2026
INTERMEDIATE MICROECONOMICS
ABBREVIATIONS AND FORMULA SHEET
KOEN HANEGREEFS
VUB
,Part 1 — Abbreviations and Definitions
This first part lists every abbreviation, symbol and shorthand used in the course, together with its full name
and a short plain-English definition. Use it as a quick lookup while reading the chapter summaries or the
formula sheet in Part 2.
Acronyms and shorthand
Abbreviation Long form Definition
AC Average Cost Total cost divided by output (same as ATC); cost per unit. U-
shaped; its minimum is the long-run break-even price.
AFC Average Fixed Cost Fixed cost divided by output (F/y); always falls as output rises.
ATC Average Total Cost Total cost per unit (= AFC + AVC); U-shaped.
AVC Average Variable Cost Variable cost per unit; U-shaped; its minimum is the short-run
shutdown price.
CE Certainty Equivalent The guaranteed amount of money that gives the same utility as
a risky gamble.
CRS Constant Returns to Scale Scaling all inputs by t scales output by exactly t.
CS Consumer Surplus Willingness to pay minus what is actually paid; area below
demand, above price.
DRS Decreasing Returns to Scale Scaling all inputs by t raises output by less than t.
DWL Deadweight Loss Surplus lost because a distortion (tax, monopoly) blocks
mutually beneficial trades.
EU Expected Utility Probability-weighted average of utility across outcomes (the
VNM criterion).
EV Expected Value Probability-weighted average of the monetary outcomes of a
gamble.
FC Fixed Cost(s) Costs that do not change with output and are paid even at zero
output.
FOC First-Order Condition The “derivative = 0” condition that locates an optimum.
FV Future Value What a present amount is worth later: FV = Y(1 + r).
HOC Hoorcollege Dutch for “lecture” — the theory classes.
IC Indifference Curve All consumption bundles that give the consumer the same
utility.
IRS Increasing Returns to Scale Scaling all inputs by t raises output by more than t.
L Lerner Index Measure of market power: L = (p − MC)/p = 1/|ε|.
LAC Long-Run Average Cost Lowest possible average cost when all inputs adjust; the
envelope of the SAC curves.
LR Long Run Period in which all inputs (incl. capital) are variable; no fixed
costs.
MC Marginal Cost Extra cost of producing one more unit (dTC/dy).
MES Minimum Efficient Scale Smallest output at which long-run average cost reaches its
minimum.
MP Marginal Product Extra output from one more unit of an input (∂f/∂xᵢ).
MR Marginal Revenue Extra revenue from selling one more unit (dTR/dy).
MRS Marginal Rate of Substitution Slope of the indifference curve; rate the consumer will swap
1
,Abbreviation Long form Definition
good 2 for good 1.
MRT Marginal Rate of Transformation Rate the market lets you swap goods; equals the price ratio
p₁/p₂.
MU Marginal Utility Extra utility from one more unit of a good (∂u/∂xᵢ).
NE Nash Equilibrium Strategy profile where no player can do better by changing
strategy alone.
PC Perfect Competition Many price-taking firms, an identical product, and free entry
and exit.
PS Producer Surplus Revenue minus variable cost; area above supply, below price (=
profit + fixed cost).
PV Present Value What a future amount is worth today: PV = X/(1 + r).
SAC Short-Run Average Cost Average cost for a fixed level of capital; lies on or above LAC.
SOC Second-Order Condition Curvature check that confirms an optimum is a maximum (or
minimum).
SPE Subgame-Perfect Equilibrium Nash equilibrium that is optimal in every subgame; found by
backward induction.
SR Short Run Period with at least one fixed input; fixed costs are positive.
TC Total Cost Total cost of producing output: TC = FC + VC.
TR Total Revenue Total sales revenue: TR = p × q.
TRS Technical Rate of Substitution Slope of the isoquant; rate one input replaces another at fixed
output (= MP₁/MP₂).
VC Variable Cost Costs that rise with output; zero when output is zero.
VMP Value of the Marginal Product Extra revenue from one more unit of an input: p × MPᵢ.
VNM Von Neumann–Morgenstern The expected-utility framework for ranking risky choices.
W Total Welfare (Total Surplus) CS + PS; maximised at the competitive equilibrium quantity.
WPO Werkcollege / Practicum Dutch for the practical exercise (tutorial) sessions.
WTA Willingness to Accept Minimum payment someone needs to give up a good.
WTP Willingness to Pay Maximum amount someone will pay for a good.
2
,Symbols and Greek letters
Abbreviation Long form Definition
ε (epsilon) Price elasticity of demand % change in quantity per 1% change in price; |ε| > 1 elastic,
< 1 inelastic.
η (eta) Income elasticity of demand % change in quantity per 1% change in income; > 1 luxury,
0–1 necessity, < 0 inferior.
λ (lambda) Lagrange multiplier Shadow price: marginal utility of income (utility) or marginal
cost (cost minimisation).
π (pi) Profit Firm profit π = TR − TC.
πₐ, πₙₐ State probabilities Probabilities of the “accident” / “no-accident” states in
choice under uncertainty.
π (inflation) Inflation rate Rate prices rise; used in the Fisher equation linking real and
nominal interest.
ρ (rho) Risk premium ρ = EV − CE; the most a risk-averse person pays to avoid a
gamble.
γ (gamma) Insurance premium rate Price per euro of coverage; “actuarially fair” when γ = πₐ.
τ (tau) Ad-valorem tax rate Proportional tax on price; effective price becomes p(1 + τ).
t Per-unit (quantity) tax Fixed tax per unit sold; also used as the scaling factor in
returns-to-scale tests.
r,i Real / nominal interest rate r is inflation-adjusted; i is the stated rate. Linked by the
Fisher equation.
Δ (delta) “Change in” A change in a variable, e.g. Δx₁ = change in quantity, Δp =
change in price.
∂ Partial derivative Rate of change of a function w.r.t. one variable, holding the
others fixed.
Σ (sigma) Summation Add a quantity over all items, e.g. market demand = Σ
individual demands.
min{·} Minimum operator Take the smallest argument; used in perfect-complements
utility and Leontief production.
≻,⪰,∼ Preference relations “strictly preferred to”, “at least as good as”, and
“indifferent to”.
m,p,w Income, price, input price m = income/budget; p = output price; w = input price (e.g.
the wage).
3
,Part 2 — Formula Sheet
Every formula you need for the course is below, grouped by topic. For each one you get the formula itself, a
one-line “what it does”, and a fully worked numerical example with every intermediate step shown, so you
can follow it even with no prior background. Numbers are chosen to be simple on purpose.
A. Budget, preferences and utility
A1. Budget line
𝑚 𝑝!
𝑝! 𝑥! + 𝑝" 𝑥" = 𝑚 ⇔ 𝑥" = − 𝑥
𝑝" 𝑝" !
What it does: describes every bundle (𝑥! , 𝑥" ) that costs exactly your income 𝑚. The slope −𝑝! /𝑝" is how
many units of good 2 you must give up to buy one more unit of good 1.
Worked example. Prices 𝑝! = 4, 𝑝" = 2, income 𝑚 = 120.
120 4
4𝑥! + 2𝑥" = 120 ⇒ 𝑥" = − 𝑥! = 60 − 2𝑥! .
2 2
If you buy 𝑥! = 10, then 𝑥" = 60 − 2(10) = 40. Check the cost: 4(10) + 2(40) = 40 + 80 = 120 ✓.
The slope is −𝑝! /𝑝" = −4/2 = −2: each extra unit of good 1 costs you 2 units of good 2.
A2. Marginal Rate of Substitution (MRS)
𝑀𝑈! 𝑎 𝑥"
MRS = − , for 𝑢 = 𝑥!# 𝑥"$ : MRS = −
𝑀𝑈" 𝑏 𝑥!
What it does: the slope of the indifference curve — how many units of good 2 the consumer will trade for one
more unit of good 1 while staying equally happy.
Worked example. Utility 𝑢 = 𝑥! 𝑥" (so 𝑎 = 𝑏 = 1). The marginal utilities are 𝑀𝑈! = 𝜕𝑢/𝜕𝑥! = 𝑥" and
𝑀𝑈" = 𝜕𝑢/𝜕𝑥" = 𝑥! . At the bundle (𝑥! , 𝑥" ) = (10,40):
𝑀𝑈! 𝑥" 40
MRS = − =− =− = −4.
𝑀𝑈" 𝑥! 10
The consumer would give up 4 units of good 2 to get 1 more unit of good 1.
4
, A3. Optimal choice — the tangency condition
𝑝!
MRS = −
𝑝"
What it does: at the best affordable bundle, the indifference curve just touches the budget line, so their
slopes are equal. Solve this together with the budget line.
Worked example. 𝑢 = 𝑥! 𝑥" , 𝑝! = 4, 𝑝" = 2, 𝑚 = 120.
%! &
1. Tangency: − = − " = −2 ⇒ 𝑥" = 2𝑥! .
%"
2. Substitute into the budget line: 4𝑥! + 2(2𝑥! ) = 120 ⇒ 8𝑥! = 120 ⇒ 𝑥! = 15.
3. Back-substitute: 𝑥" = 2(15) = 30.
Check: 4(15) + 2(30) = 60 + 60 = 120 ✓. Optimal bundle (15,30).
A4. Cobb–Douglas demand
𝑎 𝑚 𝑏 𝑚
𝑥!∗ = ⋅ , 𝑥"∗ = ⋅
𝑎 + 𝑏 𝑝! 𝑎 + 𝑏 𝑝"
What it does: for 𝑢 = 𝑥!# 𝑥"$ the consumer spends a fixed share of income on each good — share 𝑎/(𝑎 + 𝑏)
on good 1 and 𝑏/(𝑎 + 𝑏) on good 2.
Worked example. 𝑢 = 𝑥!! 𝑥"" (so 𝑎 = 1, 𝑏 = 2), 𝑚 = 120, 𝑝! = 4, 𝑝" = 2.
1 120 1 2 120 2
𝑥!∗ = ⋅ = ⋅ 30 = 10, 𝑥"∗ = ⋅ = ⋅ 60 = 40.
1+2 4 3 1+2 2 3
Check spending: 4(10) + 2(40) = 40 + 80 = 120 ✓. Note good 1 gets 1/3 of income, good 2 gets 2/3.
A5. Perfect complements demand
𝑚
𝑥!∗ = 𝑥"∗ =
𝑝! + 𝑝"
What it does: when goods must be used together in fixed proportions (left + right shoe), you buy equal
amounts and the optimum sits at the kink of the L-shaped indifference curve.
Worked example. 𝑢 = min{𝑥! , 𝑥" }, 𝑚 = 120, 𝑝! = 4, 𝑝" = 2.
120 120
𝑥!∗ = 𝑥"∗ = = = 20.
4+2 6
You buy 20 of each; total cost 4(20) + 2(20) = 80 + 40 = 120 ✓.
5
INTERMEDIATE MICROECONOMICS
ABBREVIATIONS AND FORMULA SHEET
KOEN HANEGREEFS
VUB
,Part 1 — Abbreviations and Definitions
This first part lists every abbreviation, symbol and shorthand used in the course, together with its full name
and a short plain-English definition. Use it as a quick lookup while reading the chapter summaries or the
formula sheet in Part 2.
Acronyms and shorthand
Abbreviation Long form Definition
AC Average Cost Total cost divided by output (same as ATC); cost per unit. U-
shaped; its minimum is the long-run break-even price.
AFC Average Fixed Cost Fixed cost divided by output (F/y); always falls as output rises.
ATC Average Total Cost Total cost per unit (= AFC + AVC); U-shaped.
AVC Average Variable Cost Variable cost per unit; U-shaped; its minimum is the short-run
shutdown price.
CE Certainty Equivalent The guaranteed amount of money that gives the same utility as
a risky gamble.
CRS Constant Returns to Scale Scaling all inputs by t scales output by exactly t.
CS Consumer Surplus Willingness to pay minus what is actually paid; area below
demand, above price.
DRS Decreasing Returns to Scale Scaling all inputs by t raises output by less than t.
DWL Deadweight Loss Surplus lost because a distortion (tax, monopoly) blocks
mutually beneficial trades.
EU Expected Utility Probability-weighted average of utility across outcomes (the
VNM criterion).
EV Expected Value Probability-weighted average of the monetary outcomes of a
gamble.
FC Fixed Cost(s) Costs that do not change with output and are paid even at zero
output.
FOC First-Order Condition The “derivative = 0” condition that locates an optimum.
FV Future Value What a present amount is worth later: FV = Y(1 + r).
HOC Hoorcollege Dutch for “lecture” — the theory classes.
IC Indifference Curve All consumption bundles that give the consumer the same
utility.
IRS Increasing Returns to Scale Scaling all inputs by t raises output by more than t.
L Lerner Index Measure of market power: L = (p − MC)/p = 1/|ε|.
LAC Long-Run Average Cost Lowest possible average cost when all inputs adjust; the
envelope of the SAC curves.
LR Long Run Period in which all inputs (incl. capital) are variable; no fixed
costs.
MC Marginal Cost Extra cost of producing one more unit (dTC/dy).
MES Minimum Efficient Scale Smallest output at which long-run average cost reaches its
minimum.
MP Marginal Product Extra output from one more unit of an input (∂f/∂xᵢ).
MR Marginal Revenue Extra revenue from selling one more unit (dTR/dy).
MRS Marginal Rate of Substitution Slope of the indifference curve; rate the consumer will swap
1
,Abbreviation Long form Definition
good 2 for good 1.
MRT Marginal Rate of Transformation Rate the market lets you swap goods; equals the price ratio
p₁/p₂.
MU Marginal Utility Extra utility from one more unit of a good (∂u/∂xᵢ).
NE Nash Equilibrium Strategy profile where no player can do better by changing
strategy alone.
PC Perfect Competition Many price-taking firms, an identical product, and free entry
and exit.
PS Producer Surplus Revenue minus variable cost; area above supply, below price (=
profit + fixed cost).
PV Present Value What a future amount is worth today: PV = X/(1 + r).
SAC Short-Run Average Cost Average cost for a fixed level of capital; lies on or above LAC.
SOC Second-Order Condition Curvature check that confirms an optimum is a maximum (or
minimum).
SPE Subgame-Perfect Equilibrium Nash equilibrium that is optimal in every subgame; found by
backward induction.
SR Short Run Period with at least one fixed input; fixed costs are positive.
TC Total Cost Total cost of producing output: TC = FC + VC.
TR Total Revenue Total sales revenue: TR = p × q.
TRS Technical Rate of Substitution Slope of the isoquant; rate one input replaces another at fixed
output (= MP₁/MP₂).
VC Variable Cost Costs that rise with output; zero when output is zero.
VMP Value of the Marginal Product Extra revenue from one more unit of an input: p × MPᵢ.
VNM Von Neumann–Morgenstern The expected-utility framework for ranking risky choices.
W Total Welfare (Total Surplus) CS + PS; maximised at the competitive equilibrium quantity.
WPO Werkcollege / Practicum Dutch for the practical exercise (tutorial) sessions.
WTA Willingness to Accept Minimum payment someone needs to give up a good.
WTP Willingness to Pay Maximum amount someone will pay for a good.
2
,Symbols and Greek letters
Abbreviation Long form Definition
ε (epsilon) Price elasticity of demand % change in quantity per 1% change in price; |ε| > 1 elastic,
< 1 inelastic.
η (eta) Income elasticity of demand % change in quantity per 1% change in income; > 1 luxury,
0–1 necessity, < 0 inferior.
λ (lambda) Lagrange multiplier Shadow price: marginal utility of income (utility) or marginal
cost (cost minimisation).
π (pi) Profit Firm profit π = TR − TC.
πₐ, πₙₐ State probabilities Probabilities of the “accident” / “no-accident” states in
choice under uncertainty.
π (inflation) Inflation rate Rate prices rise; used in the Fisher equation linking real and
nominal interest.
ρ (rho) Risk premium ρ = EV − CE; the most a risk-averse person pays to avoid a
gamble.
γ (gamma) Insurance premium rate Price per euro of coverage; “actuarially fair” when γ = πₐ.
τ (tau) Ad-valorem tax rate Proportional tax on price; effective price becomes p(1 + τ).
t Per-unit (quantity) tax Fixed tax per unit sold; also used as the scaling factor in
returns-to-scale tests.
r,i Real / nominal interest rate r is inflation-adjusted; i is the stated rate. Linked by the
Fisher equation.
Δ (delta) “Change in” A change in a variable, e.g. Δx₁ = change in quantity, Δp =
change in price.
∂ Partial derivative Rate of change of a function w.r.t. one variable, holding the
others fixed.
Σ (sigma) Summation Add a quantity over all items, e.g. market demand = Σ
individual demands.
min{·} Minimum operator Take the smallest argument; used in perfect-complements
utility and Leontief production.
≻,⪰,∼ Preference relations “strictly preferred to”, “at least as good as”, and
“indifferent to”.
m,p,w Income, price, input price m = income/budget; p = output price; w = input price (e.g.
the wage).
3
,Part 2 — Formula Sheet
Every formula you need for the course is below, grouped by topic. For each one you get the formula itself, a
one-line “what it does”, and a fully worked numerical example with every intermediate step shown, so you
can follow it even with no prior background. Numbers are chosen to be simple on purpose.
A. Budget, preferences and utility
A1. Budget line
𝑚 𝑝!
𝑝! 𝑥! + 𝑝" 𝑥" = 𝑚 ⇔ 𝑥" = − 𝑥
𝑝" 𝑝" !
What it does: describes every bundle (𝑥! , 𝑥" ) that costs exactly your income 𝑚. The slope −𝑝! /𝑝" is how
many units of good 2 you must give up to buy one more unit of good 1.
Worked example. Prices 𝑝! = 4, 𝑝" = 2, income 𝑚 = 120.
120 4
4𝑥! + 2𝑥" = 120 ⇒ 𝑥" = − 𝑥! = 60 − 2𝑥! .
2 2
If you buy 𝑥! = 10, then 𝑥" = 60 − 2(10) = 40. Check the cost: 4(10) + 2(40) = 40 + 80 = 120 ✓.
The slope is −𝑝! /𝑝" = −4/2 = −2: each extra unit of good 1 costs you 2 units of good 2.
A2. Marginal Rate of Substitution (MRS)
𝑀𝑈! 𝑎 𝑥"
MRS = − , for 𝑢 = 𝑥!# 𝑥"$ : MRS = −
𝑀𝑈" 𝑏 𝑥!
What it does: the slope of the indifference curve — how many units of good 2 the consumer will trade for one
more unit of good 1 while staying equally happy.
Worked example. Utility 𝑢 = 𝑥! 𝑥" (so 𝑎 = 𝑏 = 1). The marginal utilities are 𝑀𝑈! = 𝜕𝑢/𝜕𝑥! = 𝑥" and
𝑀𝑈" = 𝜕𝑢/𝜕𝑥" = 𝑥! . At the bundle (𝑥! , 𝑥" ) = (10,40):
𝑀𝑈! 𝑥" 40
MRS = − =− =− = −4.
𝑀𝑈" 𝑥! 10
The consumer would give up 4 units of good 2 to get 1 more unit of good 1.
4
, A3. Optimal choice — the tangency condition
𝑝!
MRS = −
𝑝"
What it does: at the best affordable bundle, the indifference curve just touches the budget line, so their
slopes are equal. Solve this together with the budget line.
Worked example. 𝑢 = 𝑥! 𝑥" , 𝑝! = 4, 𝑝" = 2, 𝑚 = 120.
%! &
1. Tangency: − = − " = −2 ⇒ 𝑥" = 2𝑥! .
%"
2. Substitute into the budget line: 4𝑥! + 2(2𝑥! ) = 120 ⇒ 8𝑥! = 120 ⇒ 𝑥! = 15.
3. Back-substitute: 𝑥" = 2(15) = 30.
Check: 4(15) + 2(30) = 60 + 60 = 120 ✓. Optimal bundle (15,30).
A4. Cobb–Douglas demand
𝑎 𝑚 𝑏 𝑚
𝑥!∗ = ⋅ , 𝑥"∗ = ⋅
𝑎 + 𝑏 𝑝! 𝑎 + 𝑏 𝑝"
What it does: for 𝑢 = 𝑥!# 𝑥"$ the consumer spends a fixed share of income on each good — share 𝑎/(𝑎 + 𝑏)
on good 1 and 𝑏/(𝑎 + 𝑏) on good 2.
Worked example. 𝑢 = 𝑥!! 𝑥"" (so 𝑎 = 1, 𝑏 = 2), 𝑚 = 120, 𝑝! = 4, 𝑝" = 2.
1 120 1 2 120 2
𝑥!∗ = ⋅ = ⋅ 30 = 10, 𝑥"∗ = ⋅ = ⋅ 60 = 40.
1+2 4 3 1+2 2 3
Check spending: 4(10) + 2(40) = 40 + 80 = 120 ✓. Note good 1 gets 1/3 of income, good 2 gets 2/3.
A5. Perfect complements demand
𝑚
𝑥!∗ = 𝑥"∗ =
𝑝! + 𝑝"
What it does: when goods must be used together in fixed proportions (left + right shoe), you buy equal
amounts and the optimum sits at the kink of the L-shaped indifference curve.
Worked example. 𝑢 = min{𝑥! , 𝑥" }, 𝑚 = 120, 𝑝! = 4, 𝑝" = 2.
120 120
𝑥!∗ = 𝑥"∗ = = = 20.
4+2 6
You buy 20 of each; total cost 4(20) + 2(20) = 80 + 40 = 120 ✓.
5
