Microeconomics · A module in seventeen lessons
Consumer theory, from preferences to the Slutsky equation
How does a person decide what to buy, and what does that tell us about demand? This module answers with one consumer, built up a step at a time: what a ranking of bundles must satisfy, how a utility number stands for it, what she can afford, and what she picks. Every lesson has something to move and ends on real past-paper questions, 310 in all.
310past-paper questions, each placed in a lesson
17lessons, all live
21interactive labs and tools, from a ranking tester to the Consumer Workbench
23questions left out as flawed or not markable, with the reason for each
Start at the beginning, or check where you are.All 17 lessons are ready and the course takes about 12 hours. You need nothing beyond ordinary school algebra and the idea of a slope. Each lesson opens with a real exam question, builds the idea with a diagram you can move, and ends with that question solved and a set of past papers.
The path
Five parts, seventeen lessons
The order is the logic of the subject. Preferences come first, then what she can afford, then the choice that puts the two together. Demand is that choice traced out as a price or income changes, and the later lessons ask what lies underneath it: how much of a price effect is substitution, and what a price change is worth in money.
Once you reach Lesson 14 there is a Consumer Workbench: choose tastes and prices and it computes demand, the expenditure function, elasticities, both decompositions of a price change and the money measures at once, and checks the identities between them.
0 of 17 doneYour progress is saved on this device.
- Part 1Preferences and utility
What a ranking must satisfy, how a number can stand for it, and the special kinds of taste the papers ask about.
- 1Preferences and indifference curvesCompleteness, transitivity, non-satiation and convexity; what an indifference curve is, why it slopes down and never crosses, and what curves look like for goods, bads and neutrals.35 min · 17 past questions
- 2Utility, the MRS and marginal utilityOrdinal and cardinal utility, what a monotone transformation changes and what it leaves alone, the MRS as a slope and as MU₁/MU₂, diminishing MRS, and the equi-marginal rule.40 min · 22 past questions
- 3Substitutes, complements, lexicographic, homothetic and quasi-linear preferencesStraight-line, L-shaped and dictionary preferences, the CES family that contains them, and the two classes that make demand easy: homothetic and quasi-linear.40 min · 14 past questions
- Part 2Choosing
The budget line, the best affordable bundle, corners, taxes and grants, and the same problem for work and for saving.
- 4The budget set and the budget lineWhich bundles are affordable, the slope −p₁/p₂ and the intercepts, how income and prices shift or pivot the line, and what a second constraint does to the choice.30 min · 11 past questions
- 5Utility maximisation: the interior optimumThe tangency MRS = p₁/p₂, the Lagrangian and the marginal utility of income, Cobb–Douglas demand and the budget-share rule, and shifted Cobb–Douglas.45 min · 18 past questions
- 6Corner solutions and demand for special utilitiesWhen the tangency fails: perfect substitutes, bads, max tastes, quasi-linear and kinked utilities, with the price at which the choice jumps.45 min · 18 past questions
- 7Taxes, subsidies, transfers and non-standard budgetsExcise tax against lump-sum tax, price subsidy against cash grant, in-kind grants, quantity limits and discrete goods, with the comparison examiners ask for.40 min · 12 past questions
- 8Labour supply and intertemporal choiceLeisure as a good and the wage as its price, the backward-bending labour supply curve, overtime, and the two-period budget with an interest rate.40 min · 2 past questions
- Part 3Demand
The demand curve, elasticity and revenue, Engel curves and the type of good.
- 9Demand curves, shifters and consumer surplusDeriving a demand curve from the optimum, movements along and shifts of it, and consumer surplus as an area.35 min · 16 past questions
- 10Price elasticity of demand and total revenuePoint and arc elasticity, the total revenue test and the price consumption curve.50 min · 46 past questions
- 11Income and cross elasticities, Engel curves and the type of goodNormal, inferior, luxury and necessity goods, the income consumption curve, and substitutes against complements.45 min · 40 past questions
- Part 4Substitution, duality and welfare
Income and substitution effects, revealed preference, the expenditure function, compensating variation and the properties of demand.
- 12Income and substitution effects and the Slutsky equationHicks and Slutsky decompositions, the Slutsky equation, and Giffen goods.45 min · 18 past questions
- 13Revealed preferenceWARP, SARP and GARP, and the compensated law of demand.35 min · 9 past questions
- 14Hicksian demand, the expenditure function and dualityMinimising expenditure at a given utility, Shephard's lemma and Roy's identity.50 min · 6 past questions
- 15Compensating and equivalent variationMoney measures of a price change, and how they compare with consumer surplus.40 min · 4 past questions
- 16Properties of demand and aggregationHomogeneity, adding-up, symmetry and when market demand behaves like one consumer.35 min · 7 past questions
- Part 5The hard end
The Delhi School's consumer questions, by technique.
Where to start
A two-minute check
One question from each lesson that is ready. Your first wrong answer tells you where to begin; get them all and go straight to the cheat sheet.
Question 1 of 17
A consumer prefers A to B, B to C and C to A. Which assumption fails?
Revise
Cheat sheet: every result on one screen
What each idea says, what to use it for, and the trap examiners set on it.
Completeness and transitivityLesson 1
It saysAny two bundles can be ranked, and rankings chain without a cycle
Use it forIs this ranking rational?
The trapA cycle ranks every pair, so it is complete; it fails transitivity
Indifference curvesLesson 1
It saysEqual-utility bundles; higher is better; never cross; slope down because more is better
Use it forShapes with goods, bads, neutrals
The trapA good against a bad gives an upward slope
Ordinal utilityLesson 2
It saysOnly the order of utility numbers matters: any increasing f(u) is as good
Use it forWhich function represents the same tastes?
The trapAdding a term in x or y changes the ranking; −u reverses it
MRSLesson 2
It saysMU_x/MU_y = minus the slope of the curve
Use it forMatch functions to their MRS
The trapRead 'a for b' from the first-named side; MRS is unchanged by transformations, MU is not
Equi-marginal ruleLesson 2
It saysMU_x/P_x = MU_y/P_y = marginal utility of money
Use it forFind a missing price or marginal utility
The trapIt is the same condition as MRS = price ratio
Substitutes, complementsLesson 3
It saysu = ax + by: straight lines; u = min{x/a, y/b}: L-shaped
Use it forName the curve
The trapStraight lines are substitutes, not complements
Homothetic, quasi-linearLesson 3
It saysHomothetic: the expansion path is a ray. Quasi-linear: curves are vertical translates
Use it forStatements about income response
The trapQuasi-linear is not homothetic; the price consumption curve of a homothetic taste is not a ray
Budget lineLesson 4
It saysy = m/p_y − (p_x/p_y)x; income shifts, one price pivots
Use it forPredict how the line moves
The trapDouble income and all prices: no move at all
TangencyLesson 5
It saysMRS = p_x/p_y and the budget holds
Use it forFind the optimum bundle
The trapOnly for a smooth, convex, interior optimum
Cobb–Douglas demandLesson 5
It saysx* = am/p_x, y* = (1 − a)m/p_y
Use it forQuick demand and budget shares
The trapShifted forms like (x+2)(y+1) have shares that change with income
Corner ruleLesson 6
It saysBuy only the good with more utility per rupee; list the candidates and compare
Use it forLinear, max, kinked and quasi-linear tastes
The trapA bad is bought not at all; max{x, y} has a worst tangency
Quasi-linear demandLesson 6
It saysx* = (p_y/2p_x)² for √x + y; x* = p_y/p_x for ln x + y
Use it forDemand independent of income
The trapCorner if the interior x costs more than income
Cash against subsidyLesson 7
It saysAt equal cost the cash line passes through the subsidy bundle
Use it forWelfare comparisons
The trapCompare at the same cost; a voucher binds only if bigger than she would buy
Labour supplyLesson 8
It saysLeisure is priced at the wage; full income m₀ + wT
Use it forHours worked, overtime
The trapIncome effect can bend the curve backwards
Two-period choiceLesson 8
It saysc₁ + c₂/(1+r) = y₁ + y₂/(1+r); c₂/c₁ = (1+r)/(1+ρ)
Use it forSaving and borrowing
The trapThe line's slope is −(1+r); r = ρ means flat consumption
Demand curveLesson 9
It saysx*(p_x, p_y, m) against p_x. Own price: move along. Anything else: shift
Use it forWhich event moves the curve?
The trapA fall in producers' costs shifts supply, not demand
Consumer surplusLesson 9
It saysArea under the demand curve up to Q, less p × Q
Use it forIntegrals and triangles
The trapForgetting to subtract the rectangle
Price elasticityLesson 10
It says(dQ/dP)(P/Q) = d ln Q/d ln P; straight line: P/(P_max − P)
Use it forPoint values and ranges of price
The trapA straight line has every elasticity; use the point asked
Total revenue testLesson 10
It saysElastic: price and revenue move opposite ways. Inelastic: same way. Unit: no change. MR = P(1 − 1/|e|)
Use it forEffects of a price change on spending
The trapThe test is reversed for a price fall
Income elasticityLesson 11
It says(dQ/dm)(m/Q): inferior < 0, necessity 0 to 1, luxury above 1; shares add up: Σ s·η = 1
Use it forType of good, Engel curves
The trapQuasi-linear x has zero income elasticity only while she buys y
Cross elasticityLesson 11
It says%ΔQ_Y/%ΔP_X: substitutes positive, complements negative
Use it forName the relation between goods
The trapRead the direction of the price change in the question
Slutsky equationLesson 12
It saysTotal effect = substitution + income: ∂x/∂p = ∂h/∂p − x ∂x/∂m. Hicks holds utility, Slutsky holds the old bundle affordable
Use it forSplit a price change; Giffen goods
The trapThe substitution effect is never positive; perfect complements have none; Giffen implies inferior, not the reverse
WARPLesson 13
It saysNot both: x chosen when y was affordable and y chosen when x was affordable
Use it forIs this behaviour consistent?
The trapCompare each bundle's cost at the other's prices; with two goods WARP implies SARP
Expenditure functionLesson 14
It sayse(p, u) is the least spend that reaches u: degree one, concave in prices, ∂e/∂p = Hicksian demand
Use it forShephard, Roy, duality
The trapMinimum, not maximum; degree one, not zero
CV and EVLesson 15
It saysCV = e(p¹, u⁰) − m; EV = e(p⁰, u¹) − m. Slutsky versions keep a bundle
Use it forWelfare effect of a price change
The trapNormal good, price fall: EV > ΔCS > |CV|; no income effect: all equal
Homogeneity, adding upLesson 16
It saysx(ap, am) = x(p, m); p·x = m; elasticities sum to 0; Σ s·η = 1
Use it forMissing elasticities, types of good
The trapDemand is degree zero, not one; market demand adds horizontally and needs Gorman to act as one consumer
Delhi School techniqueLesson 17
It saysKinks and corners: list candidates and compare. 'Must be true': find the counter-example. Constraints: solve, then test
Use it forDSE entrance problems
The trapTangency can be a minimum; a grant or a limit may bind after the tangency is found
Real questions
Practise across the module
JNU91
Hyderabad85
Delhi School51
CUET-PG36
UGC NET21
IIT JAM19
GATE7
Questions placed in the lessons, by exam.
JNU and Hyderabad set the most consumer-theory questions, many of them numerical: an optimum for a Cobb–Douglas or quasi-linear taste, the effect of a tax. CUET and UGC NET ask definitions and statements to judge. JAM and GATE include unusual tastes such as max, shifted and mixed utilities. The Delhi School’s questions, which are the hardest, are gathered in Lesson 17 and grouped by technique.
Foundation
Definitions and one-step calculations: the shape of a curve, a budget line, an optimum for Cobb–Douglas tastes. Most CUET, UGC NET, Hyderabad and early JNU questions sit here.
88 questionsPractise →
Standard
Statements to judge, matching lists, and demands to compute with unusual tastes, up to JAM, GATE and JNU level.
172 questionsPractise →
These are questions from the TestStop bank. A free account answers 10 a day, each with its worked solution; All-Access opens every set with no daily limit.
Quick answers
Frequently asked questions
What is an indifference curve?
The set of bundles of two goods that a consumer likes equally well. Curves further from the origin are better, they never cross, and with two goods she likes they slope down because more of one good must be traded for less of the other to stay equally well off.
What is the marginal rate of substitution?
The rate at which a consumer will give up one good for another and stay equally well off: MU of x divided by MU of y, which is also minus the slope of her indifference curve. It does not change when the utility function is replaced by an increasing transformation of itself.
What does the slope of the budget line mean?
With x on the horizontal axis it is −p_x/p_y. The size of the slope is the opportunity cost of x: the units of y she must give up to buy one more unit of x.
How do you find a consumer's best bundle?
Set the marginal rate of substitution equal to the price ratio, so that the indifference curve just touches the budget line, and then use the budget equation to fix the scale. For u = x^a y^(1−a) this gives x = a·m/p_x and y = (1−a)·m/p_y. For straight-line, L-shaped or non-convex tastes, compare the corner and kink candidates instead.
What is a corner solution?
An optimum where the consumer buys only one good. It happens with perfect substitutes when one good gives more utility per rupee, with a good she dislikes, with tastes whose curves bow away from the origin, and with quasi-linear tastes when the interior quantity costs more than her income. At a corner the MRS does not equal the price ratio.
Why is utility only an ordering?
Because any increasing transformation of a utility function ranks the bundles in exactly the same order. Only the order of the numbers is meaningful, not their size, differences or ratios, which is why the MRS, indifference curves and demand are unaffected by the transformation but marginal utility is not.
What is the difference between a movement along a demand curve and a shift of it?
A change in the price of the good itself moves the consumer along her demand curve and changes the quantity demanded. A change in anything else that affects her choice, such as income, the price of a substitute or complement, tastes or the number of buyers, shifts the whole curve and changes demand.
How do you tell elastic from inelastic demand?
Compare the size of the price elasticity with 1. If it is above 1 the quantity changes by a larger percentage than the price, so a price cut raises revenue. If it is below 1 a price cut lowers revenue. At exactly 1 revenue does not change. On a straight-line demand curve the elasticity falls from infinity at the top to zero at the bottom and equals 1 at the midpoint.
What are normal, inferior, necessity and luxury goods?
They are named by the income elasticity of demand. An inferior good has a negative one, so she buys less as her income rises. A normal good has a positive one: a necessity if it is between 0 and 1, so its share of her budget falls as she gets richer, and a luxury if it is above 1, so its share rises.
What is the Slutsky equation?
It splits the total change in the quantity demanded when a price changes into a substitution effect and an income effect: the derivative of demand with respect to its own price equals the derivative of Hicksian (compensated) demand minus the quantity times the derivative of demand with respect to income. The substitution term is never positive; the income term is positive for an inferior good.
What is the difference between Hicksian and Marshallian demand?
Marshallian demand is the quantity chosen at given prices and income. Hicksian (compensated) demand is the quantity that minimises spending to reach a given utility. They are the same bundle at the starting point and differ elsewhere by the income effect: for a normal good the Hicksian curve is the steeper.
What are compensating and equivalent variation?
Two exact money measures of the welfare effect of a price change. The compensating variation is the change in income, at the new prices, that restores the old utility. The equivalent variation is the change in income, at the old prices, that gives the new utility. For a price fall of a normal good the equivalent variation is the larger in size and the compensating variation the smaller, with the change in consumer surplus between them.
What are homothetic and quasi-linear preferences?
Homothetic preferences have a marginal rate of substitution that depends only on the ratio of the goods, so the income expansion path is a straight line from the origin. Quasi-linear preferences, u = g(x) + y, have indifference curves that are vertical translates of one another and a demand for x that does not depend on income once she is buying both goods.
Checked
What we checked, and what we left out
Every answer key in the practice sets was worked by hand and, where it is a calculation, recomputed by a script from the model behind the labs, before the question was placed. The exercises in each lesson are recomputed the same way. A question is left out when its key or its stored text cannot be defended. Those are listed here, with the reason, so that you can tell a hard question from a broken one.
- UGC NET December 2023 Q63. The printed key is 'marks to all': only the statement defining strong monotonicity is correct, and no option lists it alone.
- Hyderabad 2021 Q46. Two options are keyed (the function is continuous and strictly quasi-concave) but the question is stored as single-answer, so it cannot be marked.
- Hyderabad 2016 Q18 (pencils and pens). Which label fits two everyday goods is a judgement, not a result.
- CUET 2024 Q75 (rotis and dal). The stored text gives the budget and the calories but not the calories per item. With the figures from JNU, three of its options are true of the only bundle.
- JNU 2010 Q21 and JNU 2015 Q57 (rotis and dal). The calories are given, but 'no more than 3 rotis' and 'no more than 5 cups' are true of the only bundle, as well as the keyed option. JNU 2013, which has four exclusive options, is used instead.
- JNU 2017 Q43 and Q45, JNU 2018 Q44. Written-answer questions, which cannot be marked automatically.
- CUET 2020 Q35 (unit elasticity at P = 6). The demand Q = 24 − 2P and the supply Q = 5P are both unit elastic at that price and both are keyed, but the question is stored as single-answer.
- JNU 2020 Q24 (X = 200 − 0.5P). The keyed 0.052 matches none of the working. The elasticity at P = 5 is 0.5 × 5 ÷ 197.5 = 0.0127.
- UGC NET June 2024 Q64. Statement (B) is true in substance and false only on a literal reading of 'elasticity of log D with respect to log p'; two other statements are not consumer theory.
- JNU 2012 Q5, 2015 Q37, 2019 Q1 (cell phones). A dramatic rise in population also raises total revenue, so the keyed option is not the only one that holds. JNU 2020 Q13, the same question without that option, is used.
- JNU 2019 Q24 (coffee and tea). The stem fixes the sign of the cross elasticity but says nothing about the income elasticity of tea, which the key then asserts.
- JNU 2020 Q37 (Sulekha). The keyed −3/2 is the old quantity less the new one, the opposite of the usual change in quantity (+3/2), so the key rests on an unstated sign convention.
- UGC NET 2026 June Q55. 'Optimal choice' is keyed as the one thing that is not an assumption of revealed preference, but the stem gives no way to separate it from 'rationality'.
- JNU 2017 Q36 (Alex, Hicks and Slutsky). The keyed statement (Slutsky CV exceeds Hicks CV for a price rise) is true, but so is the one about the equivalent variation for a price fall.
- JNU 2011 Q87 (market demand). The stem is cut off and never says what the demand is the sum of.
- DSE 2007 Q05 (Anita's baskets). The question refers to a figure of budget lines and four labelled baskets, which is not stored with it.
- DSE 2008 Q44 (labour endowment). The keyed 'shifts down' does not follow: the labour supply L = L̄w^a/(1 + w^a) rises with the endowment.
- DSE 2013 Q33 (borrowing agents). Each borrower takes 1/(1 + r) units and a fraction (1 − r)/(1 + r) borrow, so demand is N(1 − r)/(1 + r)²; the key leaves out the amount borrowed.
Read next
All resources →MicroeconomicsPreferences and indifference curves: axioms, goods, bads and neutralsCompleteness and transitivity, why a cycle is a money pump, the three strengths of more-is-better, what an indifference curve is, and the curves for goods, bads, neutrals, a bliss point and a U shape.MicroeconomicsIncome and substitution effects: Hicks and SlutskyTen chapters from the basic idea to the Slutsky equation, with a step-by-step decomposition lab and normal, inferior and Giffen goods on live diagrams.MicroeconomicsElasticity and surplus, worked outSlide a price along a demand curve and watch point elasticity and consumer surplus update, with the working shown line by line.