2026
INTERMEDIATE MICROECONOMICS
SUMMARY
KOEN HANEGREEFS
VUB
,Table of Contents
Reading Guide ......................................................................................................................................... 1
Chapter 1 — Budget Constraint, Preferences & Utility (H2, H3, H4)............................................................. 2
Exercises — WPO 1 ............................................................................................................................ 13
Chapter 2 — Consumer Choice & Individual Demand (H5, H6) ................................................................. 17
Exercises — WPO 2 ............................................................................................................................ 25
Chapter 3 — Slutsky Equation & Market Demand (H8, H15)...................................................................... 29
Exercises — WPO 3 ............................................................................................................................ 37
Chapter 4 — Intertemporal Choice & Uncertainty (H10, H12) ................................................................... 41
Exercises — WPO 4 ............................................................................................................................ 56
Chapter 5 — Technology & Profit Maximisation (H19, H20) ....................................................................... 57
Exercises — WPO 5 ............................................................................................................................ 70
Chapter 6 — Cost Minimisation & Cost Curves (H21, H22) ....................................................................... 71
Exercises — WPO 6 ............................................................................................................................ 85
Chapter 7 — Firm Supply & Industry Supply (H23, H24) ............................................................................ 88
Exercises — WPO 7 .......................................................................................................................... 100
Chapter 8 — Market Equilibrium & Welfare (H16, H14) ........................................................................... 102
Chapter 9 — Monopoly & Monopoly Behaviour (H25, H26) ..................................................................... 118
Exercises — WPO 9 .......................................................................................................................... 132
Chapter 10 — Oligopoly & Game Theory (H28, H29, H30) ....................................................................... 137
Exercises — WPO 10 ........................................................................................................................ 154
Reading Guide
This document combines, for each of the ten lecture blocks of Intermediate Microeconomics at VUB
(Prof. Nikolas Vander Vennet):
1
,1. A high-quality summary of the lecture material, marked with importance levels:
– (Important) — central concepts, expected on the exam
– (Neutral) — useful supporting material
– (Less important) — context and intuition only
2. The WPO exercise questions for the matching textbook chapters.
All worked solutions are kept in a separate Solutions Manual so this study document can be used as
practice material without spoiling the answers.
Material follows Varian’s Intermediate Microeconomics with Calculus (9th/10th ed.).
Chapter 1 — Budget Constraint, Preferences & Utility (H2, H3,
H4)
Lecture HOC 1 — Budget Constraint, Preferences & Utility (Varian H2, H3, H4)
1.0 What Is Microeconomics? (Less important — context only)
Microeconomics studies the economic behavior of individual agents — consumers, firms, governments
— and how they interact in markets. It is the disciplined study of choice under constraints.
Key contrasts (Less important):
• Microeconomics vs. Macroeconomics. Macro looks at aggregates (GDP, unemployment, inflation);
micro looks at the agents whose behavior adds up to those aggregates. Modern macro is built on
“microeconomic foundations.”
• Theories vs. models. A theory explains observed phenomena with a set of assumptions; a model is a
formal, deliberately abstract description of one specific problem.
Three analytical tools used throughout the course (Important to internalise):
1. Constrained optimisation — choose the best option subject to a constraint (the foundation of every
consumer/firm problem).
2. Equilibrium analysis — a state of rest where, absent exogenous shocks, behavior persists.
3. Comparative statics — how does the equilibrium shift when an exogenous variable changes?
2
,The rationality assumption (Important). Agents are assumed to optimise their preferences with full
information. This is a useful baseline, not a literal description of human behavior. Departures (bounded
rationality — Herbert Simon; behavioural biases — Kahneman & Tversky) are studied as deviations from this
benchmark. Why this matters: even when reality deviates, the rational model gives you the yardstick to
measure the deviation.
1.1 The Budget Constraint (Important — H2)
The two-goods model
A consumer with income m chooses between two goods. The budget constraint is
𝑝! 𝑥! + 𝑝" 𝑥" ≤ 𝑚
The frontier of this set is the budget line:
𝑚 𝑝!
𝑝! 𝑥! + 𝑝" 𝑥" = 𝑚 ⇔ 𝑥" = − 𝑥
𝑝" 𝑝" !
Budget line and budget set
Why two goods? It is geometrically tractable yet still captures the essential trade-off. In practice we set
good 1 = “the good of interest” and good 2 = “money spent on everything else” — a composite good. When
𝑝" = 1, units of 𝑥" are literally euros.
3
,Intercepts and slope (Important)
• Vertical intercept 𝑚/𝑝" — maximum of good 2 if all income is spent on it.
• Horizontal intercept 𝑚/𝑝! — maximum of good 1.
• Slope −𝑝! /𝑝" — the opportunity cost of good 1: how many units of 𝑥" must be sacrificed to obtain one
unit of 𝑥! .
Comparative statics on the budget line (Important)
Income change. An increase in 𝑚 shifts the budget line outward, parallel to itself (the slope depends only
on the price ratio, which is unchanged).
Income change
Price change. A fall in 𝑝! pivots the budget line outward around the 𝑥" -intercept. The vertical intercept is
unchanged (𝑚/𝑝" ); the horizontal intercept moves from 𝑚/𝑝! to 𝑚/𝑝! ′.
4
,Price change
Taxes, subsidies, rationing (Neutral — appear in exercises)
These create kinks in the budget line because the slope changes at a threshold.
• Quantity tax 𝑡 per unit on good 1: effective price becomes 𝑝! + 𝑡; budget line is steeper.
• Value (ad-valorem) tax at rate 𝜏: effective price 𝑝! (1 + 𝜏).
• Lump-sum tax: parallel inward shift of the entire budget line.
• Quantity subsidy 𝑠: effective price 𝑝! − 𝑠.
• Rationing: vertical (or horizontal) cap that lops off part of the budget set.
• Threshold tax (e.g. tax only applies above 𝑥‾! ): a kinked budget line as shown below.
5
,Quantity tax above threshold
Numéraire trick (Less important but elegant). Multiplying 𝑝! , 𝑝" , 𝑚 by the same constant 𝜆 > 0 leaves the
budget set unchanged. We can therefore normalise one price to 1 — typically 𝑝" = 1, making good 2 the
numéraire. Only relative prices and real income matter.
1.2 Preferences (Important — H3)
The preference relation
Consumers are assumed to be able to rank any two bundles 𝑋′ = (𝑥! ′, 𝑥" ′) and 𝑋″ = (𝑥! ″, 𝑥" ″). Notation:
Symbol Meaning
𝑋′ ≻ 𝑋″ 𝑋′ strictly preferred to 𝑋″
𝑋′ ∼ 𝑋″ indifferent between 𝑋′ and 𝑋″
𝑋′ ≽ 𝑋″ 𝑋′ weakly preferred to 𝑋″
Three axioms of rational preferences (Important):
1. Completeness — for any two bundles, the consumer can rank them.
2. Reflexivity — every bundle is at least as good as itself (𝑋 ≽ 𝑋).
6
,3. Transitivity — if 𝑋′ ≽ 𝑋″ and 𝑋″ ≽ 𝑋‴, then 𝑋′ ≽ 𝑋‴.
Without these, a consistent choice theory is impossible (transitivity, in particular, rules out cycles that a
“money-pump” could exploit).
Indifference curves (Important)
An indifference curve (IC) is the locus of all bundles among which the consumer is indifferent. The whole
choice space is a field of ICs, one through every bundle.
Indifference curves — well-behaved
Key property — ICs cannot cross. A crossing would violate transitivity. Suppose 𝐴 and 𝐵 are on one IC and
𝐴 and 𝐶 are on another that also passes through the crossing point. Then 𝐵 ∼ 𝐴 ∼ 𝐶 implies 𝐵 ∼ 𝐶 —
impossible if the two ICs represent different utility levels.
A catalogue of preference types (Important — recognise on sight)
Perfect substitutes — willing to swap 𝑎 units of good 1 for 𝑏 units of good 2 at a constant rate. ICs are
straight lines with slope −𝑎/𝑏.
𝑢(𝑥! , 𝑥" ) = 𝑎𝑥! + 𝑏𝑥"
Perfect complements — goods consumed in fixed proportion (left & right shoes). ICs are L-shaped:
𝑢(𝑥! , 𝑥" ) = min{𝑎𝑥! , 𝑏𝑥" }
7
,Perfect substitutes & complements
Bads — more of the good is worse (pollution). ICs slope upward because you require compensation in the
“good” good. Neutrals — the agent doesn’t care about the good; ICs are vertical (or horizontal). Satiation
(bliss point) — there is a most-preferred bundle, and moving away in any direction reduces utility; ICs form
closed curves around the bliss point.
Bads, neutrals, satiation
“Well-behaved” preferences (Important)
We restrict attention to preferences with two desirable properties:
1. Monotonicity — more is better (no bads, no satiation in the relevant region).
2. Convexity — the consumer prefers averages to extremes. Formally, if 𝑋′ ∼ 𝑋″ then for any 𝑡 ∈ [0,1],
𝑡𝑋′ + (1 − 𝑡)𝑋″ ≽ 𝑋′
3. This rules out “I want lots of olives or lots of ice cream but not a mix.”
8
, Convex vs non-convex preferences
Marginal Rate of Substitution (Important — central concept)
The MRS is the slope of the indifference curve:
𝛥𝑥" 𝑑𝑥"
MRS = lim |' const =
#$! →& 𝛥𝑥! 𝑑𝑥!
It is the rate at which the consumer is willing to exchange good 2 for good 1 while remaining indifferent. For
goods (both monotonic), MRS < 0.
Two interpretations:
• A physical exchange rate between the two goods.
• If 𝑥" = money for other goods, then |MRS| is the marginal willingness to pay for an extra unit of good 1.
9
INTERMEDIATE MICROECONOMICS
SUMMARY
KOEN HANEGREEFS
VUB
,Table of Contents
Reading Guide ......................................................................................................................................... 1
Chapter 1 — Budget Constraint, Preferences & Utility (H2, H3, H4)............................................................. 2
Exercises — WPO 1 ............................................................................................................................ 13
Chapter 2 — Consumer Choice & Individual Demand (H5, H6) ................................................................. 17
Exercises — WPO 2 ............................................................................................................................ 25
Chapter 3 — Slutsky Equation & Market Demand (H8, H15)...................................................................... 29
Exercises — WPO 3 ............................................................................................................................ 37
Chapter 4 — Intertemporal Choice & Uncertainty (H10, H12) ................................................................... 41
Exercises — WPO 4 ............................................................................................................................ 56
Chapter 5 — Technology & Profit Maximisation (H19, H20) ....................................................................... 57
Exercises — WPO 5 ............................................................................................................................ 70
Chapter 6 — Cost Minimisation & Cost Curves (H21, H22) ....................................................................... 71
Exercises — WPO 6 ............................................................................................................................ 85
Chapter 7 — Firm Supply & Industry Supply (H23, H24) ............................................................................ 88
Exercises — WPO 7 .......................................................................................................................... 100
Chapter 8 — Market Equilibrium & Welfare (H16, H14) ........................................................................... 102
Chapter 9 — Monopoly & Monopoly Behaviour (H25, H26) ..................................................................... 118
Exercises — WPO 9 .......................................................................................................................... 132
Chapter 10 — Oligopoly & Game Theory (H28, H29, H30) ....................................................................... 137
Exercises — WPO 10 ........................................................................................................................ 154
Reading Guide
This document combines, for each of the ten lecture blocks of Intermediate Microeconomics at VUB
(Prof. Nikolas Vander Vennet):
1
,1. A high-quality summary of the lecture material, marked with importance levels:
– (Important) — central concepts, expected on the exam
– (Neutral) — useful supporting material
– (Less important) — context and intuition only
2. The WPO exercise questions for the matching textbook chapters.
All worked solutions are kept in a separate Solutions Manual so this study document can be used as
practice material without spoiling the answers.
Material follows Varian’s Intermediate Microeconomics with Calculus (9th/10th ed.).
Chapter 1 — Budget Constraint, Preferences & Utility (H2, H3,
H4)
Lecture HOC 1 — Budget Constraint, Preferences & Utility (Varian H2, H3, H4)
1.0 What Is Microeconomics? (Less important — context only)
Microeconomics studies the economic behavior of individual agents — consumers, firms, governments
— and how they interact in markets. It is the disciplined study of choice under constraints.
Key contrasts (Less important):
• Microeconomics vs. Macroeconomics. Macro looks at aggregates (GDP, unemployment, inflation);
micro looks at the agents whose behavior adds up to those aggregates. Modern macro is built on
“microeconomic foundations.”
• Theories vs. models. A theory explains observed phenomena with a set of assumptions; a model is a
formal, deliberately abstract description of one specific problem.
Three analytical tools used throughout the course (Important to internalise):
1. Constrained optimisation — choose the best option subject to a constraint (the foundation of every
consumer/firm problem).
2. Equilibrium analysis — a state of rest where, absent exogenous shocks, behavior persists.
3. Comparative statics — how does the equilibrium shift when an exogenous variable changes?
2
,The rationality assumption (Important). Agents are assumed to optimise their preferences with full
information. This is a useful baseline, not a literal description of human behavior. Departures (bounded
rationality — Herbert Simon; behavioural biases — Kahneman & Tversky) are studied as deviations from this
benchmark. Why this matters: even when reality deviates, the rational model gives you the yardstick to
measure the deviation.
1.1 The Budget Constraint (Important — H2)
The two-goods model
A consumer with income m chooses between two goods. The budget constraint is
𝑝! 𝑥! + 𝑝" 𝑥" ≤ 𝑚
The frontier of this set is the budget line:
𝑚 𝑝!
𝑝! 𝑥! + 𝑝" 𝑥" = 𝑚 ⇔ 𝑥" = − 𝑥
𝑝" 𝑝" !
Budget line and budget set
Why two goods? It is geometrically tractable yet still captures the essential trade-off. In practice we set
good 1 = “the good of interest” and good 2 = “money spent on everything else” — a composite good. When
𝑝" = 1, units of 𝑥" are literally euros.
3
,Intercepts and slope (Important)
• Vertical intercept 𝑚/𝑝" — maximum of good 2 if all income is spent on it.
• Horizontal intercept 𝑚/𝑝! — maximum of good 1.
• Slope −𝑝! /𝑝" — the opportunity cost of good 1: how many units of 𝑥" must be sacrificed to obtain one
unit of 𝑥! .
Comparative statics on the budget line (Important)
Income change. An increase in 𝑚 shifts the budget line outward, parallel to itself (the slope depends only
on the price ratio, which is unchanged).
Income change
Price change. A fall in 𝑝! pivots the budget line outward around the 𝑥" -intercept. The vertical intercept is
unchanged (𝑚/𝑝" ); the horizontal intercept moves from 𝑚/𝑝! to 𝑚/𝑝! ′.
4
,Price change
Taxes, subsidies, rationing (Neutral — appear in exercises)
These create kinks in the budget line because the slope changes at a threshold.
• Quantity tax 𝑡 per unit on good 1: effective price becomes 𝑝! + 𝑡; budget line is steeper.
• Value (ad-valorem) tax at rate 𝜏: effective price 𝑝! (1 + 𝜏).
• Lump-sum tax: parallel inward shift of the entire budget line.
• Quantity subsidy 𝑠: effective price 𝑝! − 𝑠.
• Rationing: vertical (or horizontal) cap that lops off part of the budget set.
• Threshold tax (e.g. tax only applies above 𝑥‾! ): a kinked budget line as shown below.
5
,Quantity tax above threshold
Numéraire trick (Less important but elegant). Multiplying 𝑝! , 𝑝" , 𝑚 by the same constant 𝜆 > 0 leaves the
budget set unchanged. We can therefore normalise one price to 1 — typically 𝑝" = 1, making good 2 the
numéraire. Only relative prices and real income matter.
1.2 Preferences (Important — H3)
The preference relation
Consumers are assumed to be able to rank any two bundles 𝑋′ = (𝑥! ′, 𝑥" ′) and 𝑋″ = (𝑥! ″, 𝑥" ″). Notation:
Symbol Meaning
𝑋′ ≻ 𝑋″ 𝑋′ strictly preferred to 𝑋″
𝑋′ ∼ 𝑋″ indifferent between 𝑋′ and 𝑋″
𝑋′ ≽ 𝑋″ 𝑋′ weakly preferred to 𝑋″
Three axioms of rational preferences (Important):
1. Completeness — for any two bundles, the consumer can rank them.
2. Reflexivity — every bundle is at least as good as itself (𝑋 ≽ 𝑋).
6
,3. Transitivity — if 𝑋′ ≽ 𝑋″ and 𝑋″ ≽ 𝑋‴, then 𝑋′ ≽ 𝑋‴.
Without these, a consistent choice theory is impossible (transitivity, in particular, rules out cycles that a
“money-pump” could exploit).
Indifference curves (Important)
An indifference curve (IC) is the locus of all bundles among which the consumer is indifferent. The whole
choice space is a field of ICs, one through every bundle.
Indifference curves — well-behaved
Key property — ICs cannot cross. A crossing would violate transitivity. Suppose 𝐴 and 𝐵 are on one IC and
𝐴 and 𝐶 are on another that also passes through the crossing point. Then 𝐵 ∼ 𝐴 ∼ 𝐶 implies 𝐵 ∼ 𝐶 —
impossible if the two ICs represent different utility levels.
A catalogue of preference types (Important — recognise on sight)
Perfect substitutes — willing to swap 𝑎 units of good 1 for 𝑏 units of good 2 at a constant rate. ICs are
straight lines with slope −𝑎/𝑏.
𝑢(𝑥! , 𝑥" ) = 𝑎𝑥! + 𝑏𝑥"
Perfect complements — goods consumed in fixed proportion (left & right shoes). ICs are L-shaped:
𝑢(𝑥! , 𝑥" ) = min{𝑎𝑥! , 𝑏𝑥" }
7
,Perfect substitutes & complements
Bads — more of the good is worse (pollution). ICs slope upward because you require compensation in the
“good” good. Neutrals — the agent doesn’t care about the good; ICs are vertical (or horizontal). Satiation
(bliss point) — there is a most-preferred bundle, and moving away in any direction reduces utility; ICs form
closed curves around the bliss point.
Bads, neutrals, satiation
“Well-behaved” preferences (Important)
We restrict attention to preferences with two desirable properties:
1. Monotonicity — more is better (no bads, no satiation in the relevant region).
2. Convexity — the consumer prefers averages to extremes. Formally, if 𝑋′ ∼ 𝑋″ then for any 𝑡 ∈ [0,1],
𝑡𝑋′ + (1 − 𝑡)𝑋″ ≽ 𝑋′
3. This rules out “I want lots of olives or lots of ice cream but not a mix.”
8
, Convex vs non-convex preferences
Marginal Rate of Substitution (Important — central concept)
The MRS is the slope of the indifference curve:
𝛥𝑥" 𝑑𝑥"
MRS = lim |' const =
#$! →& 𝛥𝑥! 𝑑𝑥!
It is the rate at which the consumer is willing to exchange good 2 for good 1 while remaining indifferent. For
goods (both monotonic), MRS < 0.
Two interpretations:
• A physical exchange rate between the two goods.
• If 𝑥" = money for other goods, then |MRS| is the marginal willingness to pay for an extra unit of good 1.
9
