2ECO201: Microeconomics 2 Course Notes

Microeconomics 2 typically extends the core consumer and producer theory from Microeconomics 1 into market structure, welfare analysis, factor markets, and advanced choice under constraints. In most South African economics curricula, the course is where students begin to connect micro theory to real policy debates—taxation, competition, minimum wages, and social welfare—using formal models. These notes are written to be exam-oriented, combining definitions, theorems, derivations you may be expected to sketch, and worked numerical examples that resemble the style of questions found across South African universities and TVET economics modules.

Stellenbosch University ECO201/2ECO201-Style Microeconomics 2: Market Structures, Welfare, and Game Theory Foundations

1. The Logic of Market Structure in Microeconomics 2

In Microeconomics 2, “market structure” is treated as a set of institutional conditions that shape firms’ incentives and outcomes. The most common structures you’ll see are:

• Perfect competition
• Monopolistic competition
• Oligopoly (including models like Cournot and Bertrand)
• Monopoly (often separated explicitly)

Even when the textbook focus differs slightly between institutions, exam questions usually require you to answer three interlinked prompts:

1. What is the firm’s objective and constraint?
   Example: monopoly maximizes profit subject to demand conditions; an oligopolist faces strategic interdependence.
2. How do strategic or informational assumptions affect pricing/production?
   Example: under oligopoly, rival reaction functions change your optimal quantities.
3. What is the welfare implication?
   Example: monopoly tends to reduce output and raise price compared with the competitive benchmark, generating deadweight loss.

2. Competitive Benchmark and Its Role in Exams

In perfect competition, the standard results used as benchmarks are:

• Price equals marginal cost: (P = MC)
• Profit maximization with (MR = P) and (MR = MC)
• Allocative efficiency where marginal benefit equals marginal cost

For exam purposes, you should recognize the idea: competitive outcomes are often treated as first-best for efficiency (though not necessarily for equity). Many questions ask you to compare monopoly or oligopoly outcomes to this benchmark using consumer surplus, producer surplus, and deadweight loss.

Worked Welfare Example (Monopoly vs. Competition)

Suppose the market demand is linear:
[
Q = 10 – P
]
So inverse demand is:
[
P = 10 – Q
]
Assume constant marginal cost (MC = 2) and no fixed costs.

Competitive equilibrium sets (P = MC):
[
P = 2 \Rightarrow 2 = 10 – Q \Rightarrow Q = 8
]
Then price is (P_C = 2), quantity (Q_C = 8).

Monopoly chooses output where marginal revenue equals marginal cost.
Total revenue:
[
TR = P \cdot Q = (10 – Q)Q = 10Q – Q^2
]
Marginal revenue:
[
MR = \frac{dTR}{dQ} = 10 – 2Q
]
Set (MR = MC):
[
10 – 2Q = 2 \Rightarrow 2Q = 8 \Rightarrow Q_M = 4
]
Then price:
[
P_M = 10 – 4 = 6
]

Now compute welfare measures using standard shapes (triangles/trapezoids):

• Consumer surplus (CS) under monopoly:
  CS is area between demand price and market price from 0 to (Q_M).
  Demand intercept is when (Q=0 \Rightarrow P=10).
  Thus:
  [
  CS_M = \frac{1}{2}(10 – 6)\cdot 4 = \frac{1}{2}\cdot 4\cdot 4 = 8
  ]

• Consumer surplus under competition:
  [
  CS_C = \frac{1}{2}(10 – 2)\cdot 8 = \frac{1}{2}\cdot 8\cdot 8 = 32
  ]

• Producer surplus (PS) with constant MC and zero fixed cost becomes area under price above MC up to quantity.
  Under monopoly:
  [
  PS_M = \frac{1}{2}(6 – 2)\cdot 4 = \frac{1}{2}\cdot 4\cdot 4 = 8
  ]
  Under competition:
  [
  PS_C = \frac{1}{2}(2 – 2)\cdot 8 = 0
  ]
  (Since price equals marginal cost and with no fixed cost, economic profit is zero; PS equals 0 in this simplified model.)

• Deadweight loss (DWL):
  [
  DWL = (CS_C + PS_C) – (CS_M + PS_M) = (32 + 0) – (8 + 8) = 16
  ]

Exam interpretation: The key thing is not the exact number (which depends on assumed parameters), but the method: compute outcomes, then compare areas.

3. Monopoly: Demand, MR, Elasticity, and Pricing Power

Monopoly theory is heavily used in Microeconomics 2 because it connects market power to welfare and policy.

3.1 Profit Maximization and MR vs. Demand

A monopoly faces the downward-sloping market demand curve. A central exam result is:

• Monopoly produces where (MR = MC)

Because demand is downward sloping, MR lies below demand. Students are often asked to “explain why MR < P for monopoly” and to interpret the implication for output choice.

3.2 The Lerner Index and Elasticity

A standard formula:
[
\frac{P – MC}{P} = -\frac{1}{\varepsilon}
]
where (\varepsilon) is the (absolute value of) price elasticity of demand.

Implications that exam questions target:

• If demand is more elastic (larger (|\varepsilon|)), the monopoly markup ((P-MC)/P) shrinks.
• If demand is less elastic, markup increases.

3.3 Example: Markup Under Different Elasticities

Let (MC = 2) and (P) be monopoly price. Suppose elasticity is (|\varepsilon| = 4):
[
\frac{P – 2}{P} = \frac{1}{4}
\Rightarrow P – 2 = \frac{P}{4}
\Rightarrow \frac{3P}{4} = 2
\Rightarrow P = \frac{8}{3} \approx 2.67
]
If instead demand is less elastic (|\varepsilon| = 1.5):
[
\frac{P – 2}{P} = \frac{1}{1.5} = \frac{2}{3}
\Rightarrow P – 2 = \frac{2P}{3}
\Rightarrow \frac{P}{3} = 2
\Rightarrow P = 6
]
Interpretation: When consumers have fewer alternatives (lower elasticity), the monopoly charges much higher prices.

4. Oligopoly: Strategic Interdependence and Core Models

In Microeconomics 2, oligopoly typically appears in two major forms:

• Cournot model (quantity competition)
• Bertrand model (price competition)

Sometimes variants are included: Stackelberg (leader-follower), or simplified game-theoretic framing.

4.1 Cournot Duopoly (Quantity Competition)

Assume two firms choose quantities (q_1, q_2). Market price depends on total output:
[
P = a – (q_1 + q_2)
]
Profit for firm 1:
[
\pi_1 = (P – c)q_1 = (a – q_1 – q_2 – c)q_1
]
Maximize w.r.t. (q_1):
[
\pi_1 = (a – c – q_1 – q_2)q_1 = (a-c-q_2)q_1 – q_1^2
]
FOC:
[
\frac{d\pi_1}{dq_1} = (a-c-q_2) – 2q_1 = 0
\Rightarrow q_1 = \frac{a – c – q_2}{2}
]
This is firm 1’s reaction function. In symmetric equilibrium (q_1 = q_2 = q):
[
q = \frac{a – c – q}{2}
\Rightarrow 2q = a – c – q
\Rightarrow 3q = a – c
\Rightarrow q = \frac{a – c}{3}
]
Total quantity:
[
Q = q_1 + q_2 = \frac{2(a-c)}{3}
]
Price:
[
P = a – Q = a – \frac{2(a-c)}{3} = \frac{a + 2c}{3}
]

Exam-ready comparison: Monopoly quantity is usually (\frac{a-c}{2}), while Cournot duopoly yields more output than monopoly and less than perfect competition.

4.2 Bertrand Duopoly (Price Competition)

In the simplest Bertrand model with homogeneous products and identical constant marginal cost (c), firms choose prices (p_1, p_2).

• If (p_1 < p_2), firm 1 captures all demand.
• If (p_2 < p_1), firm 2 captures all demand.
• If (p_1 = p_2), firms split demand.

With no capacity constraints and identical costs, the equilibrium is:
[
p_1 = p_2 = c
]
This yields the competitive outcome. The “Bertrand paradox” is a frequent exam topic: price competition among two firms can drive prices to marginal cost even with only two firms, provided capacity is unlimited and products are identical.

5. Game Theory Basics: Dominance, Nash Equilibrium, and Strategic Reasoning

Oligopoly is often framed as a game:

• Players = firms
• Strategies = quantities (Cournot) or prices (Bertrand)
• Payoffs = profits
• Equilibrium = Nash equilibrium (no profitable unilateral deviation)

5.1 Dominant Strategies and Rationalizability

A dominant strategy is best regardless of the opponent’s action. If one strategy dominates all others for a player, rational players choose it.

5.2 Nash Equilibrium in a Simple Pricing Game

Consider a simplified advertising game:

• If both firms advertise, each earns profit 50.
• If one advertises and the other does not, the advertiser earns 30 while the non-advertiser earns 60.
• If neither advertises, each earns 40.

Let strategies be Advertise (A) and Not Advertise (N). Payoffs (Firm 1, Firm 2):

	Firm 2: A	Firm 2: N
Firm 1: A	(50, 50)	(30, 60)
Firm 1: N	(60, 30)	(40, 40)

Find best responses:

• If Firm 2 advertises (A), Firm 1 prefers N? Payoffs: A gives 50, N gives 60 ⇒ N is best.
• If Firm 2 does not advertise (N), Firm 1 prefers A? Payoffs: A gives 30, N gives 40 ⇒ N is best.

So Firm 1’s best response is always N. Similarly Firm 2’s best response is always N. Therefore the unique Nash equilibrium is (N, N) with payoffs (40, 40).

Exam interpretation: even if advertising might seem beneficial when the other advertises, the strategic logic can lead to under-provision of advertising in equilibrium.

6. Market Power, Policy, and Welfare: Taxes, Subsidies, and Deadweight Loss

A major Microeconomics 2 theme is welfare analysis under interventions.

6.1 Standard Effects of Taxes

A per-unit tax (t) shifts up marginal cost by (t). In competitive markets, the incidence depends on elasticities:

• More inelastic side bears more of tax burden.
• More elastic side bears less.

Even if your course focuses heavily on welfare, the incidence logic is typically expected in exams.

6.2 Transfer vs. Efficiency Loss

Students sometimes confuse:

• Transfers: redistribution between consumers and producers
• Efficiency loss (deadweight loss): reduction in total surplus due to distortions

In monopoly, taxes can sometimes produce complex effects (e.g., shifting demand or markup behavior). But most exams simplify by asking you to show the triangle of DWL relative to the pre-tax benchmark.

6.3 Realistic South African Context Examples

Exam questions often invite applied reasoning. For South Africa, think of markets where firms have pricing power or high barriers:

• Telecommunications: spectrum and regulatory licensing can create barriers that yield market power.
• Energy distribution: infrastructure constraints may prevent perfect competition.
• Health services: professional licensing and information asymmetry influence competitive outcomes.

While your exam might not require specific South African statistics, the reasoning framework remains: identify elasticity, barriers, and substitutability; then use welfare logic.

University of Johannesburg / UJ-Style Microeconomics 2: Consumer Demand, Risk, and Advanced Welfare/Compensating Variation

1. Why Consumer Choice Gets Harder in Microeconomics 2

While Microeconomics 1 typically covers basic budget constraints and marginal utility, Microeconomics 2 deepens topics such as:

• Preferences and utility representations
• Indirect utility and expenditure functions
• Compensating variation and equivalent variation (welfare metrics)
• Sometimes choice under uncertainty or intertemporal consumption

Even when exact coverage differs by institution, exams often test welfare concepts alongside consumer theory.

2. Utility, Indifference Curves, and Demand Derivation

2.1 Assumptions About Preferences

You may be asked about:

• Completeness: any two bundles can be compared
• Transitivity: if A ≽ B and B ≽ C, then A ≽ C
• Local nonsatiation: more is always better in some direction

These assumptions ensure a well-defined maximization problem and facilitate the existence of demand functions.

2.2 Budget Constraint and Lagrangian Optimization

For goods (x) and (y):
[
\max_{x,y} ; u(x,y) \quad \text{s.t.} \quad p_x x + p_y y = m
]
The Lagrangian:
[
\mathcal{L} = u(x,y) + \lambda(m – p_x x – p_y y)
]
FOCs yield:
[
\frac{\partial u}{\partial x} = \lambda p_x, \quad \frac{\partial u}{\partial y} = \lambda p_y
]
Therefore:
[
\frac{MU_x}{MU_y} = \frac{p_x}{p_y}
]
This is the core marginal rate of substitution condition.

3. Income and Substitution Effects

A classic exam structure is: given changes in price, describe how quantity demanded changes via:

• Substitution effect (relative price changes; consumer substitutes away from relatively more expensive good)
• Income effect (real purchasing power changes)

For normal goods, income effect reinforces substitution effect, so demand falls when price rises. For inferior goods, income effect can offset or reverse substitution effect leading to unusual patterns.

Example: Inferior Good and Giffen Behavior (Conceptual)

• Inferior good: income effect works in opposite direction to substitution effect.
• For a Giffen good, income effect dominates substitution effect, producing upward sloping demand.

Exams often ask: “Is Giffen behavior possible? Under what conditions?” The answer: needs a strongly inferior good and the good must take a large share of the consumer’s budget; also substitution must be weak relative to income effect.

4. Indirect Utility, Expenditure Function, and Welfare Measurement

Welfare measurement is where Microeconomics 2 becomes especially exam-critical.

4.1 Indirect Utility Function

Indirect utility expresses maximum utility achievable as a function of prices and income:
[
v(p_x, p_y, m) = \max_{x,y} u(x,y) ; \text{subject to} ; p_x x + p_y y = m
]

4.2 Expenditure Function

Expenditure function (e(p_x, p_y, \bar{u})) is the minimum income required to achieve utility (\bar{u}) at given prices:
[
e(p_x, p_y, \bar{u}) = \min_{x,y} p_x x + p_y y \quad \text{s.t.} ; u(x,y) \ge \bar{u}
]

These functions allow welfare comparisons without requiring you to compute exact consumption bundles for every scenario—though exams sometimes still require explicit numbers.

5. Compensating Variation (CV) and Equivalent Variation (EV)

Suppose prices change from ((p^0)) to ((p^1)). Let initial income be (m). The consumer attains initial utility (u^0) under prices (p^0), income (m), and final utility (u^1) under prices (p^1), income (m).

5.1 Compensating Variation (CV)

CV asks: how much income would we need to take away (or give) at the new prices to keep utility at the old level (u^0)?

Formally:

• If prices rise and utility falls, CV is the amount of money taken at new prices to reduce utility back to old? In standard treatments:
  [
  CV = e(p^1, u^0) – m
  ]
  Interpretation: money required at new prices to reach old utility.

5.2 Equivalent Variation (EV)

EV asks: how much income would we change at the old prices to reach the new utility level (u^1)?

Formally:
[
EV = m – e(p^0, u^1)
]

5.3 Worked Numerical Welfare Example

Assume we can represent expenditure levels directly. Suppose:

• Initial prices (p^0) and utility level (u^0).
  Expenditure to achieve (u^0) at new prices (p^1) is (e(p^1, u^0) = 120).
• Consumer’s actual income is (m = 100).

Then:
[
CV = 120 – 100 = 20
]
So the consumer requires 20 units of income at new prices to be as well off as before.

If instead you had (e(p^0, u^1) = 90), then:
[
EV = 100 – 90 = 10
]
So at old prices, the consumer could be “given” only 10 less income to end up at new utility.

Exam note: CV and EV differ when the price change is not infinitesimal. For small changes, they approximately coincide.

6. Welfare and Policy: Consumer Surplus Is Not Always “Utility Welfare”

A common exam trap: assuming consumer surplus equals welfare change in general. The correct principle:

• Consumer surplus may approximate welfare change for certain cases (e.g., small price changes, quasi-linear utility with appropriate assumptions).
• True welfare measurement uses utility-based concepts like CV/EV.

So if an exam question asks: “Is consumer surplus equal to compensating variation?” the correct answer is: not generally, only under special functional form/conditions.

7. Applied Microeconomics: Policy Examples Relevant to South Africa

7.1 VAT Changes and Welfare

South Africa’s VAT system affects prices broadly. Suppose a VAT increase raises consumer prices for many goods. Even if the exam is theoretical, you can anchor reasoning:

• Price increases reduce real income.
• Substitution affects relative demand.
• Welfare loss depends on how sensitive demand is (elasticities) and how much of income affected goods consume.

If asked to “discuss who bears the burden,” refer to incidence: households with more inelastic consumption baskets face larger relative burden.

7.2 Food and Transport Subsidies

If policy subsidizes a staple food or transport, then:

• Consumers receive a price decrease for essential goods.
• Welfare gain depends on demand elasticity: more elastic goods yield larger quantity change, but welfare computations depend on substitution too.
• Distributional impact: lower-income households allocate a larger share to essentials, so they gain more in absolute and sometimes relative terms.

University of Cape Town (UCT) / UCT-Style Microeconomics 2: Factor Markets, Labour Supply, Human Capital, and General Equilibrium Intuition

1. From Goods Markets to Factor Markets

Microeconomics 2 often expands the analysis beyond consumer and product markets to factor markets:

• labour demand and supply
• capital
• land
• derived demand

The central idea: firms demand labour because labour helps them produce goods that consumers demand. Thus labour demand is derived demand from product markets.

2. Labour Demand: Marginal Product and Value of Marginal Product

Assume a production function (Q = F(L)) with labour input (L) and (for simplicity) fixed capital and technology. Profit for a competitive firm is:
[
\pi = P \cdot F(L) – wL
]
where (w) is wage. First-order condition:
[
\frac{d\pi}{dL} = P \cdot F'(L) – w = 0
]
So:
[
w = P \cdot MPL
]
The wage equals the value of the marginal product of labour.

If the labour market is competitive and firms are price takers, this relationship becomes the basis for labour demand curves.

3. Shifts in Labour Demand: Output Price, Productivity, and Technology

Labour demand depends on:

1. Product price (P): higher (P) raises value of marginal product at each (L), shifting labour demand right.
2. Productivity: improvements in (F(L)) (e.g., better training, technology) raise MPL, shifting demand right.
3. Marginal revenue product: if output market is not perfectly competitive, MR replaces P.

Example: Technology Improvement

Suppose before a training program, (MPL = 3). If (P = 5), then value of MPL is (15). If (w=12), firms will hire until value equals wage. After technology improvement, say (MPL) becomes (4) at relevant labour levels. Then value is (20), so the firm will hire more at the same wage.

4. Labour Supply: Income-Leisure Trade-Off

Labour supply is often modeled as choice between leisure (t) and consumption (c) with time endowment (T). If wage is (w), consumption is:
[
c = w(T – t)
]
where (T-t) is hours worked.

Consumer maximization:
[
\max_{t} u(c,t)
]
with (c = w(T-t)).

FOC yields:
[
\frac{MU_t}{MU_c} = w
]
Interpretation: the marginal rate of substitution between leisure and consumption equals wage.

Substitution vs. Income Effects for Labour

When wages rise:

• Substitution effect: leisure becomes more expensive (opportunity cost rises), so people work more.
• Income effect: higher wage increases income; leisure may be “purchased,” so people work less.

Thus labour supply can be upward or downward depending on which effect dominates.

5. Wage Determination: Competitive Equilibrium in Labour Markets

Set labour supply equals labour demand:
[
L^s(w) = L^d(w)
]
Equilibrium wage clears the market.

In many exam questions, you may need to analyze consequences of:

• minimum wages
• labour taxes
• union bargaining
• efficiency wages

Minimum Wage (Conceptual with Welfare)

If minimum wage is set above equilibrium:

• quantity of labour demanded falls
• quantity supplied rises
• unemployment can occur (excess supply of labour)

But exam answers should mention that actual outcomes depend on elasticity and compliance.

6. Efficiency Wages and Persistent Unemployment

Efficiency wage models argue that firms pay above-market wages to improve worker productivity or reduce shirking and turnover.

A stylized version:

• Higher wages reduce shirking
• Higher morale or retention reduces monitoring costs
• Thus firms have incentives to maintain wages above the competitive level

Exams sometimes ask: “Why might unemployment persist even when wages are flexible?” Efficiency wages provide a microfoundation.

7. Human Capital and Wage Differences

Human capital theory links productivity differences to investment in education and training. Even if this is not always formalized, Microeconomics 2 may ask you to connect:

• education improves productivity
• productivity raises value marginal product
• wage increases follow

You should distinguish:

• ability bias (higher ability both leads to education and higher wages)
• signaling vs productivity (education as credible signal of ability rather than direct productivity improvement)
• returns to education in labour demand

These distinctions show higher-quality exam reasoning.

General Equilibrium and Welfare Policy: UWC/NMMU/TVET-Compatible Microeconomics 2 Exam Framework

1. General Equilibrium: Linking Markets and Interdependence

Even if your course is mostly partial equilibrium, Microeconomics 2 often introduces general equilibrium intuition: what happens in one market affects others.

Examples:

• A tax on a good reduces consumption, which affects firms’ revenue and input demand (labour demand, capital demand).
• A wage change affects household income and thus market demand for goods.

The exam-relevant tool is the idea of market clearing in all markets simultaneously, and that welfare changes depend on how adjustments propagate across markets.

2. Externalities and Corrective Taxes/Subsidies

A classic welfare topic: externalities cause market outcomes to deviate from social optimum.

2.1 Negative Externality and Marginal Social Cost

If production imposes external costs, then:

• private marginal cost (MC_p)
• social marginal cost (MC_s = MC_p + MEC) where MEC is marginal external cost

Efficient output occurs where:
[
MB = MC_s
]
Market output under no intervention occurs where:
[
MB = MC_p
]
Thus externality typically leads to overproduction.

2.2 Pigouvian Tax

A corrective tax (t) set equal to the marginal external cost at the efficient output:
[
t = MEC
]
aligns private decision-making with social optimum.

3. Positive Externalities and Subsidies

If activities create benefits to others (education benefits society), then:

• private marginal benefit is less than social marginal benefit
• market underproduces relative to optimum
• subsidy equal to marginal external benefit can correct

4. Public Goods and Free-Riding

Microeconomics 2 may include public goods even if not heavily formalized. Key concepts:

• Non-excludability and non-rivalry produce incentives to free-ride.
• Efficient provision requires considering total marginal benefit across individuals.

In a simple two-person example, the efficient quantity (q^) satisfies:
[
MB_1(q^) + MB_2(q^) = MC(q^)
]

But decentralized markets yield:
[
MB_i(q) = MC
]
for each person’s contribution decision, resulting in underprovision.

5. Asymmetric Information (If Covered): Adverse Selection and Moral Hazard

Some curricula fold information economics into Microeconomics 2.

5.1 Adverse Selection (Hidden Information)

Example: insurance markets where high-risk individuals are more likely to buy insurance.

Key exam logic:

• Contracts must be designed anticipating that risk types may sort.
• The market can unravel.

5.2 Moral Hazard (Hidden Action)

Example: once insured, individuals may take less care.

Policy tools:

• deductibles, co-payments, monitoring, performance-based incentives

Even if the course does not require formal models, you should be able to describe trade-offs and why “just making insurance cheap” can fail.

6. Welfare Economics: Pareto Efficiency, Kaldor-Hicks, and Equity-Efficiency Trade-Offs

Welfare in Microeconomics 2 often includes a philosophical-economic layer:

• Pareto efficiency: no one can be made better off without making someone else worse off.
• Pareto improvement: a move where at least one person is better off and none worse off.
• Market failures: conditions preventing efficiency.

Kaldor-Hicks Criterion

A project is “socially beneficial” if winners can in principle compensate losers (even if they do not actually compensate). This supports cost-benefit approaches used in policy analysis.

7. A Full Policy Application: Taxation with Elastic Demand and Welfare Decomposition

To synthesize the topics, consider a tax policy question typical in Microeconomics 2 exams.

Suppose a per-unit tax (t) is imposed on a good in a competitive market. Use the following method:

1. Determine initial market equilibrium (without tax):
   • where (P = MC) (for competitive firm with constant MC and no fixed costs)
2. Apply tax wedge:
   • buyers pay (P_b), sellers receive (P_s = P_b – t)
3. Compute new equilibrium quantity (Q_t)
4. Calculate:
   • tax revenue: (t \cdot Q_t)
   • consumer surplus change
   • producer surplus change
   • deadweight loss: the total surplus reduction

Worked Example Setup

Demand:
[
Q = 20 – 2P
\Rightarrow P = 10 – \frac{Q}{2}
]
Supply from competitive MC:
[
P = \frac{Q}{4}
]
No tax equilibrium:
[
10 – \frac{Q}{2} = \frac{Q}{4}
\Rightarrow 10 = \frac{3Q}{4}
\Rightarrow Q_0 = \frac{40}{3}
]
Price:
[
P_0 = \frac{Q_0}{4} = \frac{10}{3}
]

Now impose tax (t = 2). Let buyers price (P_b), sellers receive (P_s = P_b – 2).
Equations:

• Demand: (P_b = 10 – \frac{Q}{2})
• Supply: (P_s = \frac{Q}{4}), so (P_b – 2 = \frac{Q}{4})

Solve:
[
10 – \frac{Q}{2} – 2 = \frac{Q}{4}
\Rightarrow 8 – \frac{Q}{2} = \frac{Q}{4}
\Rightarrow 8 = \frac{3Q}{4}
\Rightarrow Q_t = \frac{32}{3}
]

Compute DWL roughly via triangle areas under linear curves:

• Total surplus loss depends on how price changes relate to marginal changes. Since functions are linear, DWL can be computed as:
  [
  DWL = \frac{1}{2} \cdot t \cdot (Q_0 – Q_t)
  ]
  Here:
  [
  Q_0 – Q_t = \frac{40}{3} – \frac{32}{3} = \frac{8}{3}
  ]
  Thus:
  [
  DWL = \frac{1}{2}\cdot 2 \cdot \frac{8}{3} = \frac{8}{3}
  ]

Exam interpretation: DWL depends on the tax size and how much quantity shrinks (which depends on elasticities). Bigger elasticities imply larger quantity reduction and larger DWL.

8. South African Policy Lens: Competition, Consumer Protection, and Market Failures

Microeconomics 2 can be connected to South African policy debates in a way that demonstrates depth without requiring memorized statistics. Examples of policy themes consistent with micro models include:

• Competition policy: preventing market power that increases prices and reduces output (welfare loss).
• Consumer protection: information problems (advertising, product safety) relate to asymmetric information and market outcomes.
• Labour market interventions: minimum wages, training subsidies, and efficiency wages affect employment and welfare.
• Environmental regulation: negative externalities justify taxes or standards.

A strong exam answer typically:

1. identifies the relevant market failure or market structure,
2. states the behavioural prediction from the model (overproduction, underprovision, markup, unemployment),
3. proposes a policy instrument grounded in welfare theory (Pigouvian tax, subsidy, regulation),
4. notes distributional considerations (who gains/loses).

High-Yield Exam Toolkit Across 2ECO201 Microeconomics 2 Topics

1. Common Question Types and How to Answer

1.1 “Derive the equilibrium output/price”

A correct answer usually contains:

• a clear statement of the optimization objective (profit maximization or utility maximization)
• the relevant constraints
• the first-order condition
• the equilibrium condition (e.g., (MR = MC), (MR = w\cdot) etc.)
• the final computed values

1.2 “Compare welfare across regimes”

You should:

• compute quantities and prices (or at least relative output changes)
• sketch the relevant diagrams mentally (demand, MR, MC, and wedges)
• compute consumer surplus, producer surplus, and DWL using triangle/rectangle/trapezoid logic
• interpret results in words (e.g., “monopoly creates DWL because output is reduced below the social optimum where MB = MC”)

1.3 “Explain elasticity implications”

You should explicitly connect:

• elasticity to markup (Lerner index)
• elasticity to tax incidence (burden sharing)
• elasticity to policy effectiveness (bigger elasticities amplify quantity responses)

2. Diagram Logic You Should Be Able to Reconstruct Quickly

Even if your exam is not diagram-heavy, you should master diagram logic:

• Monopoly: demand curve, MR below demand, MC upward or flat, choose (MR=MC) leading to (Q_M < Q_C) and (P_M > P_C).
• Tax: competitive supply shifts up by (t); buyers price higher, sellers lower; wedge creates DWL.
• Externality: social cost curve above private cost; efficient output smaller output where MB = MSC, and market output higher where MB = MPC.
• Labour market: supply and demand curves; minimum wage above equilibrium causes excess supply (unemployment).

3. Microeconomic Algebra Patterns to Practice

You should be fluent with common algebraic steps:

1. Linear demand: if (Q = a – bP), then (P = (a – Q)/b)
2. Total revenue: (TR = P(Q)\cdot Q)
3. Marginal revenue: derivative of (TR) with respect to (Q)
4. DWL with linear curves: often (\frac{1}{2} t \Delta Q)
5. Cournot reaction functions: isolate (q_i) from FOC; then impose symmetry
6. Bertrand intuition: with homogeneous goods and no capacity constraints, equilibrium can be (p=c)

4. Worked “Exam-Style” Mixed Practice Problems (with Templates)

Problem A: Monopoly Welfare Comparison Template

Given:

• inverse demand (P = A – BQ)
• constant MC (c)

Steps:

1. Monopoly MR: (MR = A – 2BQ)
2. Set (MR = c) ⇒ solve for (Q_M)
3. Price: (P_M = A – BQ_M)
4. Competitive (P_C=c), solve for (Q_C)
5. Compute welfare areas:
   • CS: (\frac{1}{2}(P_{max} – P)\cdot Q)
   • PS: (\frac{1}{2}(P – c)\cdot Q) if linear and zero fixed costs
   • DWL: difference between total surplus

Problem B: Cournot Duopoly Template

Given:

• (P = a – (q_1+q_2))
• constant marginal cost (c)

Steps:

1. Write (\pi_1 = (P-c)q_1)
2. Differentiate w.r.t. (q_1): find reaction function
3. Apply symmetry: (q_1=q_2=q)
4. Find (Q=2q) and (P)

5. Common Mistakes That Cost Marks

• Mixing up price elasticity and income elasticity
• Confusing consumer surplus with welfare change in general
• Forgetting that MR differs from P for monopoly
• Omitting the strategic logic in oligopoly (e.g., not including the rival’s action)
• In tax problems: failing to identify whether the question asks for buyers’ price or sellers’ price
• In welfare decomposition: adding transfers incorrectly to DWL (transfers are not efficiency loss)

Institution-Focused Practice Clusters (South Africa Context)

Cluster 1: Stellenbosch University-Minded Focus — Market Structures and Welfare with Clear Mathematical Comparisons

A typical Stellenbosch-style approach rewards:

• explicit comparison between monopoly/oligopoly and competitive benchmark
• clean derivation using (MR=MC)
• welfare computations using surplus areas
• short but sharp economic interpretation

Practice emphasis:

• monopoly markup and DWL
• Cournot vs. monopoly outputs
• strategic reasoning in simple game tables

Cluster 2: University of Johannesburg / UJ Focus — Consumer Theory and Welfare Metrics (CV/EV)

A typical Johannesburg approach (as reflected across many SA modules) rewards:

• ability to define indirect utility/expenditure
• correct interpretation of CV and EV
• understanding when CS approximates welfare and when it doesn’t
• decomposing price changes into substitution/income effects

Practice emphasis:

• explain labour/consumption trade-offs (if included)
• compute CV/EV in simple expenditure-function setups
• connect elasticities to welfare and incidence

Cluster 3: University of Cape Town Focus — Factor Markets, Derived Demand, and Efficiency

A typical UCT-style marking tends to prefer:

• rigorous logic connecting MPL to wages
• clear explanation of what shifts labour demand/supply
• linking technology/human capital to marginal product
• nuanced discussion of unemployment persistence (efficiency wages)

Practice emphasis:

• value of marginal product
• labour supply decomposition
• human capital interpretations (ability vs signaling)

Cluster 4: South African TVET-Appropriate Focus — General Equilibrium Intuition, Externalities, and Policy Instrument Design

For TVET-aligned teaching styles, emphasis is often on:

• recognizing market failure
• explaining why markets fail to reach efficient outcomes
• choosing the correct policy instrument (tax, subsidy, regulation)
• presenting diagrams clearly and describing welfare outcomes

Practice emphasis:

• negative externality with social vs private costs
• positive externality and subsidy
• public goods and free riding using marginal benefit aggregation

Final Consolidation: One-Page “If You Remember Only This” Checklist

Microeconomics 2 Core Deliverables

• Monopoly: choose (MR=MC); interpret markup using elasticity (Lerner index).
• Cournot: reaction functions → symmetric equilibrium; outputs fall between monopoly and competition.
• Bertrand: with identical products and unlimited capacity, equilibrium can be (p=c) (Bertrand paradox).
• Welfare: compute CS/PS/DWL via correct areas; transfers ≠ DWL.
• Consumer welfare: CV/EV are utility-based; consumer surplus is not always exact welfare change.
• Labour markets: wage equals value marginal product under competitive assumptions.
• Externalities: social marginal cost/benefit vs private leads to over/underproduction; Pigouvian instruments correct.
• Policy application: explain who gains/loses and why elasticity matters for size of effects.

Rapid Verification Steps for Exam Calculations

1. Did you find quantity before price when the model requires it?
2. Did you compute MR correctly from the revenue function?
3. Did you match the correct equilibrium condition (competitive: (P=MC); monopoly: (MR=MC))?
4. For welfare, did you separate DWL from transfers?
5. For tax incidence, did you clearly label buyer price and seller price?

These notes are designed to support full-credit exam solutions across the main Microeconomics 2 themes typically assessed across South African institutions—balancing derivations, conceptual explanations, and welfare/policy reasoning grounded in microeconomic theory.