.

• Cost of a bundle = p₁x₁ + p₂x₂.

• Worked example: p₁ = ₹5, p₂ = ₹5, bundle (2, 3). Cost = 5×2 + 5×3 = ₹25.

• Economists use the same kind of formula. Britannica writes the budget constraint as P_B·B + P_Z·Z = Y. Here P_B and P_Z are the prices of goods B and Z, and Y is income [2].

2. Budget constraint

• Budget constraint: the condition that a bundle can be bought only if its cost is not more than income.

• p₁x₁ + p₂x₂ ≤ M

• It is written as "≤" (less than or equal to) because she may leave some money unspent. She can never spend more than M.

• Why it matters: wants are unlimited, but income is limited. The constraint puts this scarcity into a formula. (Class 7 NCERT makes the same point through needs and wants.)

3. Budget set

• Budget set: the collection of all bundles she can buy with income M at current market prices.
• Example 2.1: M = ₹20, p₁ = p₂ = ₹5. Goods are sold only in whole units.
• The most she can buy of either good is 20/5 = 4 units.
• 15 affordable bundles: (0,0), (0,1), (0,2), (0,3), (0,4), (1,0), (1,1), (1,2), (1,3), (2,0), (2,1), (2,2), (3,0), (3,1), (4,0).
• Quick count check: with x₁ = 0, 1, 2, 3, 4 bananas, she can have 5, 4, 3, 2, 1 mango choices. 5+4+3+2+1 = 15.
• Five bundles cost exactly ₹20: (0,4), (1,3), (2,2), (3,1), (4,0).

• Not affordable: (3,3) costs ₹30 and (4,5) costs ₹45. Both are more than ₹20.

• Indivisible vs divisible goods:

• Indivisible goods are sold only in whole units, such as oranges and bananas. For these, the budget set is a group of separate dots.
• Divisible goods can be bought in parts, such as half a kg of rice or a quarter litre of milk. For these, the budget set is the whole triangle on and below the budget line, including the axes.

4. Budget line

• Budget line: all bundles that cost exactly M.

• p₁x₁ + p₂x₂ = M

• Rearranged as a straight line (y = c + mx):

• x₂ = M/p₂ − (p₁/p₂)x₁
• Horizontal intercept = M/p₁: all income spent on bananas.
• Vertical intercept = M/p₂: all income spent on mangoes.

• Slope = −p₁/p₂.

• Three areas on the diagram:

• On the line: costs exactly M, so the whole income is spent.
• Below the line: costs less than M. She can afford it and has money left over.

• Above the line: costs more than M. She cannot buy it.

• Worked example: M = ₹100, p₁ = ₹10, p₂ = ₹20.

• Line: 10x₁ + 20x₂ = 100, which gives x₂ = 5 − 0.5x₁.
• Intercepts: 10 bananas and 5 mangoes. Slope = −1/2.
• Check a point: (4, 3) costs 40 + 60 = ₹100, so it lies on the line.

5. Why the slope is −p₁/p₂

• Take two points on the same budget line:
• p₁x₁ + p₂x₂ = M

• p₁(x₁ + Δx₁) + p₂(x₂ + Δx₂) = M

• Subtract the first from the second: p₁Δx₁ + p₂Δx₂ = 0, so Δx₂/Δx₁ = −p₁/p₂.

• Why the line slopes down:
• The whole budget is already spent.
• To buy one more banana, she has to give up some mangoes.

• So more of one good always means less of the other.

• The slope is the opportunity cost (what she gives up) of one more banana, measured in mangoes.

• Worked example: p₁ = ₹10, p₂ = ₹20. One extra banana costs ₹10, which buys ½ mango. So she gives up ½ mango.

6. Price ratio vs MRS

• Price ratio (p₁/p₂): the rate at which the market lets her swap bananas for mangoes.

• One extra banana costs p₁. That money buys p₁/p₂ mangoes.

• MRS (marginal rate of substitution): the number of mangoes she is willing to give up for one more banana while staying equally satisfied. It comes from her preferences.

• Key contrast:
• The price ratio is objective. The market sets it.

• MRS is subjective. Her tastes set it.

• She reaches her optimum (best bundle) where the two are equal: MRS = p₁/p₂. This is covered in section 5.

7. Shift of the budget line: change in income (prices fixed)

• The line moves parallel. The slope −p₁/p₂ does not change because prices do not change.
• M rises: both intercepts (M/p₁ and M/p₂) rise, and the line moves outward. The budget set gets bigger.

• M falls: the line moves inward. The budget set gets smaller.

• Worked example: p₁ = ₹4, p₂ = ₹5.

• M = ₹20 gives intercepts 5 and 4.

• M = ₹40 gives intercepts 10 and 8. The slope stays −4/5.

• Policy link: income tax relief is a parallel outward shift.

• Union Budget 2025-26 made income up to ₹12 lakh tax-free under the new regime. The limit is ₹12.75 lakh for salaried people because of the ₹75,000 standard deduction [3].
• Take-home income (M) rises while market prices stay the same, so the budget line moves outward.
• The government expected about ₹1 lakh crore in lost revenue from these direct tax proposals. Its stated aim was to leave more money with the middle class for consumption, savings and investment [3].

8. Shift of the budget line: change in one price

• p₁ changes while p₂ and M stay fixed: the line pivots (rotates) around the vertical intercept M/p₂. The mango-only point does not move.
• p₁ rises: the line gets steeper and the horizontal intercept M/p₁ falls. The budget set shrinks.

• p₁ falls: the line gets flatter and the horizontal intercept rises. The budget set grows.

• p₂ changes: the mirror image. The line pivots around the horizontal intercept M/p₁.

• Britannica says the same: a fall in the price of good B moves the line outward along the B-axis, while the point on the Z-axis stays where it is [2].
• Worked example: M = ₹100, p₂ = ₹20, and p₁ falls from ₹10 to ₹5.
• The horizontal intercept rises from 10 to 20. The vertical intercept stays at 5.

• The slope changes from −1/2 to −1/4, so the line is flatter.

• Policy link: a GST rate cut is like a fall in price.

• The GST Council cut the main slabs from four (5%, 12%, 18%, 28%) to two: 5% (merit rate) and 18% (standard rate). It added a 40% special rate for sin and luxury goods [4].
• The new rates applied from 22 September 2025 [4].
• Items such as UHT milk, paneer, roti and paratha moved to 5% or Nil. Many medicines moved to 5% or Nil, and health insurance became exempt [4].

• If the tax cut reaches the shop price, the line pivots outward along the axis of the cheaper good.

• A fall in price has two effects, which come later in the chapter [2]:

• Substitution effect: the good is now relatively cheaper, so she buys more of it in place of the other good.
• Income effect: her money now buys more, so her real income (purchasing power) rises.

9. Special cases (Class 12 exercise drills)

• Drill 1: p₁ = ₹4, p₂ = ₹5, M = ₹20.

• Line: 4x₁ + 5x₂ = 20. Intercepts 5 (bananas) and 4 (mangoes). Slope −4/5.

• Drill 2: M rises to ₹40. The line makes a parallel outward shift, and the intercepts become 10 and 8.

• Drill 3: p₂ falls to ₹4 (M = ₹20).
• The vertical intercept rises from 4 to 5. The horizontal intercept stays at 5.

• The slope becomes −4/4 = −1.

• Drill 4: doubling income and both prices leaves the budget set unchanged.

• 2p₁x₁ + 2p₂x₂ = 2M reduces to p₁x₁ + p₂x₂ = M.
• Lesson: only relative prices and real income matter. Money amounts on their own do not.

• Real-life meaning: if wages rise by the same percentage as inflation, what a household can buy does not change.

• Drill 5: bundle (6, 8) at prices ₹6 and ₹8 uses her whole income.

• M = 6×6 + 8×8 = 36 + 64 = ₹100.

• Extra trap: both prices double while M stays the same.

• The slope does not change: 2p₁/2p₂ = p₁/p₂.
• Both intercepts halve, so the line makes a parallel inward shift.
• This has the same effect as halving income. Inflation without a matching rise in income works this way.

10. The Indian household's real budget (data)

• The Household Consumption Expenditure Survey (HCES) 2023-24 (by MoSPI, the government's statistics ministry) measured average MPCE (monthly per capita consumption expenditure, which is spending per person per month) [5][6]:
• Rural: ₹4,122
• Urban: ₹6,996

• These figures leave out items that households got free through welfare schemes [5].

• Share of spending on food (2023-24) [5][6]:

• Rural households: 47.04%
• Urban households: 39.68%

• Poorer budgets go mostly to food, so price changes in food items (a pivot of the budget line) hit rural households harder.

• Sample: 2,61,953 households (1,54,357 rural and 1,07,596 urban), covering all States and UTs [5].

• Free goods (like PDS grain) enlarge the budget set without any cash changing hands. This is why MoSPI reports MPCE both with and without "imputed" (estimated) values of free items [5].

Prelims Hooks

• Budget constraint: p₁x₁ + p₂x₂ ≤ M. Budget line: p₁x₁ + p₂x₂ = M. Trap: the line uses "=" and the constraint uses "≤".
• Slope of the budget line = −p₁/p₂ (price ratio). It does not depend on income M.
• Intercepts: M/p₁ on the horizontal axis and M/p₂ on the vertical axis.
• Change in income → parallel shift. Change in one price → pivot around the other good's intercept.
• Income and all prices change by the same proportion → no change in the budget line or budget set.
• All prices double with income fixed → parallel inward shift, the same as halving income. It is not a pivot.
• Example 2.1 (M = ₹20, prices ₹5 each, whole units): 15 affordable bundles, 5 on the budget line.
• Budget set for divisible goods = the whole triangle on and below the line. For indivisible goods = separate dots.
• HCES 2023-24 average MPCE: Rural ₹4,122, Urban ₹6,996. Food share: 47.04% rural, 39.68% urban [5].
• GST 2.0 (effective 22 September 2025): two main slabs of 5% and 18%, plus a 40% special rate [4].

Mains Points

• Tax policy works through the budget line:
• A cut in income tax, such as the ₹12 lakh zero-tax limit in 2025-26, raises M. The line shifts outward in parallel [3].
• A GST cut lowers the price of the taxed goods. The line pivots outward along those goods' axes [4].

• Income tax relief helps only people who pay income tax. A GST cut on essentials reaches every buyer, including rural households, who spend about 47% of their budget on food [4][5].

• Inflation vs real income:

• The "double M and all prices" result shows that welfare depends on real income, not nominal (money) income.

• Supporting purchasing power through inflation control or through wage and DA (dearness allowance) indexation protects the budget set. Raising money wages alone does not.

• In-kind transfers vs cash transfers:

• Free food under PDS enlarges the budget set only along one good's axis.
• Cash transfers (DBT) shift the whole line outward.

• MoSPI reports MPCE both with and without imputed free items, which shows these transfers matter to household welfare [5].

• Relative-price changes hurt budgets unevenly:

• A rise in food prices pivots the line inward more sharply for households that spend most of their budget on food.
• This supports targeted relief and GST exemptions on essentials [4][5].