Theory of Consumer Behaviour for UGC NET Economics

UGC NET ECONOMICS • MICROECONOMICS

Theory of Consumer Behaviour

Learn the idea. Work the numbers. Check your reasoning.

Ten connected lessons, 16 knowledge checks, interactive laboratories and a 30-question final test.

Study in order on your first visit. Try each question before checking; revisit the explanation if you miss it. Answers and progress last for this page visit. Reloading resets them.

1. Utility and consumer preferences

A consumer chooses the most preferred affordable bundle. Utility represents satisfaction or preference; it is not the same as usefulness, health benefits or moral value. A bundle is a combination of quantities, such as A = (4 books, 2 meals).

Preference language

A ≻ B: A is strictly preferred to B.
A ∼ B: A and B are equally preferred.
A ≽ B: A is at least as good as B.

Standard assumptions

Completeness: any two bundles can be compared.
Transitivity: A ≽ B and B ≽ C imply A ≽ C.
Continuity: small bundle changes do not create abrupt preference reversals.
Monotonicity: more desirable goods are preferred.
Convexity: mixtures are weakly preferred to equally good extremes.

Local non-satiation is weaker than “more of every good is better”: some better bundle exists arbitrarily close to any bundle. It helps explain why the optimum exhausts the budget.

Ranking trick: if U represents ordinal preferences, any strictly increasing transformation f(U) preserves them. U = XY and V = ln(XY), for X,Y > 0, rank bundles identically. Their utility numbers and marginal utilities differ, but their MRS does not.

Think first: does twice the utility number mean twice the happiness?

No. Under ordinal utility, numbers only rank bundles. U(A)=20 and U(B)=10 establish that A is preferred, not that satisfaction is twice as large.

2. Cardinal and ordinal utility

Feature	Cardinal approach	Ordinal approach
Utility	Assumed measurable in utils	Bundles can be ranked
Main tools	TU, MU, equimarginal principle	ICs, MRS, budget constraint
Traditional names	Marshall; Gossen’s laws	Pareto; Hicks and Allen
Key caution	Constant MU of money is restrictive	Utility numbers are not welfare ratios

Total and marginal utility

MU_x = ΔTU / ΔX; continuously, MU_x = ∂U / ∂X

Diminishing MU: successive units add less satisfaction, other things equal. TU rises when MU > 0, reaches a stationary point when MU = 0, and falls when MU < 0. A maximum additionally requires the appropriate change of sign or second-order condition.

X	0	1	2	3	4	5
TU	0	12	22	30	36	40
MU	—	12	10	8	6	4

Here MU declines but remains positive: TU keeps rising. Do not confuse falling MU with falling TU.

Equimarginal principle

MU_x/P_x = MU_y/P_y = MU of money

For divisible goods consumed in positive amounts, allocate spending until the marginal utility per rupee is equal. If MU_x/P_x = 6 and MU_y/P_y = 3, shift spending toward X. Corner solutions and indivisible goods need separate treatment.

Exam distinction: diminishing MU depends on the utility representation. Diminishing MRS concerns preference shape and survives strictly increasing utility transformations. Neither concept should be substituted mechanically for the other.

3. Indifference curves and their properties

An indifference curve (IC) joins bundles providing the same utility. An indifference map is a collection of ICs.

Downward slope: with two desirable goods, more X requires less Y to maintain satisfaction.
Convex to the origin: diminishing willingness to substitute Y for X; strict convexity produces smoothly bowed curves in the standard case.
No intersection of distinct utility levels: crossing would contradict a consistent preference ordering.
Northeast is better: under monotonicity, more of both goods raises preference.

MRS_xy = −dY/dX along an IC = MU_x/MU_y

MRS is expressed here as a positive amount of Y sacrificed per extra X. The IC’s slope is −MRS. For a finite segment, −ΔY/ΔX is an average, not necessarily the exact point MRS.

Preferences	Utility example	IC shape	MRS
Perfect substitutes	U = aX + bY	Straight line	a/b, constant
Perfect complements	U = min(X/a, Y/b)	L-shaped; kink at X/a = Y/b	Not defined at kink; no substitution of the required pair
Cobb–Douglas	U = X^αY^β, α,β > 0	Smooth, strictly convex for positive bundles	αY/(βX)
Quasilinear	U = v(X) + Y	Vertically translated ICs	v′(X); X has zero income effect at an interior solution

Explore IC shapes

Preference type

4. Budget constraint and budget line

Budget set: P_xX + P_yY ≤ M, X,Y ≥ 0
Budget line: P_xX + P_yY = M

With X horizontal and Y vertical: Y = M/P_y − (P_x/P_y)X. X-intercept = M/P_x; Y-intercept = M/P_y; slope = −P_x/P_y.

Income changes alone: parallel shift.
P_x falls alone: outward rotation around the unchanged Y-intercept; line becomes flatter.
P_y falls alone: outward rotation around the unchanged X-intercept; line becomes steeper.
All prices and income multiply by the same positive factor: budget set unchanged.

With positive prices, finite nonnegative income and nonnegative quantities, the budget set is closed, bounded and convex. A zero-priced good can make it unbounded. Strictly positive quantity restrictions can alter closedness.

Budget and equilibrium laboratory

Model: U = XY. A dashed line shows the baseline M=100, P_x=10, P_y=10. Change one control at a time to identify a shift or rotation.

Income M Price of X Price of Y

5. Consumer equilibrium

The optimum is the most preferred feasible bundle. With continuous preferences and a compact budget set, an optimum exists. Local non-satiation implies full spending.

Smooth interior solution

MRS_xy = P_x/P_y
P_xX + P_yY = M

Tangency is a first-order condition. Appropriate convexity of preferences supports optimality; strict convexity gives a unique optimum. Tangency alone is not sufficient for arbitrary preferences.

Worked example: U = XY

M = 100, P_x = 10, P_y = 5. MU_x = Y and MU_y = X. Thus Y/X = 2, or Y = 2X. Substitute into 10X + 5Y = 100: 20X = 100, so X = 5 and Y = 10.

For U = X^αY^β: X* = [α/(α+β)]M/P_x and Y* = [β/(α+β)]M/P_y. Budget shares are α/(α+β) and β/(α+β).

Corners and kinks

Perfect substitutes: compare a/P_x with b/P_y. Buy only the good giving higher utility per rupee. If equal, every bundle on the budget line is optimal.

Perfect complements: use the fixed-proportion condition, not tangency. For U = min(X,Y), choose X = Y. If M = 90 and prices are 10 and 5, then X = Y = 6.

Try: U = 3X + Y, M = 60, both prices = 10. What is optimal?

Utility per rupee is 3/10 for X and 1/10 for Y. Buy X = 6, Y = 0. A smooth tangency is unnecessary.

6. Income, price and substitution effects

Curve	What changes?	What stays fixed?
Income consumption curve (ICC)	Income	Prices and preferences
Price consumption curve (PCC)	One price	Money income, other prices, preferences
Engel curve	Income plotted against demand for one good	Prices and preferences

Income effect: a demand change caused by changed purchasing power. Normal good: demand rises with income. Inferior good: demand falls with income over the relevant range. A good can change classification at different income levels.

Price effect: total change in quantity after an own-price change at fixed money income. It combines a substitution effect and an income effect.

Price effect = Substitution effect + Income effect

Substitution effect: response to relative-price change after compensation. Own-price compensated demand is non-increasing under standard rational preferences; the effect can be zero for perfect complements.

When P_x falls	Substitution effect on X	Income effect on X	Total effect
Normal good	Nonnegative	Positive	X rises
Inferior, non-Giffen	Positive	Negative, smaller in magnitude	X rises
Giffen	Nonnegative	Negative, larger in magnitude	X falls

Sign trick: write “price rises” or “price falls” before assigning signs. “Negative income effect” often means inferior-good income response, not that every price-change income component is negative. For a price rise, the income component for an inferior good is positive.

All Giffen goods are inferior; not all inferior goods are Giffen. A large budget share, strong inferiority and limited substitution can support Giffen behaviour. A Veblen effect concerns status and can alter preferences; it is not the standard Giffen mechanism.

Classify the effect

A price FALL produces SE = +4 units. Select the income component and inspect the total.

Income component

7. Hicks and Slutsky: compensation and demand

Feature	Hicks	Slutsky
Compensation holds fixed	Original utility	Affordability of original bundle
Compensated budget line	Tangent to original IC at new prices	Passes through original bundle at new prices
Finite-change compensated utility	Exactly original utility	At least original utility after reoptimising
Memory cue	H = Happiness held	S = Same shopping basket affordable

One numerical example, two decompositions

U = XY; M = 100; initial prices = (10,10). Initial A = (5,5), U = 25. P_x falls to 5, P_y stays 10. Final C = (10,5), U = 50. Total X effect = +5.

Hicks: at new prices, minimise expenditure while XY = 25. Y/X = 0.5, so compensated B_H = (√50, √12.5) ≈ (7.071,3.536). Compensated spending ≈ 70.711. SE ≈ +2.071; IE ≈ +2.929.

Slutsky: original bundle now costs 5×5 + 10×5 = 75. At income 75, reoptimisation gives B_S = (7.5,3.75). SE = +2.5; IE = +2.5. The compensated utility is 28.125, above 25.

Both decompositions sum to +5. Finite-change components differ; their local substitution effects coincide at the original optimum under differentiability.

Marshallian versus Hicksian demand

Marshallian x(p,M): maximise utility given income. Hicksian h(p,u): minimise spending to achieve a target utility. Expenditure function e(p,u): minimum required spending.

∂x/∂P_x = ∂h/∂P_x − x(∂x/∂M)

The compensated derivative is evaluated at the utility attained by the original Marshallian choice. This is the own-price Slutsky equation. More generally: ∂x_i/∂p_j = ∂h_i/∂p_j − x_j∂x_i/∂M.

Normal good: ∂x/∂M > 0, so the income term reinforces the nonpositive substitution derivative.
Inferior good: ∂x/∂M < 0, so the income term is positive and can outweigh substitution.
Shephard’s lemma: ∂e/∂p_i = h_i, where differentiable.
Under standard regularity, e is homogeneous of degree one, nondecreasing and concave in prices. Hicksian demand is homogeneous of degree zero in all prices.
Marshallian demand is homogeneous of degree zero in prices AND income together.

UGC NET stretch: Roy’s identity

If v(p,M) is indirect utility and derivatives exist with ∂v/∂M > 0, then x_i = −(∂v/∂p_i)/(∂v/∂M). Do not confuse Roy (Marshallian demand) with Shephard (Hicksian demand).

8. Revealed preference theory

Samuelson’s revealed preference approach, introduced in 1938, uses observed choices. If A is chosen while B is affordable, A is directly revealed preferred to B. Comparisons require stable preferences and correctly observed budget opportunities.

WARP, SARP and GARP

WARP: excludes direct two-way choice reversals. In the usual unique-choice version, if A is chosen over affordable B, B cannot later be chosen when A is affordable.
SARP: rules out cycles through chains of direct and indirect revealed preference between distinct bundles; suited to the standard unique-choice formulation.
GARP: permits indifference but rules out a strict revealed-preference reversal. In finite-data tests, it characterises rationalisation by locally non-satiated utility under the standard conditions.

Affordability test

A = (4,2), B = (2,4). At prices (1,2), A costs 8 and B costs 10. Choosing A with income 8 reveals nothing about A versus B, because B is unaffordable. At prices (2,1), both are affordable with income 10; choosing A now reveals A over B. If the consumer later chooses B at prices (1,1), income 6, both bundles cost 6: under unique choice, this reverses the previous observation and violates WARP.

Trap: revealed preference does not require identical tastes across people, positive income elasticity, or the exclusion of Giffen goods. Rational Giffen behaviour can satisfy revealed preference restrictions.

9. Demand and elasticity of demand

Demand is willingness and ability to purchase at given prices. Own-price changes cause movement along a demand curve; income, tastes and related-good prices can shift it. An inverse demand function expresses price as a function of quantity: P = f(Q).

Signed price elasticity ε_p = (dQ/dP)(P/Q)
Income elasticity ε_M = (∂Q/∂M)(M/Q)
Cross elasticity ε_xy = (∂Q_x/∂P_y) (P_y/Q_x)

For ordinary downward-sloping demand, ε_p is negative. Classification usually uses the absolute magnitude E = |ε_p|: E>1 elastic, E=1 unit elastic, E<1 inelastic. E=0 perfectly inelastic; perfectly elastic demand is the horizontal limiting case.

Elasticity	Interpretation
Income < 0	Inferior good
0 < income < 1	Normal necessity
Income > 1	Normal luxury
Cross > 0	Gross substitutes
Cross < 0	Gross complements

Gross cross-price effects include income effects. Do not assume they must be symmetric between goods. Compensated substitution effects have symmetry under regularity.

Point, arc and total expenditure methods

Arc ε = [(Q₂−Q₁)/((Q₁+Q₂)/2)] ÷ [(P₂−P₁)/((P₁+P₂)/2)]

Use the midpoint formula for a finite move between two observations; it gives the same result in either direction. If P rises 10→12 and Q falls 100→80, arc ε = (−20/90)/(2/11) ≈ −1.222.

Elastic demand: price and total expenditure PQ move in opposite directions locally.
Inelastic demand: price and total expenditure move in the same direction locally.
Unit elasticity: revenue is locally stationary. Q=k/P makes revenue constant along the whole curve.
Linear Q=a−bP: E=bP/Q. Elasticity falls as you move down the curve, although slope is constant. Midpoint E=1.
Constant-elasticity Q=kP^−r, r>0: ε=−r and E=r.

MR = P(1 − 1/E); E = AR/(AR−MR)

The revenue formula above uses positive elasticity magnitude for downward-sloping demand. If AR=15 and MR=5, E=15/10=1.5.

Determinants: more close substitutes, broader adjustment time and often larger budget share make demand more elastic. Narrowly defined goods usually have more substitutes than broad categories. These are tendencies, not universal laws.

Demand, revenue and surplus laboratory

Demand Q = 100 − 2P, inverse demand P = 50 − Q/2. Move the price and compare elasticity with revenue.

Price

10. Consumer surplus and welfare

Consumer surplus is total willingness to pay minus total expenditure. It is the area below inverse demand and above the market price, up to the purchased quantity. It is an area, not merely a vertical distance.

CS = ∫₀^Q* P(q)dq − P*Q*
Linear demand: CS = ½ × Q* × (choke price − P*)

Linear example

Q=10−2P. At P=2, Q=6; choke price = 5. CS = ½×6×(5−2) = 9.

Nonlinear example

P=27−3Q−Q². At Q=3, P=9. Total willingness to pay = [27Q−1.5Q²−Q³/3]₀³ = 58.5. Expenditure = 9×3 = 27. CS = 31.5.

Subtracting monetary expenditure from TU measured in utils is invalid. TU−PQ needs TU expressed in money units. Consumer surplus can apply to necessities; measurement may be difficult.

Compensating and equivalent variation

Let u₀ be initial utility and u₁ final utility after a price change at unchanged income M. For a price rise, define positive welfare-loss amounts:

CV = e(p₁,u₀) − M
EV = M − e(p₀,u₁)

CV: compensation needed at new prices to restore old utility. EV: income taken away at old prices that creates the new, lower utility. For price falls, explicitly state your sign convention; these loss formulas become negative.

Ordinary consumer-surplus changes can differ from CV and EV when income effects matter. With no relevant income effect, as in an interior quasilinear case, they coincide for the price change.

Memory cue: CV uses the Changed prices; EV asks for an Equivalent change at the Earlier prices.

Revision: ten exam-saving checks

Ordinal utility ranks; it does not measure happiness ratios.
MU falling does not mean TU falling.
IC slope is −MRS; budget slope is −Px/Py.
Budget line uses equality; budget set uses ≤.
Tangency is for an interior smooth optimum; check corners and kinks.
Write the price-change direction before signing effects.
Inferior does not automatically mean Giffen.
Hicks fixes utility; Slutsky fixes old-bundle affordability.
Elasticity is not slope. Use absolute magnitude only when stated.
Surplus is an area; use monetary willingness to pay.

Final test: 30 MCQs

One question per flip. Select an option, then check to lock that answer and see the explanation. You can navigate before checking. There is no negative marking in this practice test.

Questions labelled “Adapted PYQ” are reformulations of items in the supplied book; dates and question numbers follow that compilation. Other questions are original practice. This is not an official NTA answer key.