ECO09X7: Economics Honours: Microeconomics Study Guide

Economics Honours in Microeconomics typically sharpens the tools from undergraduate theory into more rigorous, model-driven analysis: utility and producer behaviour, market structure, general equilibrium intuition, welfare analysis, and the strategic logic of incomplete information and games. This study guide is designed for South African pathways through universities, colleges, and TVET articulation routes that commonly feed into Honours Economics micro modules, with emphasis on exam-style reasoning, diagram competence, and mathematically grounded economic arguments. It is structured into five major sections, each building the core microeconomics “stack” from consumer and firm optimisation to market equilibrium and policy/welfare, including how to answer common Honours-level questions.

Section 1: Stellenbosch University — Microeconomics Core Tools (Optimisation, Preferences, Demand)

1.1 Why Honours Micro Begins with Optimisation

Honours microeconomics at South African universities often starts by making the assumptions do work. Rather than treating demand and supply as given, you derive them from:

• Consumer optimisation: preferences + budget constraint → Marshallian demand (and possibly Hicksian demand).
• Firm optimisation: technology + costs → cost minimisation, profit maximisation, supply relations.
• Comparative statics: how equilibrium changes when prices, income, technology, or taxes shift.

A typical exam question is not only “derive demand,” but also:

• interpret parameters (e.g., risk aversion, elasticity),
• check conditions (e.g., convexity, interior solution),
• compute how welfare changes under policy.

A key Honours skill is distinguishing:

• The primal problem (direct optimisation),
• The dual problem (indirect objects like expenditure function, cost function),
• and how duality helps prove results cleanly.

1.2 Consumer Theory: Utility Maximisation to Demand

Consider a consumer choosing bundle (x=(x_1,\dots,x_n)) to maximise utility (u(x)) subject to:
[
\sum_{i=1}^n p_i x_i \le m
]
For an interior solution, the Lagrangian is:
[
\mathcal{L} = u(x) + \lambda \left(m – \sum_{i=1}^n p_i x_i\right)
]
First-order conditions:
[
\frac{\partial u}{\partial x_i} = \lambda p_i \quad \forall i
]
So:
[
\frac{\partial u/\partial x_i}{\partial u/\partial x_j} = \frac{p_i}{p_j}
]
The left side is the marginal rate of substitution (MRS):
[
\text{MRS}_{ij} = \frac{MU_i}{MU_j}
]
In an exam, you must state clearly what “optimality” means: the consumer equates the marginal trade-off to the relative price.

Concrete example: Cobb–Douglas

Let utility be:
[
u(x_1,x_2)=x_1^{\alpha}x_2^{1-\alpha}, \quad 0<\alpha<1
]
Budget: (p_1x_1+p_2x_2=m). Standard result (derive using FOCs or known properties):
[
x_1^=\alpha \frac{m}{p_1}, \qquad x_2^=(1-\alpha)\frac{m}{p_2}
]
Interpretation:

• Income elasticity: (=1) for both goods (proportional spending shares).
• Price elasticity for each good is (-1).

This is exam gold because students often can compute but forget to interpret elasticity and spending shares.

1.3 Indirect Utility and Expenditure (Duality)

If you have utility maximisation, you can define:

• Indirect utility (v(p,m)): maximum utility achievable given prices (p) and income (m).
• Expenditure function (e(p,u)): minimum expenditure needed to reach utility level (u).

A common Honours task is to show:

• demand is “derived” from dual objects,
• expenditure is increasing and homogeneous in prices.

Example: Expenditure for Cobb–Douglas

For the Cobb–Douglas above, expenditure to reach utility (u) is:
[
e(p,u)=\frac{u}{\alpha^{\alpha}(1-\alpha)^{1-\alpha}} , p_1^{\alpha}p_2^{1-\alpha}
]
Then Hicksian demands (compensated demands) satisfy:
[
h_i(p,u) = \frac{\partial e(p,u)}{\partial p_i}
]
Duality matters because welfare analysis often needs compensated changes (Hicksian) rather than uncompensated (Marshallian).

1.4 Preferences, Convexity, and Market Outcomes

Honours-level micro asks about the assumptions behind the derivations.
Key preference conditions:

• Completeness: can compare any two bundles.
• Transitivity: if (A\succcurlyeq B) and (B\succcurlyeq C), then (A\succcurlyeq C).
• Local nonsatiation (or strict monotonicity in many models): more is better at least locally.
• Convexity: diminishing marginal rates of substitution (for interior solutions and uniqueness).
• Strict convexity: ensures uniqueness of optimum.

Risk of marks loss

In exams, students sometimes:

• derive demand assuming smoothness and interior solutions,
• then fail to mention conditions for existence/uniqueness.

Even if the final numeric expression is correct, the marker may penalise missing justification.

1.5 From Individual Demand to Market Demand

To move from micro theory to “microeconomics of markets,” you aggregate:
[
D(p) = \sum_{k} x^k(p,m_k)
]
In a representative agent model, (D(p)) is total demand from a single consumer type. In heterogeneous models, you may need to handle:

• different incomes (m_k),
• different preference parameters (\alpha_k),
• or different endowments.

A typical exam question:

• Given two consumers with different incomes and a Cobb–Douglas form, compute market demand and deduce how it responds to a price change.

1.6 Comparative Statics and Elasticities

Comparative statics is “how the optimum responds.”
For Cobb–Douglas:
[
x_1^*=\alpha \frac{m}{p_1}
]
So:

• if (p_1) rises by 10%, (x_1^*) falls by 10% (own-price elasticity (-1)),
• if income rises by 10%, (x_1^*) rises by 10% (income elasticity (+1)).

For more general preferences, you often use:

• Slutsky decomposition: total effect of price change = substitution effect + income effect.
• Diagram reasoning: rotation of budget line and movement along indifference curves.

1.7 Producer Theory: Cost Minimisation and Supply

Honours micro then complements consumer theory with producer theory:

• technology described by production function (f(\ell,K)) or (f(x)),
• profit maximisation:
  [
  \max_{y} \pi = Py – C(y)
  ]
  or cost minimisation given an output target:
  [
  \min_{x} \sum_i w_i x_i \quad \text{s.t.} \quad f(x)\ge y
  ]
  Then:
• cost function (C(y)),
• marginal cost (MC(y)=C'(y)),
• supply condition often involves (MC=price) under competitive assumptions.

Worked intuition: Monotonic costs and supply

If competitive firm sets output where:
[
P = MC(q)
]
Then:

• higher (P) → higher (q) (more output),
• shifts in technology change (MC) and thus shift supply.

1.8 Exam-Style Checklist for Section 1

When answering demand/supply derivations in Honours exams, ensure:

1. State the optimisation problem and variables clearly.
2. Use FOCs and interpret them economically.
3. Mention conditions: convexity, interior solution, differentiability (where required).
4. Provide comparative statics/elasticities or welfare interpretation if asked.
5. For duality, connect expenditure/cost to welfare objects.

South African Honours markers often reward structured mathematical steps paired with short economic interpretation.

Section 2: University of Pretoria — Market Structure and Strategic Pricing (Perfect Competition to Monopoly)

2.1 Competitive Markets: Equilibrium and Welfare Intuition

In a microeconomics module, perfect competition provides a baseline:

• firms are price-takers,
• output decision: maximise profit ( \pi(q)=Pq – C(q)),
• with (P) given, FOC yields (P=MC(q)) when producing.

Market equilibrium:

• supply (S(P)) aggregated from firms,
• demand (D(P)) from consumers.

If the market is efficient under standard conditions (convex preferences, cost minimisation, no externalities), then:

• competitive equilibrium is Pareto efficient (often shown via welfare theorems).

Exam tip: Even if the model’s proof is long, you can summarise the logic:

• at optimum, marginal willingness to pay equals marginal cost,
• no gains from trade remain.

2.2 Monopolies: Profit Maximisation and Markups

For a monopolist with inverse demand (P(Q)) and cost (C(Q)), the firm chooses (Q) to maximise:
[
\pi(Q)=P(Q)Q – C(Q)
]
FOC:
[
\frac{d}{dQ}[P(Q)Q] = C'(Q)
]
Using product rule:
[
P(Q) + P'(Q)Q = MC(Q)
]
Define marginal revenue:
[
MR(Q)=P(Q)+P'(Q)Q
]
So the rule is:
[
MR(Q)=MC(Q)
]

Example with linear demand

Let:
[
P(Q)=a-bQ
]
Then:
[
MR(Q)=a-2bQ
]
Set (a-2bQ=MC(Q)). If marginal cost is constant (MC=c), then:
[
a-2bQ=c \Rightarrow Q_m=\frac{a-c}{2b}
]
Price:
[
P_m=a-bQ_m=a-b\left(\frac{a-c}{2b}\right)=a-\frac{a-c}{2}=\frac{a+c}{2}
]
Compare with competitive outcome where (P=MC=c):
[
Q_c=\frac{a-c}{b}
]
Monopoly produces less quantity and charges a higher price than competition in this classic model.

Lerner index (markup formula)

With demand elasticity (\varepsilon) at the monopoly quantity:
[
\frac{P_m – MC}{P_m}=\frac{1}{|\varepsilon|}
]
Honours exams often ask:

• derive this relationship,
• interpret the sign and magnitude,
• discuss conditions when markup is larger.

2.3 Price Discrimination: Third-Degree and Welfare

A crucial micro extension is price discrimination when the firm can segment consumers.
Third-degree discrimination assumes demand differs by group:

• group (i) has inverse demand (P_i(Q_i)),
• total output (Q = \sum_i Q_i).

The monopolist chooses ({Q_i}) to maximise:
[
\pi = \sum_i P_i(Q_i)Q_i – C(Q)
]
FOCs:
[
MR_i(Q_i)=MC(Q)
]
If discrimination allows better extraction of consumer surplus, total welfare can increase, sometimes reaching (or approaching) first-best under perfect discrimination.

Concrete two-group numerical example

Suppose two markets with inverse demands:

• Segment 1: (P_1(Q_1)=10- Q_1)
• Segment 2: (P_2(Q_2)=8-2Q_2)
  Constant marginal cost (c=2).
  Then MR functions:
• (MR_1=10-2Q_1)
• (MR_2=8-4Q_2)

FOCs set:

• (MR_1=c \Rightarrow 10-2Q_1=2 \Rightarrow Q_1=4)
• (MR_2=c \Rightarrow 8-4Q_2=2 \Rightarrow Q_2=1.5)

Prices:

• (P_1=10-4=6)
• (P_2=8-2(1.5)=5)

You can compute group profits and consumer surplus if asked. The key is showing you can set MR equal to MC separately.

2.4 Oligopoly: Strategic Interaction and the Logic of Games

When moving from monopoly to oligopoly, the marker expects you to use game theory consistently:

• strategies: price, quantity, entry decisions,
• payoffs: profits from choices,
• equilibrium: Nash equilibrium (often also subgame perfect equilibrium in dynamic games).

Cournot duopoly: quantity competition

Two firms choose quantities (q_1,q_2). Total (Q=q_1+q_2). With inverse demand (P(Q)) and constant marginal cost (c), profits:
[
\pi_1=(P(q_1+q_2)-c)q_1
]
FOC for firm 1 yields best response:
[
q_1 = BR_1(q_2)
]
Solve simultaneously for Nash equilibrium.

Often, you’ll compare Cournot output to monopoly:

• Cournot tends to produce more than monopoly (more competition),
• but less than perfect competition.

Bertrand duopoly: price competition

With homogeneous goods and identical costs, Bertrand’s classic result:

• in pure strategies, equilibrium price equals marginal cost: (p=c),
• even with only two firms, outcomes resemble perfect competition.

Honours exams may ask for:

• conditions where Bertrand result fails (capacity constraints, differentiated products, search frictions),
• equilibrium in mixed strategies with non-uniqueness.

2.5 Collusion, Cartels, and Enforcement

In repeated games, collusion can be sustained through trigger strategies.
For example, if firms discount the future with factor (\delta), then collusion is sustainable if:
[
\text{Present value gain from deviation} \le \text{Foregone collusive profit due to punishment}
]
Even if the exact inequality depends on the numerical payoff matrix, the logic is consistent:

• higher (\delta) (more patience) makes collusion easier to sustain,
• stronger punishments make collusion harder to deviate from.

Application-style thinking

South African exam questions may use institutional contexts like:

• competition law and cartel enforcement,
• but the micro logic remains the same: incentives under repeated interaction.

2.6 Welfare Analysis Across Market Structures

A common Honours question: rank market structures by efficiency.
In standard models:

• Perfect competition: efficient (under assumptions).
• Monopoly: allocative inefficiency (deadweight loss).
• Price discrimination: can reduce deadweight loss depending on discrimination ability.

Make sure you can:

• compute deadweight loss areas for simple demand-cost shapes,
• or express them qualitatively with clear reasoning.

Section 3: University of the Witwatersrand (Wits) — General Equilibrium, Welfare Theorems, and Market Failure

3.1 From Partial to General Equilibrium

Microeconomics Honours typically progresses from single-market reasoning to general equilibrium:

• multiple markets,
• interdependence via income effects and resource constraints.

General equilibrium (GE) conceptually involves:

• consumers who demand bundles affecting multiple markets,
• firms that supply outputs across multiple markets,
• equilibrium where:
  • each market clears (aggregate excess demand = 0),
  • budget constraints hold,
  • firms maximise profits (or choose optimal plans),
  • and aggregate endowments/resources are satisfied.

Honours-level exams may not ask for full existence proofs, but they often ask you to:

• interpret GE equilibrium,
• explain the First and Second Welfare Theorems in words and in simple diagrams.

3.2 The First Welfare Theorem (Efficient Markets Under Ideal Conditions)

The first welfare theorem states that under conditions like:

• convex preferences,
• locally non-satiated preferences,
• competitive markets,
• and standard assumptions about production,

a competitive equilibrium allocation is Pareto efficient.

Economically, the intuition:

• if a marginal trade could make someone better off without harming others, then at equilibrium it would contradict optimisation and market clearing.

Exam technique:

• identify whether the policy question preserves assumptions,
• and if not, specify which assumption fails (e.g., non-convexities, externalities, missing markets).

3.3 The Second Welfare Theorem (Efficiency Achieved Through Transfers)

The second welfare theorem states that if preferences and production satisfy appropriate regularity conditions, then for any Pareto efficient allocation, there exists a set of lump-sum transfers that supports it as a competitive equilibrium.

This theorem matters for policy:

• redistribution via transfers can address equity,
• then efficiency can be achieved without distorting production/consumption choices.

However, Honours exams often test understanding that real-world policy instruments are not lump-sum; distortionary taxes and information asymmetry can break the practical relevance.

3.4 Pareto Efficiency, Social Surplus, and Compensating Variation

Welfare analysis hinges on the distinction between:

• Pareto improvements (cannot make anyone worse off),
• social welfare changes under a chosen criterion.

When you use consumer surplus and producer surplus in partial equilibrium, you are implicitly using quasi-linear or specific demand assumptions.
In more rigorous micro, you often use:

• compensating variation (CV) and equivalent variation (EV),
• or welfare measures derived from utility/expenditure functions.

CV/EV intuition (exam-ready)

Suppose price changes. The question: how much money would you take away (CV) to keep utility at the post-change level? Or give (EV) to reach the pre-change level.

Even if not asked to compute CV precisely, show conceptual understanding:

• CV depends on compensated demand (Hicksian),
• EV depends on the reference utility baseline.

3.5 Externalities and Market Failure: Pigou and Beyond

Externalities occur when actions impose costs/benefits on others not captured in market prices.

• Positive externality: e.g., vaccination in public health.
• Negative externality: e.g., pollution.

A standard negative externality model:

• private marginal cost (MC_p),
• social marginal cost (MC_s = MC_p + MEC) (marginal external cost).

Efficient output solves:
[
P(Q)=MC_s
]
Competitive output solves:
[
P(Q)=MC_p
]
So the market overproduces relative to the social optimum.

Policy instruments

• Pigouvian tax equal to marginal external damage (MEC) at the efficient quantity.
• Subsidy for positive externalities equal to marginal external benefit.

Honours exams ask you to:

• show why tax internalises the externality,
• discuss that optimal tax depends on the magnitude of MEC,
• mention uncertainty and administrative costs.

Example: compute optimal tax in a simple model

If demand is linear and (MC_s=MC_p + t), then the tax can shift the private marginal cost to align with social marginal cost. You compute the efficient quantity and infer the required tax.

Even when numeric values are given, the key is the relationship:

• tax makes firms face the social cost.

3.6 Public Goods and Free Rider Problem

Public goods are non-excludable and non-rival, leading to under-provision in private markets.
A classic result:

• For efficient provision, sum marginal benefits across individuals equals marginal cost.
• In private markets, each individual ignores others’ benefits and therefore has incentives to free ride.

In Honours exams, you may be asked to:

• explain how the free rider problem distorts demand,
• connect to why government provision or collective action mechanisms are needed.

3.7 Asymmetric Information: Adverse Selection and Moral Hazard (Micro Extensions)

While pure general equilibrium focuses on efficient markets under ideal assumptions, Honours micro often includes basic information asymmetry.

Adverse selection (hidden types)

Example story:

• consumers cannot distinguish quality, leading to “lemons” markets,
• the average quality deteriorates.

Moral hazard (hidden action)

Example story:

• once insured, individuals take less care,
• insurer cannot observe effort.

Even if details vary, always:

• state what is hidden (type vs action),
• explain the incentive effect.

3.8 Link to South African Teaching Contexts

At major South African universities, students often encounter these topics with both:

• diagram-based partial equilibrium and
• formal GE/Welfare framing.

Exam markers typically reward answers that:

• combine diagram logic (MEC vs MPC, MBB vs MC for public goods),
• with formal statements (welfare theorems, conditions under which they hold).

Section 4: University of KwaZulu-Natal (UKZN) — Game Theory and Market Institutions (Entry, Auctions, and Incentives)

4.1 Entry Deterrence and Strategic Commitment

Oligopoly and entry are common Honours micro themes:

• firms decide whether to enter a market,
• incumbents may respond strategically,
• outcomes depend on credibility of threats.

A simple entry game:

1. Incumbent chooses price (p) or output (q).
2. Potential entrant decides entry (E) or no entry (N).
   Payoffs depend on who enters and how competition proceeds.

Honours answers often require:

• solve for Nash equilibrium(s),
• discuss credibility (subgame perfection in dynamic games),
• consider “empty threats” and why they fail.

4.2 Auctions: Mechanisms and Expected Revenue

Auctions are micro institutions that test mechanism design intuition, often at a beginner-to-intermediate Honours level.

First-price sealed-bid auction intuition

Bidders submit bids without knowing others’ bids.
Each bidder shades bid below true valuation to avoid overpaying. Equilibrium strategies depend on:

• valuation distribution,
• risk preferences.

Second-price sealed-bid auction intuition

Truth-telling is a dominant strategy under standard assumptions:

• you bid your valuation because paying second-highest price aligns incentives.

Honours exams may ask:

• explain why truthful bidding is rational in second-price auctions,
• compare efficiency and revenue outcomes.

4.3 Incentives in Contracts: Hidden Action (Moral Hazard)

A typical principal-agent setup:

• the agent chooses effort (e),
• output depends on effort plus noise,
• the principal cannot observe effort but can design a contract based on observed output.

Contracting problem:

• choose contract to align incentives,
• manage risk-sharing: risk-averse agents require compensation to bear uncertainty.

Key trade-off:

• higher-powered incentives can increase moral hazard costs through risk to the agent.

Honours-level exam answers often need to:

• describe incentive compatibility,
• identify binding constraints (e.g., participation/individual rationality, incentive constraints).

4.4 Market Design: Regulations, Competition Policy, and External Constraints

South African microeconomics courses frequently connect theory to institutional settings:

• competition policy,
• regulation of utilities and telecommunications,
• procurement and auctions.

While micro theory is universal, exam questions may include South African references such as:

• public procurement mechanisms,
• licensing and access obligations in telecoms,
• price regulation in certain sectors.

In your answers, it’s important to keep the theory front-and-centre:

• show how the policy changes constraints and incentives,
• identify which equilibrium concept applies (Nash, subgame perfect, etc.),
• discuss how welfare could improve or worsen depending on assumptions.

4.5 Quantitative Game Theory Skills: Solving Equilibrium Systems

Honours exams often demand computational competence, for example:

• solve simultaneous best response functions,
• compute equilibrium bids or outputs given linear demands and costs.

When bids or quantities are linear functions, you often solve:

• system of equations,
• then compute profits.

Keep your algebra clean and show substitutions.

Worked template: Cournot with linear demand and quadratic costs

Suppose:

• inverse demand (P(Q)=a-bQ),
• cost for firm (i): (C(q_i)=c q_i + d q_i^2),
• profit:
  [
  \pi_i=(a-b(q_1+q_2))q_i – c q_i – d q_i^2
  ]
  FOC:
  [
  \frac{\partial \pi_i}{\partial q_i}=a-b(q_1+q_2)-bq_i – c – 2dq_i=0
  ]
  Simplify to best response:
  [
  (2b+2d)q_i + b q_j = a-c
  ]
  Then solve two linear equations for (q_1,q_2).
  Exam markers reward when you:
• derive best response correctly,
• show symmetry logic if (a,b,c,d) identical for both firms,
• compute equilibrium output and price.

4.6 Answering “Discuss” Questions: Strategic Reasoning Without Full Proof

Many Honours exams mix calculations with discursive prompts, e.g.:

• “Discuss whether entry will occur under given payoffs.”
• “Discuss the efficiency of second-price auctions.”

A high-scoring structure:

1. State the strategic logic (incentives and constraints).
2. Identify equilibrium prediction.
3. Explain how changes in parameter (e.g., discount factor, valuation distribution) alter the result.
4. Mention limitations or realistic deviations.

Section 5: South African TVET & College Pathways — Applied Microeconomics for Honours Preparation (Bridging Skills, Exam Technique, and Worked Practice)

5.1 Why a TVET-to-Honours Bridge Matters

Many South African learners enter university Honours Economics after formal vocational or college pathways (e.g., advanced diplomas, extended curricula, or bridging programmes). Microeconomics Honours expects fluency in:

• algebra,
• calculus-based optimisation (at least basic derivatives and FOCs),
• diagram interpretation (supply/demand, welfare, market failures),
• and coherent economic writing.

This section is not a replacement for university notes; it is a targeted bridge that helps you meet Honours expectations and avoid common pitfalls.

5.2 Core Skills Checklist (Mathematical and Logical)

To excel in Honours micro exams, you should be comfortable with:

Mathematics

• Solving linear equations and systems.
• Differentiation and using FOCs.
• Interpreting second-order conditions (where required).
• Elasticity computations from functional forms.
• Correct use of inequalities (e.g., budget constraints and corner solutions).

Economics

• Interpreting MRS, MR, MC, and marginal conditions.
• Explaining welfare impacts (deadweight loss, consumer surplus changes).
• Identifying market failure sources: externalities, public goods, information problems.
• Linking assumptions to conclusions.

Communication

• Present a complete logical chain: model → assumptions → derivation → interpretation.
• Use consistent notation and define it once.

5.3 Diagram Discipline: Reading and Drawing Like a Marker

Even when questions are numerical, diagrams often accompany them.

Common diagram expectations

1. Perfect competition: demand and supply, equilibrium at intersection; show surplus areas if asked.
2. Monopoly: marginal revenue below demand; show (MR=MC) and where price lies on demand.
3. Externality: MPC vs MSC; show overproduction relative to efficient quantity.
4. Public goods: sum of marginal benefits relative to marginal cost.

How to avoid losing marks

• Draw marginal revenue correctly (below demand for downward sloping demand).
• Label axes and key points (quantity and price for each market structure).
• Mention deadweight loss as a clear area and relate it to policy or welfare.

5.4 Worked Practice Set 1: Monopoly vs Competition with Linear Demand

Suppose demand:
[
P(Q)=20- Q
]
Marginal cost is constant:
[
MC(Q)=5
]
Competitive equilibrium: set (P=MC):
[
20-Q=5 \Rightarrow Q_c=15,\quad P_c=5
]
Monopoly: find MR.
Total revenue: (TR=P(Q)Q=(20-Q)Q=20Q-Q^2)
Marginal revenue:
[
MR(Q)=20-2Q
]
Set (MR=MC):
[
20-2Q_m=5 \Rightarrow 2Q_m=15 \Rightarrow Q_m=7.5
]
Price:
[
P_m=20-7.5=12.5
]

Welfare:

• Consumer surplus and producer surplus can be computed using triangle areas.
• Deadweight loss equals area between demand and cost curves from (Q_m) to (Q_c):
  Demand above cost for (Q\in(Q_m,Q_c)).

Even without computing numeric welfare, the correct inequalities matter:
[
Q_m < Q_c,\quad P_m>P_c
]

This is the kind of clean, complete logic that markers reward.

5.5 Worked Practice Set 2: Externality Tax with Simple Supply-Demand

Let inverse demand:
[
P(Q)=30-2Q
]
Private marginal cost equals marginal cost:
[
MC_p(Q)=10+Q
]
With negative externality:
[
MC_s(Q)=MC_p(Q)+MEC(Q)
]
Assume marginal external cost is constant:
[
MEC(Q)=4
]
So:
[
MC_s(Q)=14+Q
]

Market (no tax): set (P=MC_p):
[
30-2Q = 10+Q \Rightarrow 30-10=3Q \Rightarrow Q_m= \frac{20}{3}\approx 6.67
]
Efficient (social): set (P=MC_s):
[
30-2Q = 14+Q \Rightarrow 30-14=3Q \Rightarrow Q^*= \frac{16}{3}\approx 5.33
]

Pigouvian tax (t) should shift private incentives so firms face:
[
MC_p(Q)+t = MC_s(Q)=MC_p(Q)+4
]
Thus:
[
t=4
]

In exams, you often don’t need to calculate all surplus changes, but it’s valuable to state:

• tax reduces output from (Q_m) to (Q^*),
• welfare improves if tax is set correctly.

5.6 Worked Practice Set 3: Cournot Equilibrium with Symmetry

Two firms choose outputs (q_1,q_2).
Demand:
[
P(Q)=100- Q,\quad Q=q_1+q_2
]
Constant marginal cost:
[
c=20
]
Profit of firm (i):
[
\pi_i=(100-(q_1+q_2))q_i – 20q_i = (80 – q_1-q_2)q_i
]
For firm 1:
[
\pi_1=(80-q_1-q_2)q_1 = 80q_1 – q_1^2 – q_1q_2
]
FOC:
[
\frac{\partial \pi_1}{\partial q_1}=80 – 2q_1 – q_2=0 \Rightarrow q_1=\frac{80-q_2}{2}
]
Symmetry equilibrium (q_1=q_2=q):
[
q=\frac{80-q}{2} \Rightarrow 2q=80-q \Rightarrow 3q=80 \Rightarrow q=\frac{80}{3}\approx 26.67
]
Total output:
[
Q=\frac{160}{3}\approx 53.33
]
Price:
[
P=100-Q = 100-\frac{160}{3}=\frac{140}{3}\approx 46.67
]

This is a typical Honours calculation—simple but structured.

5.7 How to Write High-Scoring Answers in Honours Exams

A consistent pattern for high marks in microeconomics essays and problem sections:

For derivations

1. Define variables and functions.
2. Write the optimisation problem and constraints.
3. Compute FOCs.
4. State solution conditions (interior vs boundary).
5. Interpret economically.

For “discuss” questions

1. Identify the core claim (e.g., “monopoly produces less than competition”).
2. Support with mechanism (e.g., MR=MC).
3. Provide comparison and welfare implication.
4. Mention when results might fail (assumption limits).

For welfare/policy

1. Identify the market failure or inefficiency.
2. Map to the correct welfare criterion.
3. State the policy mechanism.
4. Discuss practical limitations (information, enforcement, measurement error).

5.8 South African Exam Readiness: Strategy Under Time Pressure

A practical Honours exam strategy adapted to South African university formats:

Before the exam

• Compile a one-page notation sheet: symbols and standard results (Marshallian vs Hicksian, MR formula, welfare conditions).
• Practise 2–3 full problems under timed conditions.

During the exam

1. Spend 5–10 minutes reading and breaking down the question:
   • What is being derived?
   • What is being compared?
   • Is a diagram required?
2. Start with the easiest part (e.g., compute MR, write FOCs).
3. Keep algebra visible and consistent.
4. If stuck, write what you know:
   • set up the correct equation even if you can’t solve fully.
   • define the equilibrium condition (e.g., (MR=MC)).

After the exam

• Review not just mistakes, but also why the mistake happened:
  • incorrect derivative,
  • wrong equilibrium concept,
  • missing interpretation.

5.9 Institution-Aligned Learning Priorities (Non-Negotiable Micro Topics)

Even across different South African institutions and programmes, Honours micro tends to converge on these core topics:

• Consumer optimisation and demand derivations.
• Producer optimisation, cost, marginal cost, and supply logic.
• Market structures: competition, monopoly, price discrimination.
• Oligopoly: Cournot/Bertrand basics, Nash equilibrium reasoning.
• Welfare: surplus, welfare theorems, externalities/public goods.
• Information asymmetry basics: adverse selection and moral hazard.
• Strategic tools: entry deterrence, auctions, incentive-compatible thinking.

In your revision schedule, allocate more time to topics that combine:

• derivations + interpretation,
• and where exam questions frequently ask for both.

Final Consolidation: What to Master for ECO09X7 Microeconomics (South Africa-Focused)

To be fully exam-ready for ECO09X7: Economics Honours: Microeconomics, ensure you can do the following without hesitation:

1. Derive demand and supply from optimisation and interpret FOCs.
2. Use MR, MC, elasticity, and equilibrium conditions correctly.
3. Compare perfect competition vs monopoly vs discrimination vs oligopoly and interpret welfare consequences.
4. Explain welfare theorems and identify when assumptions fail (market failure).
5. Apply game theory at the equilibrium level (Nash, best responses) and show incentive logic.
6. Answer exam prompts with clean structure, correct algebra, correct diagrams, and brief but rigorous interpretation.

This guide prioritises the exact mechanics Honours markers look for—mathematical coherence paired with economic meaning—so you can turn microeconomic theory into exam performance.