HUL211 Microeconomics Cheat Sheet
Lectures 1–12: Terms, Definitions, Formulae, Relations
IIT Delhi style revision sheet — MCQ + Major exam focus
Lecture 1: Homo Economicus, GDP, Pareto Apartment Model
• Inner-ring apartments preferred to outer-ring.
Core Economic Ideas
• Perfect competition: price clears market; highest reservation price people get apartments; Pareto efficient.
• Microeconomics:
study of optimizing individuals/firms and their interactions.
• Monopoly: price above competitive price; may leave
apartments unrented; Pareto inefficient.
• Macroeconomics: study of economy-wide phenomena.
• Scarcity: wants are unlimited, resources are limited.
• Optimization: choosing the best feasible option.
• Rent control: price cap below equilibrium; allocation
may be arbitrary; can be Pareto inefficient.
• Equilibrium: situation where no agent wants to change
behavior, often demand = supply.
Lecture 2: Consumer, Budget, Preferences
Homo Economicus
Budget Constraint
• Rational optimizing individual.
p1 x1 + p2 x2 ≤ m
• Chooses best affordable bundle.
• x1 , x2 : quantities of goods.
• Tries to satisfy own preferences.
• p1 , p2 : prices.
• Can explain many decisions, but not all human behavior.
• m: income.
Incentives, Interactions, Institutions
• Budget set: all affordable bundles.
• Incentive: something that induces action, e.g. tax, subsidy, fine.
• Budget line: bundles costing exactly income.
• Interaction: one person’s outcome depends on actions Budget Line
of others.
p1 x1 + p2 x2 = m
• Institution: formal/informal rules shaping behavior.
x2 =
Positive vs Normative
Positive
Normative
Describes what is; testable by data.
Example: tax increases price.
Describes what should be; value
judgment. Example: tax should be
lower.
m p1
− x1
p2
p2
slope = −
p1
p2
• x1 intercept: pm1 .
• x2 intercept: pm2 .
• Slope = opportunity cost of good 1 in terms of good 2.
GDP
• GDP: market value of final goods and services produced
in an economy in a given period.
Changes in Budget Line
• Income m ↑: parallel outward shift.
• Intermediate goods excluded to avoid double counting.
• Income m ↓: parallel inward shift.
• GDP per capita = average income/output per person.
• p1 ↑: x1 intercept falls, budget line pivots inward.
• GDP does not fully measure inequality, happiness, un• p1 ↓: x1 intercept rises, budget line pivots outward.
paid work, environmental damage, distribution.
• Same logic for p2 and vertical intercept.
Pareto Efficiency
Preference Notation
• Pareto improvement: making someone better off
without making anyone worse off.
X≻Y
X⪰Y
X∼Y
• Pareto efficient allocation: no Pareto improvement
possible.
• Efficiency ̸= fairness.
1
X strictly preferred to Y .
X weakly preferred to Y .
Consumer indifferent between X and
Y.
Preference Assumptions
• Tangency: slope of IC = slope of budget line.
• Completeness: any two bundles can be compared.
• Budget exhausted for monotonic preferences.
p1 x∗1 + p2 x∗2 = m
• Reflexivity: X ⪰ X.
• Transitivity: if X ⪰ Y and Y ⪰ Z, then X ⪰ Z.
Interior vs Boundary
• Weak monotonicity: more is at least as good.
• Strong monotonicity: more of one good and no less • Interior solution: x∗1 > 0, x∗2 > 0; tangency condition
of others is strictly better.
applies.
• Continuity: no jumps/holes in preferences.
• Convexity: averages preferred to extremes.
• Boundary/corner solution: one good consumed zero;
tangency may fail.
Indifference Curves (IC)
Demand Functions
• IC: all bundles giving same utility.
x1 = x1 (p1 , p2 , m),
• Higher IC = higher utility, if goods are goods.
x2 = x2 (p1 , p2 , m)
• Demand function gives optimal quantity as function of
prices and income.
• ICs usually slope downward.
• ICs do not intersect.
• Convex ICs reflect diminishing MRS.
• Individual demand curve: vary own price, hold other
price and income fixed.
MRS
Cobb–Douglas Utility
M RS12 =
M U1
M U2
• Rate at which consumer gives up good 2 for one more
unit of good 1 keeping utility same.
x∗1 =
• Slope of IC: −M RS12 .
a m
,
a + b p1
x∗2 =
b m
a + b p2
a
• Share on good 1: a+b
.
b
• Share on good 2: a+b
.
• Represents preferences numerically.
• Only ranking matters, not absolute value.
Perfect Substitutes
• Any strictly increasing transformation represents same
preferences.
U = ax1 + bx2
′
f (U ) > 0 ⇒ V represents same preferences
• Compare utility per rupee: pa1 vs pb2 .
• If pa1 > pb2 : buy only good 1.
Lecture 3: Utility Maximization, Demand
• If pa1 < pb2 : buy only good 2.
Consumer Problem
• If equal: any bundle on budget line is optimal.
max U (x1 , x2 )
x1 ,x2
a, b > 0
• Consumer spends fixed income shares.
Utility Function
V = f (U ),
U = xa1 xb2 ,
s.t.
p1 x 1 + p 2 x 2 ≤ m
Perfect Complements
U = min{ax1 , bx2 }
Lagrangian
• Fixed proportion: ax1 = bx2 .
L = U (x1 , x2 ) + λ(m − p1 x1 − p2 x2 )
• Solve with budget line.
FOCs for Interior Solution
∂U
= λp1 ,
∂x1
For U = min{x1 , x2 } :
∂U
= λp2
∂x2
m
p1 + p 2
Quasi-linear Utility
M U1
p1
=
M U2
p2
M RS12 =
x∗1 = x∗2 =
U = v(x1 ) + x2
• Interior condition: v ′ (x1 ) = pp12 .
p1
p2
• Demand for x1 often independent of income if interior.
2
Common Goods Classification
Price Elasticity of Demand
Income ↑⇒ demand ↑.
Income ↑⇒ demand ↓.
Demand rises more than proportional to income.
Demand rises less than proportional to income.
Normal good
Inferior good
Luxury good
Necessity
ε=
%∆Q
%∆P
ε=
dQ P
dP Q
• Engel curve: demand for one good as function of income.
Elastic
Inelastic
Unit elastic
Perfectly inelastic
Perfectly elastic
Lecture 4: Slutsky Equation, Elasticity
Revenue and Elasticity
Price Change Effects
• T R = P · Q.
• Price change affects demand through two channels:
• If demand elastic: price decrease increases revenue.
1. Substitution effect: relative price changes.
• If demand inelastic: price decrease decreases revenue.
2. Income effect: purchasing power changes.
• If unit elastic: revenue unchanged for small price change.
Income Offer Curve / Engel Curve
• Income offer curve: optimal bundles as income changes,
prices fixed.
ε > 1.
ε < 1.
ε = 1.
vertical demand, ε = 0.
horizontal demand, ε = ∞.
∆x1 = ∆xs1 + ∆xn1
Lecture 5: Revealed Preference
Slutsky Decomposition
Core Idea
• Step 1: Change price and adjust income so old bundle is
just affordable.
• Preferences are not directly observable.
• Choices/demand are observable.
• Step 2: Move from compensated income to actual income.
• Revealed preference uses observed choices to infer preferences.
∆m = x1 ∆p1
∆xs1 = x1 (p′1 , p2 , m′ ) − x1 (p1 , p2 , m)
Direct Revealed Preference (DRP)
∆xn1 = x1 (p′1 , p2 , m) − x1 (p′1 , p2 , m′ )
• If x is chosen when y was affordable, then x is directly
revealed preferred to y.
∆x1 = ∆xs1 + ∆xn1
p·x≥p·y
Sign Rules
Substitution effect
Normal good
Inferior good
Giffen good
⇒
x DRP y
Indirect Revealed Preference (IRP)
Always opposite to own price
change.
IE reinforces SE.
IE opposes SE.
Inferior good where IE dominates
SE; demand rises when price rises.
• If x DRP y and y DRP z, then x is indirectly revealed
preferred to z.
WARP
• Weak Axiom of Revealed Preference: if x is directly revealed preferred to y, then y cannot be directly
revealed preferred to x.
Law of Demand
x DRP y, x ̸= y ⇒ ¬(y DRP x)
• If a good is normal, demand falls when own price rises.
• Giffen goods violate ordinary law of demand.
WARP Test for Two Observations
Market Demand
• Observation 1: x chosen at prices p.
• Market demand = horizontal sum of individual demands.
X(p) =
n
X
• Observation 2: y chosen at prices q.
• WARP violation if:
xi (p)
p·x≥p·y
i=1
3
and
q·y ≥q·x
SARP
Exam Trap
• Strong Axiom of Revealed Preference: rules out
cycles in direct and indirect revealed preference.
• Chosen bundle cost is the budget/income level.
• If another bundle costs less or equal at those prices, it
was affordable.
• Necessary and sufficient condition for finite data to be
rationalized by utility maximization.
• Chosen bundle is revealed preferred to every affordable
unchosen bundle.
GARP
• Generalized Axiom of Revealed Preference.
Lecture 6: Producer and Technology
• Used when weak inequalities and indifference may occur.
Technology and Production
Index Numbers and Quantity Indices
• Technology: process by which inputs are converted into
output.
• Index numbers compare consumption bundles across two
periods.
•
•
• Inputs are factors of production: land, labor, capital.
• Capital goods are produced inputs used in production.
t
Period t: prices p = (pt1 , pt2 ), bundle xt = (xt1 , xt2 ).
Period b: prices pb = (pb1 , pb2 ), bundle xb = (xb1 , xb2 ).
Production Function
General Quantity Index
y = f (x1 , x2 , . . . , xn )
w1 xt1 + w2 xt2
Iq =
w1 xb1 + w2 xb2
• w1 , w2 are weights.
• Gives maximum output possible from input bundle.
• Technically efficient production lies on production function.
• Usually prices are used as weights.
Production Plan and Set
Paasche Quantity Index
Pq =
• Production plan: (x1 , x2 , . . . , xn ; y).
pt1 xt1 + pt2 xt2
pt1 xb1 + pt2 xb2
• Feasible if y ≤ f (x1 , x2 , . . . , xn ).
• Production set: all feasible production plans.
• Uses current-period prices pt .
• Compares current bundle and base bundle using period
Isoquant
t prices.
• Isoquant: all input bundles producing same output.
Laspeyres Quantity Index
• Similar to indifference curve, but for production.
pb xt + pb2 xt2
Lq = 1b 1b
p1 x1 + pb2 xb2
• Higher isoquant = higher output.
• Uses base-period prices pb .
MRTS
• Compares current bundle and base bundle using period
b prices.
M RT S12 =
Revealed Preference Interpretation
M P1
M P2
• Rate at which input 2 can be substituted by input 1
while holding output constant.
If
• Slope of isoquant: −M RT S.
Pq > 1
Marginal Product
then
pt xt > pt xb
M Pi =
• At period t prices, xb was affordable.
• Consumer chose xt .
∂f
∂xi
Technology Types
• So xt is revealed preferred to xb .
Fixed Proportions / Perfect Complements
Pq > 1 ⇒ consumer is better off in period t than period b
y = min{ax1 , bx2 }
• Inputs used in fixed ratio.
• L-shaped isoquants.
Paasche uses current prices; Laspeyres uses base prices
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• Hire input until value of marginal product equals input
price.
Perfect Substitutes
y = ax1 + bx2
• If pM P1 > w1 : use more input.
• Inputs can replace each other at constant rate.
• If pM P1 < w1 : use less input.
• Straight-line isoquants.
Isoprofit Line
Cobb–Douglas Production
π = py − w1 x1 − w2 x̄2
y = Axa1 xb2
• Smooth convex isoquants.
y=
• Marginal products positive if a, b > 0.
π + w2 x̄2
w1
+
x1
p
p
• Slope: wp1 .
Returns to Scale
• Higher isoprofit line = higher profit.
• Scale all inputs by t > 1.
CRS
IRS
DRS
Comparative Statics
f (tx) = tf (x).
f (tx) > tf (x).
f (tx) < tf (x).
• p ↑: isoprofit flatter; output and variable input increase.
• w1 ↑: isoprofit steeper; output and variable input decrease.
a + b = 1 ⇒ CRS, a + b > 1 ⇒ IRS, a + b < 1 ⇒ DRS
• w2 ↑ in short run: fixed factor cost rises; output/input
choice may not change; profit falls.
For y = Axa1 xb2 :
Lecture 7: Profit Max and Cost Min
Cost Minimization
Profit
min w1 x1 + w2 x2
π = Revenue − Cost
x1 ,x2
s.t.
f (x1 , x2 ) = y
π = py − w1 x1 − w2 x2
Isocost Line
• p: output price.
• y: output.
C = w1 x1 + w2 x2
• wi : price of input i.
• xi : quantity of input i.
x2 =
• Economic profit includes opportunity costs.
slope = −
Present Value of Profit Stream
P V = π0 +
C
w1
−
x1
w2
w2
π1
π2
+
+ ···
1 + r (1 + r)2
w1
w2
Cost-Minimizing Tangency
M RT S12 =
Fixed, Variable, Quasi-Fixed Inputs
• Fixed factor: quantity cannot adjust in short run.
M P1
w1
=
M P2
w2
• Variable factor: quantity can adjust.
• At optimum: isoquant tangent to lowest possible isocost
line.
• Quasi-fixed factor: paid only if output is positive.
• If corner solution or kink, tangency may not hold.
• Short run: some fixed factors.
• Long run: all factors variable.
Profit Max Implies Cost Min
Short-Run Profit Maximization
• If firm maximizes profit and produces y, it must produce
y at minimum cost.
y = f (x1 , x̄2 )
Lecture 8: Cost Curves
max pf (x1 , x̄2 ) − w1 x1 − w2 x̄2
x1
Cost Function
p · M P1 (x∗1 , x̄2 ) = w1
M P1 (x∗1 , x̄2 ) =
c(w1 , w2 , y) = minimum cost of producing y
w1
p
• If input prices fixed: c(y).
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Lecture 9: Firm Supply
Fixed, Variable, Total Cost
c(y) = cv (y) + F
Market Environments
• F : fixed cost.
Monopoly
Oligopoly
Dominant firm
Monopolistic
competition
Pure competition
• cv (y): variable cost.
• c(y): total cost.
Average Costs
AC(y) =
One seller.
Few firms; strategic interaction.
One large firm plus small firms.
Many firms, differentiated products.
Many firms, identical product,
price-taking.
c(y)
y
Perfectly Competitive Firm
cv (y)
AV C(y) =
y
• Price taker.
• Faces horizontal demand curve at market price.
F
AF C(y) =
y
• If charges above market price, demand is zero.
AC(y) = AV C(y) + AF C(y)
Short-Run Supply Decision
• AFC decreases as output rises.
max π(y) = py − c(y)
• AVC often U-shaped.
y
• AC lies above AVC by AFC.
dπ
= p − M C(y) = 0
dy
Marginal Cost
M C(y) =
dc(y)
dcv (y)
=
dy
dy
p = M C(y)
• Interior profit-max output satisfies p = M C.
• Extra cost of producing one more unit.
• Need second-order condition / upward-sloping MC region.
• Fixed cost does not affect MC.
MC and Average Cost Rules
M C < AV C
M C > AV C
M C = AV C
M C < AC
M C > AC
M C = AC
Shutdown Rule
AVC falling.
AVC rising.
AVC minimum.
AC falling.
AC rising.
AC minimum.
• If produce: profit = py − V C(y) − F .
• If shut down: profit = −F .
• Produce if revenue covers variable cost.
py ≥ V C(y)
cs (y, x̄2 ) = min w1 x1 + w2 x̄2
s.t.
x1
f (x1 , x̄2 ) = y
Short-Run Firm Supply Curve
Supply = upward-sloping part of MC above minimum AVC
Long-Run Cost Function
x1 ,x2
p ≥ AV C(y)
Short-run shutdown if p < min AV C
Short-Run Cost Function
cl (y) = min w1 x1 + w2 x2
⇐⇒
s.t.
f (x1 , x2 ) = y
Profit and Loss
π = (p − AC(y))y
Short Run vs Long Run
• p > AC: positive economic profit.
• Long-run cost ≤ short-run cost because firm has more
flexibility.
• p = AC: zero economic profit.
• Long-run AC is envelope of short-run AC curves.
LRAC(y) ≤ SRAC(y)
• AV C ≤ p < AC: produce at loss but cover variable cost.
• p < AV C: shut down.
for same y
6
Lecture 10: Industry Supply
Lecture 11: Game Theory Basics
Firm’s Long-Run Supply
Game Theory
• Study of strategic interactions.
p = M Cl (y) = M C(y, k(y))
• Strategic interaction: each player’s payoff depends on
own and others’ actions.
• Long-run supply is more elastic because all inputs/plant
size adjustable.
Elements of a Game
Long-Run Shutdown Rule
1. Players: who interacts.
• In long run, firm can avoid all costs by exiting.
2. Strategies: feasible actions/action plans.
• Produce only if profit nonnegative.
py − c(y) ≥ 0
⇐⇒
3. Order of play: simultaneous or sequential.
p ≥ AC(y)
4. Information: what players know.
5. Payoffs: outcomes for each strategy combination.
Long-run firm supply = M C above AC
Strategy
Short-Run Industry Supply
S(p) =
n
X
• Complete action plan of a player.
• In sequential games, strategy specifies actions after every
possible history.
Si (p)
i=1
• Horizontal sum of firm supply curves.
Common Knowledge
• Number of firms fixed in short run.
• Everyone knows the game.
• Everyone knows everyone knows.
Short-Run Industry Equilibrium
• This continues infinitely.
• Market price clears demand and supply.
• Some firms may earn positive profit, zero profit, or losses.
Muddy Children Logic
• Loss-making firms may still operate if p ≥ AV C.
• Parent announcement creates common knowledge.
• If k children have mud, they identify themselves in round
k.
Long-Run Industry Equilibrium
• Free entry and exit.
• Positive profit ⇒ entry ⇒ supply rises ⇒ price falls.
Lecture 12: Nash Equilibrium, Repeated
Games
• Negative profit ⇒ exit ⇒ supply falls ⇒ price rises.
• Long-run equilibrium: zero economic profit.
Dominated and Dominant Strategy
p = min AC(y)
• Strictly dominated strategy: gives lower payoff than
another strategy for every opponent action.
y>0
p = M C(y) = AC(y)
at minimum AC
• Dominant strategy: best regardless of opponent action.
Producer Surplus
Nash Equilibrium
• Short-run producer surplus = revenue minus variable
cost.
• Strategy profile where each player is best responding to
others.
• Graphically: area above supply curve and below price.
• No player can improve payoff by unilateral deviation.
P S = py − V C(y)
ui (s∗i , s∗−i ) ≥ ui (si , s∗−i )
∀si , ∀i
Economic Rent
Pure Strategy Nash Equilibrium
• Payment to an input above minimum needed to supply
that input.
• Each player chooses one strategy with probability 1.
• Long-run fixed input/license can earn economic rent.
• Find by best responses in payoff matrix.
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Mixed Strategy Nash Equilibrium
Ultra-High-Yield Formula Box
• Players randomize over pure strategies.
Consumer Theory
• Key principle: player must be indifferent among pure
strategies used with positive probability.
p1 x1 + p2 x2 ≤ m
slope budget line = −
Mixed Strategy 2x2 Method
p1
p2
M U1
p1
=
M U2
p2
m
a
b m
, xCD
xCD
=
=
1
2
a + b p1
a + b p2
m
U = min(x1 , x2 ) : x1 = x2 =
p1 + p2
∆x = SE + IE
• Let Row play Top with probability p.
M RS =
• Let Column play Left with probability q.
• Make Column indifferent to solve for p.
• Make Row indifferent to solve for q.
Prisoner’s Dilemma
dQ P
dP Q
ε=
• Both players have dominant strategy to confess/defect.
• Nash equilibrium: both confess/defect.
Revealed Preference
• Outcome is Pareto inefficient if both could be better off
by cooperating.
p · x ≥ p · y ⇒ x DRP y
WARP violation: p · x ≥ p · y and q · y ≥ q · x
Pareto Efficiency in Games
• Outcome Pareto efficient if no other outcome makes one Producer Theory
player better off without making another worse off.
• Nash equilibrium need not be Pareto efficient.
y = f (x1 , x2 ),
M Pi =
∂f
∂xi
M P1
M P2
π = py − w1 x1 − w2 x2
M RT S =
Repeated Games
• Finite repeated prisoner’s dilemma: backward induction
gives defect/confess every round.
pM P1 = w1
• Infinite repeated game: cooperation may be sustained if
future matters enough.
C = w 1 x1 + w 2 x2 ,
slope isocost = −
w1
w2
M P1
w1
=
M P2
w2
∞
X
ut
V =
(1 + r)t
t=0
Cost and Supply
Lecture Example: Infinite Repeated PD
Vcooperate = 3 +
3
3
3(1 + r)
+
+ ··· =
1 + r (1 + r)2
r
Vdeviate = 4 +
1
1
1
+
+ ··· = 4 +
2
1 + r (1 + r)
r
Cooperation sustainable if
C(y) = V C(y) + F
C
VC
F
AC = , AV C =
, AF C =
y
y
y
AC = AV C + AF C
dV C
dC
MC =
=
dy
dy
p = M C competitive firm supply condition
3(1 + r)
1
≥4+
r
r
SR shutdown: p < min AV C
LR shutdown/exit: p < min AC
X
S(p) =
Si (p)
Sequential Games
i
• Players move in sequence.
LR competitive equilibrium: p = min AC = M C
• Later players may observe earlier actions.
Game Theory
• Solve using backward induction.
• Nash equilibrium in every subgame.
Nash: ui (s∗i , s∗−i ) ≥ ui (si , s∗−i )
∞
X
ut
V =
(1 + r)t
t=0
• Removes non-credible threats.
SPE: Nash equilibrium in every subgame
Subgame Perfect Equilibrium (SPE)
8
Common MCQ Traps
• Nash equilibrium need not be Pareto efficient.
• M RS = M U1 /M U2 , but slope of IC is −M RS.
• Dominant strategy equilibrium is a Nash equilibrium,
but Nash need not use dominant strategies.
• Budget slope is −p1 /p2 , not −p2 /p1 .
• Cobb-Douglas exponents are income shares only after
dividing by sum of exponents.
Last-Day Revision Order
• Perfect substitutes: compare utility per rupee.
1. Budget, MRS, utility maximization.
• Perfect complements: set required ratio first, then use
budget.
2. Cobb-Douglas, substitutes, complements.
3. Slutsky + elasticity.
• Substitution effect is always opposite to own price
change.
4. Revealed preference/WARP.
• Giffen good must be inferior, but all inferior goods are
not Giffen.
5. Production functions + returns to scale.
• WARP violation requires mutual affordability.
6. Profit max: pM P = w.
• Fixed cost does not affect marginal cost.
7. Cost curves: AC, AVC, AFC, MC.
• MC cuts AVC and AC at their minimum points.
8. Firm supply + shutdown.
• Short-run shutdown uses AVC; long-run exit uses AC.
9. Industry supply + long-run equilibrium.
• Competitive firm chooses output, not price.
10. Nash equilibrium + repeated/sequential games.
9