ECO231: Microeconomics 231 Course Notes

ECO231 (Microeconomics 231) is a second- or third-year microeconomics course that typically develops the tools needed to analyze how economic agents make choices under constraints, how markets reach (or fail to reach) equilibrium, and how policy and market frictions affect outcomes. These notes focus on the core microeconomic models—consumer and firm behavior, market structure, welfare analysis, and the economics of uncertainty and information—using explanations and worked examples that align well with South African university and TVET assessment styles. Throughout, emphasis is placed on exam-ready problem solving: diagram interpretation, algebraic setup, correct economic reasoning, and transparent calculations.

Section 1: Core Microeconomic Foundations (Preferences, Demand, and Utility Maximization)

1.1 The Microeconomic Problem: Choice Under Constraints

Microeconomics begins with a simple but powerful idea: individuals and firms make choices. In a typical ECO231 setting, choices are modeled as optimization problems.

Households (consumers)

A consumer chooses a bundle of goods ( (x, y) ) to maximize utility subject to a budget constraint:
[
\max_{x,y} ; U(x,y) \quad \text{s.t.} \quad p_x x + p_y y \le I
]

• (p_x, p_y): prices of goods (x) and (y)
• (I): income
• (U(x,y)): preference ranking (utility)

Firms (producers)

A firm chooses inputs (or outputs) to maximize profit or minimize cost.
Profit maximization:
[
\max_{q} ; \pi(q)=p q – C(q)
]
Or cost minimization:
[
\min_{x_1,x_2} ; w_1 x_1 + w_2 x_2 \quad \text{s.t.} \quad f(x_1,x_2)\ge q
]

Exam skill: When asked to interpret results, you must connect mathematics to economics: constraint binding vs non-binding, marginal conditions, and how changes in prices/income shift demand or factor demand.

1.2 Preferences, Utility, and Indifference Curves

Indifference curves

An indifference curve shows bundles giving equal utility. Standard properties:

• Downward sloping: more of one good requires less of another.
• Convex to the origin: diminishing marginal rate of substitution (MRS).
• No intersections: otherwise preferences are inconsistent.

Marginal Rate of Substitution (MRS)

[
\text{MRS}{xy} = -\frac{dy}{dx}\Bigg|{U=\bar U}
]
At the optimum (interior solution):
[
\text{MRS}_{xy} = \frac{p_x}{p_y}
]
This equation says: the consumer is willing to trade goods at a rate equal to the market trade-off.

Perfect substitutes and perfect complements (common exam cases)

1. Perfect substitutes: (U = ax + by). Indifference curves are linear.
   • Consumer chooses the higher “utility-per-rand” good.
2. Perfect complements: (U=\min{x/a,; y/b}). Indifference curves are L-shaped.
   • Consumption is at fixed proportions.

Example (worked intuition)
Suppose (U(x,y)=x+y) (perfect substitutes). If prices are (p_x=2), (p_y=3), consumer buys only (x) because per-rand (x) gives more utility (relative price lower).

1.3 Budget Line and Comparative Statics

Budget constraint:
[
p_x x + p_y y = I
]
Budget line intercepts:

• If (x=0), then (y = I/p_y)
• If (y=0), then (x = I/p_x)

Changes in income

• If (I) increases, the budget line shifts outward parallelly.
• If normal goods, demand increases with income.

Changes in price

• If (p_x) decreases, budget line pivots outward around the (y)-intercept.
• Demand effect is decomposed into:
  • Substitution effect: relative price changes alter relative attractiveness.
  • Income effect: purchasing power changes.

Key exam requirement: Use the right language. Even if a problem gives only numbers, your reasoning should identify what effect dominates.

1.4 Deriving Demand: Utility Maximization to Marshallian Demand

In many ECO231 assessments, you may need to derive Marshallian (uncompensated) demand.

Using Lagrangian method

Set:
[
\mathcal{L} = U(x,y) + \lambda (I – p_x x – p_y y)
]
First-order conditions:
[
\frac{\partial U}{\partial x} = \lambda p_x,\quad \frac{\partial U}{\partial y}=\lambda p_y,\quad I-p_x x-p_y y=0
]
Then solve for (x^(p_x,p_y,I)), (y^(p_x,p_y,I)).

Example: Cobb–Douglas preferences

Let:
[
U(x,y)=x^{\alpha} y^{1-\alpha}, \quad 0<\alpha<1
]
Then Marshallian demand:
[
x^* = \alpha \frac{I}{p_x}, \quad y^*=(1-\alpha)\frac{I}{p_y}
]
Interpretation:

• Demand shares expenditure: (p_x x^* = \alpha I)
• Income elasticity:
  • (x) is normal: elasticity (=1)
• Price elasticity:
  • Unit elastic: elasticity (=-1) (for Cobb–Douglas)

Exam-style numeric
Let (\alpha=0.4), income (I=R1200), (p_x=R5). Then:
[
x^* = 0.4\cdot \frac{1200}{5} = 0.4\cdot 240 = 96
]

1.5 Slutsky Decomposition and Elasticities

Substitution vs income effects

For a good (x), Slutsky decomposition:
[
\frac{\partial x}{\partial p_x} = \frac{\partial h_x(p_x,p_y,\bar u)}{\partial p_x} – x\frac{\partial x}{\partial I}
]
Where (h_x) is Hicks (compensated) demand.

• The compensated demand effect is typically negative (law of demand under standard assumptions).
• The total sign depends on the income effect: Giffen goods are rare but possible (when income effect is strongly positive and dominates).

Elasticities

Price elasticity of demand:
[
E_p = \frac{\partial x}{\partial p}\cdot \frac{p}{x}
]
Income elasticity:
[
E_I = \frac{\partial x}{\partial I}\cdot \frac{I}{x}
]

Practical exam tip: Many problems ask you to determine whether demand is elastic/inelastic using elasticity values:

• (|E_p|>1): elastic (big response)
• (|E_p|<1): inelastic (small response)
• (|E_p|=1): unit elastic

1.6 From Demand to Market Demand

Market demand aggregates across consumers. For linear demand functions:
[
q_i(p)=a_i – b_i p
]
Then market demand:
[
Q(p)=\sum_i q_i(p)=\left(\sum_i a_i\right) – \left(\sum_i b_i\right)p
]
Aggregating preserves linearity but shifts intercept and slope.

South African exam angle: Often questions connect market behavior to “number of households” or “students” (e.g., can be a proxy for consumers). The method is the same: sum individual quantities at the same price.

1.7 Supply Basics: Producers, Costs, and Short-Run vs Long-Run

Firms face technological and cost constraints. ECO231 commonly distinguishes:

• Short run: some inputs fixed (e.g., capital).
• Long run: all inputs variable.

A typical cost structure:

• Total cost (C(q))
• Marginal cost:
  [
  MC(q) = \frac{dC(q)}{dq}
  ]
• Average cost:
  [
  AC(q)=\frac{C(q)}{q}
  ]

Link to supply: In competitive markets, firms supply where (p \ge AVC) and (q) maximizes profit, often described by:
[
p = MC(q)
]
in the interior optimum.

Section 2: Market Structure and Firm Behavior (Competition, Monopoly, and Oligopoly)

2.1 Perfect Competition: Profit Maximization and Market Supply

Assumptions

Perfect competition includes:

• Many firms
• Identical products
• Firms are price takers (each takes market price (p) as given)
• Free entry/exit in long-run equilibrium

Profit:
[
\pi(q)=p q – C(q)
]
First-order condition (interior):
[
\frac{d\pi}{dq} = p – MC(q)=0 \quad \Rightarrow \quad p = MC(q)
]
Second-order condition requires (MC) increasing (typical in standard convex cost).

Shutdown condition

If prices are too low, the firm may produce zero in the short run. Shutdown when:
[
p < \min AVC
]
Because if (p<AVC), revenue cannot cover variable costs.

Numerical exam template
Suppose (C(q)=q^2+4q+10). Then:

• (MC = 2q+4)
• (AC = (q^2+4q+10)/q = q+4+10/q)
• (AVC) depends on fixed/variable structure. If fixed cost is (10), then (VC=q^2+4q), so:
  [
  AVC = q+4
  ]
  Shutdown if (p<\min(q+4)). Minimum occurs at (q\to 0) giving (AVC\to 4), so shutdown if (p<4).

If market price (p=10), solve (p=MC):
[
10=2q+4 \Rightarrow q=3
]
Profit:
[
\pi=10(3)-(9+12+10)=30-31=-1
]
Loss implies the firm might still produce in the short run if (p\ge AVC). Here (AVC=q+4=7), and (p=10>7), so producing yields a loss but avoids worse losses from shutting down (fixed costs still must be paid).

2.2 Long-Run Competitive Equilibrium

In the long run, entry and exit drive profits toward zero economic profit (not accounting profits). Under standard assumptions:

• If firms earn positive economic profit, entry increases supply, pushing down price.
• If firms earn negative economic profit, exit reduces supply, pushing up price.

At long-run equilibrium:
[
\pi = 0 \quad \Rightarrow \quad p = AC_{min}
]
And efficiency implies (p=MC) and (AC=MC) at the efficient scale.

Welfare relevance: Competitive markets achieve allocative efficiency (under complete markets, no externalities, etc.). This connects to later welfare analysis.

2.3 Monopoly: Market Power and Deadweight Loss

Monopoly demand and marginal revenue

A monopolist faces the market demand curve (Q(p)). If demand is downward sloping, marginal revenue (MR) lies below demand (p).

If inverse demand is:
[
p(Q)=a-bQ
]
Then total revenue (TR = pQ = aQ – bQ^2).
[
MR = \frac{dTR}{dQ} = a – 2bQ
]
Monopoly chooses (Q_m) where:
[
MR(Q_m)=MC(Q_m)
]
and then sets price (p_m=p(Q_m)).

Example

Let demand: (p = 20 – Q) (so (a=20, b=1)), and let (MC=4) constant.
Then:
[
MR = 20 – 2Q
]
Set (20 – 2Q = 4\Rightarrow 2Q=16\Rightarrow Q_m=8
]
Price:
[
p_m = 20-8=12
]

If competition with the same demand and constant MC implies:
[
p=MC=4 \Rightarrow Q_c=16
]
Compare welfare:

• Monopoly reduces quantity from 16 to 8.
• Consumers pay higher price.
• Deadweight loss arises from trades not made due to lower monopoly quantity.

2.4 Price Discrimination (An Important ECO231 Extension)

Price discrimination allows the monopolist to charge different prices to different consumers (or groups), increasing output and possibly revenue.

Three degrees:

1. First-degree (perfect): charges each consumer their maximum willingness to pay; outcome approximates efficiency.
2. Second-degree: nonlinear pricing/quantity discounts; consumers self-select based on usage.
3. Third-degree: separate groups with different elasticities; charge different per-group prices.

Third-degree discrimination logic

Let group 1 and 2 have demand:
[
p_1(Q_1),; p_2(Q_2)
]
Monopolist sets prices:
[
\frac{p_i – MC}{p_i} = \frac{1}{|\epsilon_i|}
]
Equivalently:
[
p_i = \frac{MC}{1 – \frac{1}{|\epsilon_i|}}
]
Thus:

• Lower elasticity group (more inelastic) faces higher price.
• Output tends to expand compared to single-price monopoly (but depends on elasticities and cost structure).

South Africa context connection: Many markets in practice resemble monopolistic competition or segmented markets due to regulation, transport costs, or segmented demand across regions (e.g., insurance, healthcare services, certain utilities). While ECO231 formalizes the model, interpreting it in local market realities helps in exam essays.

2.5 Oligopoly: Strategic Interaction and the Cournot Model

Oligopoly consists of a small number of firms where each firm’s output (or price) affects others.

Cournot competition (quantity setting)

Two firms choose quantities (q_1, q_2) simultaneously. Market price:
[
p = a – b(q_1+q_2)
]
Firm (i) profit:
[
\pi_i = p q_i – C_i(q_i)
]
Cournot equilibrium uses best responses.

Two-firm symmetric example
Let (C_i(q)=cq) constant marginal cost (c). If (a=60), (b=1), (c=10):
Price:
[
p=60-(q_1+q_2)
]
Profit:
[
\pi_1 = [60-(q_1+q_2)]q_1 – 10q_1
= (50 – q_1 – q_2)q_1
]
Best response:
[
\frac{\partial \pi_1}{\partial q_1} = 50 – 2q_1 – q_2 = 0
\Rightarrow q_1 = \frac{50 – q_2}{2}
]
Symmetry in equilibrium implies (q_1=q_2=q):
[
q = \frac{50 – q}{2}\Rightarrow 2q=50-q \Rightarrow 3q=50 \Rightarrow q=\frac{50}{3}
]
Total quantity (Q=2q=\frac{100}{3}). Price:
[
p=60-\frac{100}{3}=\frac{80}{3}\approx 26.67
]

Compare outcomes:

• Monopoly would have higher price and lower quantity.
• Competition would have lower price (closer to marginal cost) and higher quantity.

2.6 Oligopoly: Bertrand Competition and Price Wars

Bertrand model sets prices. With homogeneous goods and identical marginal cost, equilibrium often predicts price equals marginal cost (like perfect competition) due to undercutting.

Assume:

• Two firms
• Marginal cost (c)
• Demand chooses the lower price.

If both set prices simultaneously, any firm pricing above (c) can be undercut to gain market share. With identical costs, equilibrium tends to:
[
p=c
]
But this requires assumptions—when goods are differentiated or capacity constraints bind, prices may be above (c).

2.7 Game Theory Essentials for ECO231

Oligopoly analysis is a game. Key terms:

• Players: firms
• Strategies: quantities or prices
• Payoffs: profits
• Equilibrium: outcome stable to unilateral deviation

Nash equilibrium

A strategy profile where no player can improve payoff by changing their own strategy while others keep theirs fixed.

Exam technique: When given a payoff matrix:

1. Identify best responses row by row and column by column.
2. Nash equilibrium occurs at mutual best responses.
3. Use it to interpret whether outcomes resemble cooperation or conflict.

2.8 Market Power, Markups, and Lerner Index

For firms with market power, a relationship between price and marginal cost:
[
\frac{p-MC}{p} = \frac{1}{|\epsilon|}
]
where (|\epsilon|) is elasticity of demand faced by the firm.

Define Lerner Index:
[
L=\frac{p-MC}{p}
]
Higher elasticity implies smaller markup (more competitive environment).

Interpretation:

• If demand is very elastic, firms cannot raise prices much above marginal cost.
• If demand is inelastic, firms sustain higher markups.

Section 3: Welfare Analysis, Externalities, and Public Policy (Taxation, Subsidies, and Efficiency)

3.1 Consumer Surplus and Producer Surplus

Consumer surplus (CS)

Difference between willingness to pay and price:
[
CS = \int_{0}^{Q} [p(Q') – p] , dQ'
]
Graphically, CS is the area under the demand curve above the market price line.

Producer surplus (PS)

Difference between price received and marginal cost (or willingness to supply):
[
PS=\int_{0}^{Q} [p – s(Q')], dQ'
]

Welfare principle: In competitive equilibrium, total surplus (TS = CS + PS) is maximized among feasible allocations (with key assumptions).

3.2 Taxes: Incidence and Deadweight Loss

A tax introduces a wedge between consumer price (p_c) and producer price (p_p):

• Consumer pays (p_c = p_p + t) where (t) is the per-unit tax.

Tax incidence

Even if a tax is “levied on consumers” or “levied on producers,” the economic burden depends on elasticities:

• More inelastic side pays more.
• Less elastic demand or supply means that side cannot reduce quantity much.

Deadweight loss (DWL)

Occurs because tax prevents mutually beneficial trades. DWL increases with:

• Larger tax (t)
• More inelastic or elastic? The key is the reduction in trade; DWL depends on both elasticities. In general, DWL rises when tax reduces quantity more significantly.

Exam-ready approach:

1. Determine pre-tax equilibrium quantity (Q_0) and price.
2. Determine post-tax equilibrium quantity (Q_t).
3. Compute CS loss and PS loss.
4. Tax revenue equals (t \times Q_t).
5. DWL:
   [
   DWL = (CS\text{ loss}+PS\text{ loss}) – \text{tax revenue}
   ]
   If you use areas on a diagram, make sure those areas correspond.

3.3 Subsidies and Price Floors/ceilings

Subsidy:

• Reduces effective marginal cost or increases consumers’ effective income.
• In competitive markets, subsidies increase quantity beyond efficient level if not designed to address externalities.

Price ceilings (e.g., rent control):

• Create shortages when set below equilibrium.
• Can cause non-price rationing (queues, informal payments).

Price floors (e.g., minimum wage):

• If above equilibrium, create surpluses.
• For minimum wage, unemployment can result (especially in labor markets), but outcomes depend on labor demand/supply elasticities and institutional factors.

South African exam relevance: Labor market policy is frequently discussed in local economics syllabi. While ECO231 is micro-focused, exam essays sometimes require linking price control theory to real-world institutions like collective bargaining or regulatory enforcement. Keep it theoretical with correct incidence logic.

3.4 Externalities: Social vs Private Costs/Benefits

Externalities occur when individuals’ actions affect others without compensation.

Negative externalities

Example: pollution from production.

• Private marginal cost: (MPC)
• Marginal external cost: (MEC)
• Social marginal cost:
  [
  MSC = MPC + MEC
  ]
  Efficient output equates:
  [
  MB = MSC
  ]
  Market outcome equates:
  [
  MB = MPC
  ]
  Thus market overproduces relative to efficiency.

Positive externalities

Example: education that benefits society.

• Private marginal benefit: (MPB)
• Marginal external benefit: (MEB)
• Social marginal benefit:
  [
  MSB = MPB + MEB
  ]
  Efficient output where (MSB = MC) typically exceeds market output where (MPB = MC).

3.5 Policy Tools for Externalities

Pigouvian taxes

Impose a per-unit tax equal to marginal external cost at the efficient level:
[
t = MEC(Q^)
]
This shifts private marginal cost upward to match social marginal cost, reducing output to (Q^).

Subsidies for positive externalities

Subsidize per unit equal to marginal external benefit:
[
s = MEB(Q^*)
]
This increases output toward the efficient level.

Exam caution: In problems, you might be given demand/supply curves and external cost functions. Ensure you construct social marginal cost and social marginal benefit correctly before solving the efficient equilibrium.

3.6 Tradable permits (cap-and-trade)

An alternative to taxes is cap-and-trade, where:

• Government sets a quantity cap on pollution.
• Firms must hold permits for each unit emitted.
• Market determines permit price.

In welfare terms, if the cap corresponds to the efficient level of externalities, outcomes can be efficient similarly to Pigouvian taxes, but tax and cap differ in:

• Revenue vs market price stability
• Uncertainty management (if marginal damage is uncertain, firms might prefer one instrument)

Exam angle: If asked “compare,” highlight efficiency conditions and practical pros/cons: enforcement costs, information requirements, volatility.

3.7 Coase Theorem and Property Rights

Coase theorem says that if:

• Property rights are well-defined
• Transaction costs are low
• Parties can bargain
  Then the market can reach an efficient outcome regardless of initial allocation of rights.

Externalities:

• Negative: polluter vs victim bargaining
• Positive: benefactor vs non-beneficiary bargaining

Counterpoint exam essays often mention:

• Transaction costs exist (real-world bargaining is costly)
• Information asymmetry and legal barriers can prevent bargaining
• Bargaining may not be feasible when there are many affected parties

3.8 Information Failures and Market Outcomes

Information is critical in markets. When buyers cannot observe quality or sellers cannot commit credibly, markets can fail.

Key concepts:

• Asymmetric information
• Moral hazard (hidden actions after contract)
• Adverse selection (hidden types before contract)

Adverse selection example

If higher-quality sellers are less likely to participate at certain contract terms, average quality declines.

Classic model intuition:

• Contracts must be designed so that participation constraints for good types hold.
• In insurance, adverse selection can lead to underinsurance or market breakdown.

Moral hazard example

After insurance is purchased, insured may take more risk since costs are partially borne by insurer.

Policy tools:

• deductibles, co-payments (reduce moral hazard)
• monitoring and incentives (align private actions with social outcomes)

Section 4: Risk, Uncertainty, and Decision-Making (Expected Utility, Insurance, and Behavioral Traps)

4.1 Risk vs Uncertainty

• Risk: probabilities are known (or assumed known). Expected value and variance can be computed.
• Uncertainty: probabilities unknown or not well-defined.

Many ECO231 models emphasize risk and decision under it.

4.2 Expected Value and Variance

For a lottery with outcomes (x_1, x_2, …) and probabilities (p_1, p_2, …):
[
E[X] = \sum_i p_i x_i
]
Variance:
[
Var(X)=E[(X-E[X])^2]
]
Risk-averse individuals do not choose solely based on expected value; they consider utility curvature and the distribution of outcomes.

Exam-ready note: If a question asks “why might risk-averse agents prefer diversification,” connect to variance reduction and concavity of utility.

4.3 Expected Utility Theory

Utility function (u(w)), where (w) is wealth.

Choose option maximizing:
[
E[u(w)] = \sum_i p_i u(w_i)
]
Risk aversion corresponds to concave utility: (u''(w)<0).

Types of risk preferences

• Risk-neutral: (u(w)) linear ⇒ chooses based on (E[X]).
• Risk-averse: concave (u) ⇒ prefers certain equivalent with same expected utility.
• Risk-seeking: convex (u).

4.4 Insurance Demand Under Risk Aversion

Consider wealth (w), probability of loss (p), loss size (L). If uninsured:

• Wealth in good state: (w)
• Wealth in bad state: (w-L)

If insured with coverage (y) (pays (y) in bad state):

• Wealth good: (w – \text{premium})
• Wealth bad: (w-L + y – \text{premium})

For an insurer, premium depends on expected payout plus loading cost or admin costs. In many exam problems, premium equals actuarially fair price (pL) if no loading.

Actuarially fair insurance

If premium equals expected loss:
[
\text{premium} = pL
]
Risk-averse agents may fully insure (choose (y=L)) if insurers can provide it and contracts are enforceable.

Practical translation: People buy insurance because it converts uncertain outcomes into a more certain wealth path, raising expected utility.

4.5 Moral Hazard and Deductibles

With moral hazard, the insured changes behavior after purchase, raising probability or size of loss. Suppose insured can take action (a) affecting loss probability; action is unobservable.

If insurance fully covers losses, incentives for precaution are weak. Deductibles or co-payments restore incentives: insured bears some marginal cost, so precaution becomes privately beneficial.

Exam essay prompt pattern:

• Define moral hazard
• Explain why full insurance can worsen outcomes
• Show how deductibles align incentives
• Connect to empirical and regulatory tools: risk-based premiums, monitoring, verification of claims

4.6 Diversification and Portfolio Choice (Exam Option)

In a simple setting, wealth outcomes depend on investment in risky assets. A classic result:

• With risk-averse utility, diversification can increase expected utility by lowering variance.
• Portfolio selection balances expected return against risk.

Even when probabilities are known, the key is the curvature of utility and how combining assets affects distribution.

4.7 Intertemporal Choice and Discounting (Where ECO231 Often Extends)

Intertemporal choice models include:

• Present value
• Discount factor (\beta)
• Utility (u(c_t)) over time

Typical setup:
[
\max \sum_{t=0}^{T} \beta^t u(c_t)
]
Budget constraint over time includes income and interest rates.

Exam technique: Always interpret (\beta). A higher (\beta) indicates stronger preference for future consumption (less impatience). If interest rates change, compare how consumption smoothing changes.

Section 5: Applied Microeconomics for South African Contexts (Competition Policy, Labor Markets, and Exam Problem Solving)

5.1 Competition, Market Power, and Policy in South Africa

South African economic policy discussions often emphasize:

• Protecting consumers from excessive pricing and collusion
• Encouraging entry and innovation
• Addressing market power in sectors with barriers or natural monopoly characteristics

In ECO231, competition policy is grounded in micro theory:

• Antitrust seeks to reduce harm from monopoly and collusion
• Regulation may set prices when market forces fail (e.g., utilities)

Natural monopoly and regulation

If marginal cost rises only weakly but fixed costs are huge, average cost can fall over relevant output ranges. In that case, competitive entry is inefficient, leading to natural monopoly.

Regulation strategies:

• Price cap to mimic marginal cost outcomes
• Rate-of-return regulation (with incentives issues)
• Efficiency-based benchmarks

Exam connection: When asked to “evaluate regulation,” compare efficiency, incentives, information requirements, and risk of regulatory capture.

5.2 Labor Markets: Minimum Wages, Search, and Incentives

Labor markets can be modeled like other markets but with institutional specifics:

• Wages are negotiated and regulated
• Worker heterogeneity
• Unemployment and search frictions

Minimum wage effects

• If minimum wage is set above equilibrium, standard theory predicts unemployment.
• However, real-world impacts depend on elasticity, compliance, and the role of unemployment in collective bargaining.

Exam nuance: For essays, include that minimum wages can also increase productivity, reduce turnover, and improve bargaining outcomes—so the net impact on employment is an empirical question even if the model predicts a tradeoff.

5.3 Monopsony in Labor Markets

In monopsony, one or few employers set wages because workers face limited outside options. Profit-maximizing monopsonist hires where:

• wage equals marginal cost of labor? In monopsony:
  [
  w = MPL \quad \text{but marginal cost of labor } MC_L > w
  ]
  The firm hires where (MRP) equals (MC_L), leading to lower employment and wages compared to competition.

Exam advantage: If a question provides data suggesting wage suppression without comparable supply shifts, monopsony can be an interpretive model.

5.4 Problem-Solving Playbook (What Examiners Expect)

This section consolidates exam strategies for ECO231-type questions. The goal is to help you produce correct and clearly argued solutions under time pressure.

5.4.1 Diagrams: what to label and how to read them

When using supply-demand diagrams:

• Identify equilibrium (Q^) and (p^).
• For taxes, show wedge (t) between consumer and producer prices.
• For monopolies, show (MR), (MC), and demand to derive price.
• For externalities, show (MPC) and (MSC) (negative) or (MPB) and (MSB) (positive).

Common marks lost:

• Mixing up (MC) and (AC)
• Using demand slope to state (MR) incorrectly in nonlinear demand settings
• Forgetting to compute equilibrium quantity from the intersection of correct curves

5.4.2 Algebra: set up the right equations first

A consistent exam workflow:

1. Write the objective (profit max, utility max, maximize surplus, etc.).
2. Write the constraints (budget, quantity constraint, capacity, etc.).
3. Compute marginal conditions (FOC/Marginal equality).
4. Solve for quantity and price (if monopoly) or quantity only (if supply).
5. Check feasibility and boundaries (shutdown, corner solutions).
6. Compute welfare (CS, PS, tax revenue, DWL) if asked.

5.4.3 Elasticities: connect math to interpretation

If you’re given demand:
[
Q = A p^{-k}
]
Then elasticity:
[
E_p = -k
]
This helps in incidence:

• If (E_d) is highly elastic, consumers respond strongly to price changes.
• If (E_s) is inelastic, suppliers absorb more of the tax burden.

Practice numeric
If demand is elastic relative to supply, after a tax the consumer price increases less and producer receives less more? The rigorous rule:

• Burden heavier on the more inelastic side.

5.5 Worked Integrated Case Study (Monopoly with Externality and Policy Response)

Consider a market with inverse demand:
[
p(Q)=30 – Q
]
and marginal cost:
[
MC(Q)=10
]
Additionally, production creates a negative externality with marginal external cost:
[
MEC(Q)=0.5Q
]
So social marginal cost:
[
MSC(Q)=MC(Q)+MEC(Q)=10+0.5Q
]

Step 1: Monopoly outcome (private)

First compute monopolist MR:
[
TR=pQ=(30-Q)Q=30Q-Q^2
\Rightarrow MR=30-2Q
]
Set MR = MC:
[
30-2Q=10\Rightarrow 2Q=20\Rightarrow Q_M=10
]
Price:
[
p_M=30-10=20
]

Step 2: Socially efficient outcome

Set MSB (from demand) equals MSC. Since demand is willingness to pay, marginal benefit equals price on demand:
[
MB(Q)=p(Q)=30-Q
]
Efficient (Q^) solves:
[
30-Q = 10+0.5Q
\Rightarrow 30-10 = Q+0.5Q
\Rightarrow 20 = 1.5Q
\Rightarrow Q^=\frac{40}{3}\approx 13.33
]

Interpretation: With a negative externality, the social optimum is usually lower than competitive output, but comparing monopoly vs social efficiency is subtle because monopoly already restricts output. Here social optimum is actually higher than monopoly because monopoly restricts output too much relative to social efficiency in this parameterization—this highlights why exam questions often require actual calculations rather than intuition alone.

Step 3: Policy via Pigouvian tax (to reach efficient quantity)

Pigouvian tax per unit at (Q^):
[
t = MEC(Q^)=0.5Q^* = 0.5\cdot \frac{40}{3}=\frac{20}{3}\approx 6.67
]
If a tax is imposed, the monopolist’s effective marginal cost becomes:
[
MC_t(Q)=MC(Q)+t=10+\frac{20}{3}
]
The monopolist then chooses (Q) where (MR=MC_t).
But note: in real regulation, implementing a per-unit tax to achieve a precise (Q^*) under monopoly requires the regulator to account for how monopoly MR/Mc intersections shift—still, the tax equal to marginal external cost at the optimum is the standard Pigouvian logic.

Exam insight: When asked “find tax,” always compute it from MEC at (Q^*), even if further algebra is needed for confirmatory steps.

5.6 Exam-Writing for Theory Questions (How to Earn Method Marks)

Many ECO231 questions reward structure, not only final numbers. A strong answer includes:

1. Definition: e.g., “Consumer surplus is the area under demand above price.”
2. Model statement: e.g., “Monopoly sets (MR=MC).”
3. Mechanism: e.g., “Because demand is downward sloping, MR lies below price.”
4. Implication: e.g., “Thus monopoly restricts quantity, leading to deadweight loss.”
5. Graph or algebra: show the relationship.
6. Conclusion: summarize with direction of change.

South African marking style often emphasizes:

• Clear diagram interpretation and labeling
• Correct use of economic terms
• Consistency of units and reasoning

5.7 Mini-Question Bank (Practice Scenarios)

These are not official exam questions, but they mirror common patterns.

5.7.1 Competitive firm with shutdown

Given (C(q)=50+q^2). Then:

• (MC=2q)
• Variable cost (VC=q^2)
• (AVC=q)

If (p=10), find (q).
[
p=MC \Rightarrow 10=2q \Rightarrow q=5
]
Check shutdown: (p\ge \min AVC). As (q\to 0), (AVC\to 0), so produce.

Compute profit:
[
\pi=10(5)-\left(50+25\right)=50-75=-25
]
Loss in short run if still covers variable costs:

• (AVC=5), (p=10>5) so it produces.

5.7.2 Monopoly with constant marginal cost

Demand: (p=60-Q), (MC=20).
MR: (60-2Q). Set MR=MC:
[
60-2Q=20 \Rightarrow Q=20
]
Price:
[
p=60-20=40
]

5.7.3 Tax incidence logic

If demand is more inelastic than supply, then the burden shifts to consumers or producers? More inelastic side pays more tax burden. You can justify using the fact that inelastic side cannot reduce quantity/adjust behavior much.

5.8 Synthesis: How All Topics Fit Together

ECO231 is not a list of isolated models. The course tends to test whether you can connect:

• Optimization (utility and profit maximization) explains behavior.
• Behavior determines market outcomes (equilibrium price/quantity).
• Outcomes determine welfare (surplus and deadweight loss).
• Market imperfections like externalities and information asymmetries change the efficiency of outcomes.
• Policy tools (taxes, subsidies, permits, regulation) aim to correct inefficiencies but can introduce their own distortions.

In exams, the hardest problems often combine these components. For example:

• A monopoly faces externalities and the question asks for Pigouvian policy.
• A tax is applied and you must use elasticities to compute incidence.
• A market with asymmetric information requires incentive design (deductibles, signaling).

If you can carry these connections consistently—definitions first, model correct, algebra careful, and interpretation precise—you are positioned to score highly.

End of ECO231 Course Notes