ECON2000 Microeconomics IIA Full Course Notes (Wits)

These notes cover ECON2000 Microeconomics IIA in a full-course exam-ready way: core theory, the “how to solve” toolkit, and typical assessment-style reasoning for undergraduate microeconomics at the University of the Witwatersrand (Wits). The focus is on consumer theory, production and cost, market structures, and the strategic logic behind imperfect competition, including applications that commonly appear in South African university and TVET-style economics assessments. Throughout, emphasis is placed on translating diagrams and verbal statements into correct algebra, conditions, and economic interpretation.

Section 1: Core Foundations, Consumer Choice, and Demand

Microeconomics IIA typically assumes you already know basic demand/supply and equilibrium reasoning from an introductory course. The “IIA” part usually deepens your understanding of micro foundations: preferences, utility maximization, expenditure minimization, and how those concepts generate demand. It also strengthens the ability to move between verbal intuition, mathematical optimization, and graphical representations.

Preferences, Utility, and the Behavioural Meaning of Assumptions

A standard starting point is modelling individual choice using preferences. The main assumptions (often tested directly) are:

1. Completeness: For any two bundles (A) and (B), the consumer can say whether they prefer one to the other or are indifferent.
2. Transitivity: If (A \succ B) and (B \succ C), then (A \succ C).
3. Reflexivity (sometimes implicit): (A) is at least as good as itself ((A \succeq A)).
4. Continuity (often implicit): Preference ordering changes “smoothly” enough to guarantee maximizers exist.
5. Monotonicity: More of a good is weakly preferred (often used to derive “inner” solutions).
6. Convexity: The consumer prefers mixtures of bundles to extreme bundles.

The exam-relevant point: these assumptions are not just academic—they determine the shape of indifference curves and therefore the behaviour of demand.

• Convex preferences (\Rightarrow) indifference curves are convex to the origin.
  Intuition: consumers dislike “corner solutions” when interior alternatives are feasible.
• Monotonicity (\Rightarrow) indifference curves “move up and right” in a way consistent with willingness to pay for more.
• Transitivity + Completeness (\Rightarrow) you can represent preferences with a utility function (in many common treatments).

In SA university exam questions, you’re often asked to interpret what convexity means: it ensures that when income changes, demand responds smoothly and “ordinary” comparative statics apply.

Utility Maximization and the Budget Constraint

Consider a consumer choosing between two goods (x) and (y), with prices (p_x, p_y) and income (m). The budget constraint is:

[
p_x x + p_y y \le m
]

For typical interior solutions (where both goods are consumed), the budget constraint binds:

[
p_x x + p_y y = m
]

The consumer’s problem is:

[
\max_{x,y} ; U(x,y) \quad \text{s.t.} \quad p_x x + p_y y \le m
]

A standard Lagrangian approach is:

[
\mathcal{L} = U(x,y) + \lambda(m – p_x x – p_y y)
]

First-order conditions (FOCs):

[
\frac{\partial U}{\partial x} = \lambda p_x,\quad \frac{\partial U}{\partial y} = \lambda p_y
]

Dividing the two FOCs:

[
\frac{\partial U/\partial x}{\partial U/\partial y} = \frac{p_x}{p_y}
]

Interpretation using marginal utility:

[
\frac{MU_x}{MU_y} = \frac{p_x}{p_y}
]

Another common way to express it is:

[
\frac{MU_x}{p_x} = \frac{MU_y}{p_y}
]

This is the “equalize marginal utility per rand” rule: the consumer reallocates consumption until the last rand spent on each good yields equal marginal utility.

Why it matters for exams: Many questions ask you to explain economically why this condition holds or to justify why optimal choices depend on relative prices rather than absolute prices.

Indifference Curves and the Marginal Rate of Substitution (MRS)

Indifference curves represent bundles that yield the same utility level. The MRS is the rate at which the consumer is willing to trade one good for another while keeping utility constant.

Graphically, for a consumer maximizing utility, the optimal tangency point satisfies:

[
\text{MRS}_{xy} = \frac{p_x}{p_y}
]

At tangency:

• The slope of the indifference curve equals the slope of the budget line (in absolute value).
• The consumer cannot get to a higher indifference curve without violating the budget constraint.

Convexity ensures that the tangency point is unique (for most “regular” utility functions).

Expenditure Minimization and Cost-of-Living Intuition

Another dual approach (often tested conceptually) is expenditure minimization. Instead of maximizing utility subject to a budget, you minimize spending subject to achieving a target utility (\bar{U}).

[
\min_{x,y} ; p_x x + p_y y \quad \text{s.t.} \quad U(x,y) \ge \bar{U}
]

The solution yields a cost function (e(p_x,p_y,\bar{U})), and optimal bundles depend on prices only through cost minimization logic.

Exam insight: If a question asks about “consumer demand from the perspective of cost,” expenditure minimization is the conceptual tool. If asked to interpret “the consumer chooses the cheapest way to reach utility (\bar{U}),” you’re in the dual model.

Demand Derivation: Marshallian and Hicksian Demand

When you do utility maximization with income (m), the resulting demand is usually Marshallian (uncompensated) demand:

[
x^M(p_x,p_y,m), \quad y^M(p_x,p_y,m)
]

When you do expenditure minimization to reach a utility target (\bar{U}), the resulting demand is Hicksian (compensated) demand:

[
x^H(p_x,p_y,\bar{U}), \quad y^H(p_x,p_y,\bar{U})
]

The key difference (important for exam essays):

• Marshallian demand reflects both substitution and income effects.
• Hicksian demand reflects substitution effect only (income effect is “compensated away”).

Substitution and Income Effects: Normal vs Inferior Goods

The total effect of a price change on quantity demanded is decomposed into:

1. Substitution effect: movement along a constant utility contour (compensated).
2. Income effect: movement due to purchasing power changing after the price change.

A price increase of good (x) from (p_x) to (p_x') typically:

• Encourages substitution away from (x).
• Reduces real income (purchasing power), potentially further decreasing demand if (x) is normal.

Normal good: Income effect reinforces substitution effect (\Rightarrow) demand decreases when price increases.

Inferior good: Income effect works opposite substitution effect; demand may not fall as much or may even rise (Giffen behaviour is an extreme case usually tied to strong income effects and specific poverty constraints).

The Slutsky Equation (The Workhorse)

The Slutsky equation formalizes the decomposition:

[
\frac{\partial x}{\partial p_x} = \frac{\partial x^H}{\partial p_x} – x \cdot \frac{\partial x}{\partial m}
]

Often more memorably:

• The uncompensated price effect equals:
  • the compensated price effect (substitution effect), plus
  • a term capturing income effect scaled by initial consumption (x).

Exam use:
If a question provides sign information (e.g., Hicksian demand decreases in own price under standard assumptions), you can determine the sign of the total effect given whether the good is normal or inferior.

Case-Style Practice: Translating a Word Problem Into Equations

A typical micro exam scenario: A student chooses between bread ((x)) and rice ((y)). Prices change due to supply shocks. Income stays constant.

You would:

1. Write the budget: (p_b b + p_r r = m).
2. State MRS condition at optimum: (\frac{MU_b}{MU_r} = \frac{p_b}{p_r}).
3. Predict qualitative changes:
   • If (p_b) rises, (b) likely falls.
   • If bread is normal, income effect further reduces bread consumption.

If the exam asks for income vs substitution direction, you reference compensated demand and show the “new tangency” holding utility constant.

Market Demand Aggregation (Conceptual Link)

Micro IIA also often connects individual demand to market demand:

• Market demand is horizontal sum of individual demands (for identical pricing).
• Under standard assumptions, downward-sloping market demand arises because each consumer’s demand obeys the substitution effect logic.

You may be asked to compute market demand from a set of consumer demands:

• If (x_i(p) = a_i – b_i p), then (X(p) = \sum_i x_i(p)).

The exam skill is algebraic consistency, not just theory.

Section 2: Elasticity, Consumer Surplus, Welfare, and Choice Under Constraints

After building demand theory, Microeconomics IIA usually shifts to elasticities, welfare measures, and the deeper welfare implications of price changes. These topics appear frequently in applied SA contexts (tax incidence, minimum prices, and efficiency analysis).

Price Elasticity of Demand: Definitions and Economic Meaning

Price elasticity of demand measures responsiveness of quantity demanded to price:

• Point elasticity:

[
\varepsilon = \frac{\partial x}{\partial p}\cdot \frac{p}{x}
]

• Arc elasticity (for discrete changes) often uses average values:

[
\varepsilon_{arc} = \frac{\Delta x}{\Delta p}\cdot \frac{(p_{avg})}{(x_{avg})}
]

Economic meaning: If (|\varepsilon|) is high, demand is elastic: quantity changes strongly when price changes. If (|\varepsilon|) is low, demand is inelastic.

Exam interpretation tips:

• Elasticity magnitudes inform tax revenue and deadweight loss.
• Elasticity shape depends on substitution possibilities and time horizon.

Total Revenue Test and Elasticity Intuition

The relationship between price and total revenue (TR = p \cdot x(p)) depends on elasticity:

• If demand is elastic ((|\varepsilon| > 1)): price increases reduce total revenue.
• If demand is inelastic ((|\varepsilon| < 1)): price increases increase total revenue.
• If demand is unit elastic ((|\varepsilon| = 1)): total revenue is unchanged for small changes.

A common exam question: given qualitative info or calculations of (TR), infer elasticity region.

Elasticities with Linear Demand: A Worked Pattern

For linear demand (x(p) = \alpha – \beta p):
[
\frac{\partial x}{\partial p} = -\beta
]
[
\varepsilon(p) = -\beta \cdot \frac{p}{\alpha – \beta p}
]

Thus elasticity varies along the curve:

• At low prices (near intercept), elasticity is smaller in magnitude (more inelastic).
• Near the choke price, elasticity becomes large in magnitude (more elastic).

This is a recurring graph interpretation skill.

Income Elasticity and Engel Curves

Income elasticity of demand:

[
\varepsilon_m = \frac{\partial x}{\partial m}\cdot \frac{m}{x}
]

• (\varepsilon_m > 0): normal goods.
• (0 < \varepsilon_m < 1): necessities.
• (\varepsilon_m > 1): luxury goods.
• (\varepsilon_m < 0): inferior goods.

Engel curves plot (x) against income (m). Many exam questions ask for shapes consistent with elasticity signs.

Cross-Price Elasticity: Substitutes vs Complements

Cross-price elasticity of demand for good (x) with respect to price of good (z):

[
\varepsilon_{xz} = \frac{\partial x}{\partial p_z}\cdot \frac{p_z}{x}
]

• Positive: substitutes (increase in (p_z) increases demand for (x)).
• Negative: complements (increase in (p_z) reduces demand for (x)).

A standard exam application: if tea and coffee are substitutes, a rise in coffee price shifts tea demand rightward.

Consumer Surplus and Welfare Interpretation

Consumer surplus (CS) is the area under the demand curve above the price line (for a price taking model). If demand is inverse (p(x)), and consumers pay (p) for quantity (x):

[
CS = \int_0^{x(p)} [p(x) – p], dx
]

In a typical triangular linear demand:

• If demand intersects price axis at (a) and quantity axis at (b),
• and equilibrium price is (p^*), then:
  • consumed quantity is (x^* = b(1 – \frac{p^*}{a})),
  • CS is roughly (\frac{1}{2}(x^)(p_{max} – p^)).

Why exams love CS: it links to welfare changes from taxes, subsidies, and price controls.

Efficiency: Pareto, Kaldor–Hicks, and Deadweight Loss

• Pareto efficiency: no one can be made better off without making someone else worse off.
• Competitive markets under standard assumptions reach allocative efficiency (no feasible reallocation increases total surplus).
• When distortions occur (taxes, externalities, monopoly power), total surplus decreases.

Deadweight loss (DWL) is the reduction in total surplus due to inefficient trades that would have happened without the distortion.

For a unit tax:

• Buyers pay (p_b),
• sellers receive (p_s),
• tax wedge (p_b – p_s = t).

DWL is area of the triangle between supply and demand over the reduced quantity.

Incidence of Taxes: Who Pays Depends on Elasticities

Tax incidence analysis is a classic Micro IIA topic. Under partial equilibrium:

• The side with more elastic demand/supply bears less of the tax burden because they can adjust quantity more easily.

Typical rule:

• Inelastic side bears a larger share of the tax.

In exam answers, you should not just state “elastic side pays less.” You should also show:

1. the tax wedge,
2. shifts in equilibrium,
3. how the change in quantity differs due to elasticities,
4. resulting changes in producer and consumer prices.

Indifference Curves, Hicks Compensation, and Welfare Measures

Beyond CS, utility-based welfare measures like compensating variation (CV) and equivalent variation (EV) are sometimes tested. These require understanding how much income must change to keep utility constant when prices change.

• Compensating variation: extra income needed after a price increase to reach the original utility.
• Equivalent variation: income taken away before the price increase to reach the new utility.

The student-level exam often asks for direction and economic interpretation rather than full derivation.

Case: Tax on a Staple Good in South African Context

Consider a stylized staple like maize meal (good (x)). Suppose a tax raises its consumer price. If demand is relatively inelastic (necessity), consumers reduce quantity but less than if the good were optional. In that case:

• consumer prices rise significantly,
• producer prices fall less,
• and DWL can still be sizable due to large expenditure base.

In exam language:

• Necessities have lower price elasticity,
• so tax incidence shifts more to consumers,
• and distributional impacts can be emphasized.

Demand Systems and Budget Sets (Constraint Geometry)

Even when not fully developed into advanced systems, exam problems often require geometry skills:

1. Budget line slope: (-\frac{p_x}{p_y}).
2. Feasible set: all bundles satisfying (p_x x + p_y y \le m).
3. Optimal choice is where the highest attainable indifference curve touches the budget line.

You might be asked: “Show the effect of an increase in income”:

• budget line shifts outward parallelly if prices unchanged,
• consumption bundles move to higher indifference curves.

If asked about changes in one price:

• budget line rotates around the intercept on the other good’s axis.

Section 3: Production, Cost Functions, and Competitive Supply

Microeconomics IIA typically transitions from consumer behaviour to the firm: production functions, costs, and how firms supply output under different market assumptions. This section builds the foundations for later monopoly and oligopoly cost-output reasoning.

Production Functions: Inputs, Output, and Marginal Products

A production function relates inputs (K) (capital), (L) (labour), and output (q):

[
q = f(K,L)
]

Key concepts:

• Marginal product of labour:

[
MP_L = \frac{\partial f}{\partial L}
]

• Diminishing marginal returns: holding one input fixed, additional units of the other eventually yield lower increments to output.
• Returns to scale:
  • Increasing returns: scaling all inputs multiplies output by more than the same factor.
  • Constant returns: output scales proportionally.
  • Decreasing returns: output scales less than proportionally.

Exam questions often ask you to identify which property holds given a functional form or a numerical example.

Isoquants and MRTS

For two-input production:

• Isoquant: all input combinations yielding the same output.
• Marginal Rate of Technical Substitution (MRTS): trade-off between inputs at constant output.

Profit-maximizing production given input prices (w) (wage for (L)) and (r) (rent for (K)) often has a tangency condition:

[
\frac{MP_L}{MP_K} = \frac{w}{r}
]

Meaning: inputs are chosen so the marginal product ratio equals the marginal cost ratio.

The exam expects you to interpret tangency and justify it economically: the firm chooses the least-cost way to achieve a target output.

Cost Minimization and Cost Curves

If output is (q), and firm chooses inputs to minimize cost:

[
\min_{K,L} ; wL + rK \quad \text{s.t.}\quad f(K,L) \ge q
]

The minimized cost is the cost function (C(q)). From it you derive:

• Average cost (AC(q) = \frac{C(q)}{q})
• Average variable cost (AVC(q)=\frac{VC(q)}{q})
• Marginal cost (MC(q) = \frac{dC}{dq}) (or discrete approximation)
• Fixed cost (FC): cost that doesn’t change with output.

A standard result:

• (MC) intersects (AC) at (AC)’s minimum (under regularity conditions).
• Similarly (MC) intersects (AVC) at (AVC)’s minimum.

These relationships are often tested with graphs.

Short Run vs Long Run

Short run: at least one factor is fixed (e.g., capital (K) fixed). So you have:

• fixed cost,
• variable cost,
• short-run cost curves depend on fixed input levels.

Long run: all factors are variable; firms can adjust all inputs. Consequently:

• long-run average cost (LRAC) is the lower envelope of short-run average costs (SRAC).

In exams, you often justify:

• why LRAC is below any SRAC at a given output (because the firm can pick the best fixed-factor configuration in long run).

Economies and Diseconomies of Scale

Scale effects determine whether unit cost falls or rises with size.

• Economies of scale: as output increases, average cost declines.
• Diseconomies of scale: as output increases, average cost rises.
• Minimum efficient scale: output at which AC is minimized and scale efficiencies stop improving.

You may be asked to interpret shapes:

• downward-sloping AC at low outputs suggests economies of scale,
• upward trend at high outputs suggests diseconomies.

In applied settings, this can connect to manufacturing learning-by-doing, fixed overheads, and managerial coordination.

Profit Maximization and the Competitive Firm’s Output Decision

Assume a competitive firm is a price taker, so output price (P) is given. Profit:

[
\pi(q) = Pq – C(q)
]

First-order condition for interior optimum (or where marginal condition holds):

[
MR = P = MC(q)
]

Second-order conditions (or practical graph reasoning) ensure a maximum.

Shutdown decision in the short run:
A firm will produce if it can cover variable cost:

• Produce if (P \ge AVC(q)).
• Shutdown if (P < AVC) (since fixed cost still must be paid, but producing increases losses beyond variable costs).

Exam tip: Many candidates confuse fixed cost coverage with shutdown. Correct logic:

• You do not need to cover fixed cost to stay open in short run; you must cover variable cost.

Supply Curve: From Firm to Industry

For the competitive firm, the short-run supply curve corresponds to the MC curve above AVC. To build industry supply:

• horizontally sum across firms at each price.

If asked with numbers:

1. determine firm quantities at each price using (P=MC),
2. discard quantities below shutdown threshold,
3. add quantities across firms.

The key is correct piecewise definition.

Example Pattern: Piecewise Cost with Shutdown Price

Suppose a firm’s marginal cost is:

• (MC(q)=2q),
  and average variable cost is:
• (AVC(q)=q).

Shutdown where (P = AVC) in the short run:

• if (P < AVC), shutdown.
• if (P \ge AVC), produce where (P=MC).

If (P=6):

• production: solve (6=2q \Rightarrow q=3),
• check: (AVC(3)=3), and since (6 \ge 3), production is allowed.

Exam marking often checks these consistency steps.

Cost Curves and Comparative Statics

If a factor price changes (e.g., wages rise), cost curves shift upward:

• MC shifts upward,
• supply shifts left (higher price required to produce given output).

Comparative statics questions frequently ask:

• “If wages increase, what happens to equilibrium output and price in competitive markets?”
  You answer:

1. firm costs rise,
2. supply decreases,
3. equilibrium price rises, quantity falls (assuming demand downward sloping).

You must also explain that changes in supply are distinct from movements along demand.

Section 4: Monopoly, Market Power, and Strategic Price-Quantity Logic

Once the firm’s cost and competitive supply are established, Microeconomics IIA often introduces imperfect competition—starting with monopoly and moving toward strategic interactions.

Monopoly Basics: Total Revenue, Marginal Revenue, and Deadweight Loss

A monopoly faces the market demand curve, so price is not fixed. If demand is (P(q)), revenue is:

[
TR(q) = P(q)\cdot q
]

Marginal revenue:

[
MR(q) = \frac{dTR}{dq}
]

For downward-sloping demand, (MR < P). Therefore monopoly chooses:

[
MR = MC
]

Then sets the price from the demand curve at the monopoly quantity.

Deadweight loss arises because monopoly restricts output below the competitive level, generating inefficient trades that are mutually beneficial.

Exam diagrams:

• Competitive: (P=MC) at quantity (q_c).
• Monopoly: (MR=MC) at quantity (q_m < q_c).
• Monopoly price (P_m) exceeds competitive price (P_c).

Monopoly Profit Decomposition: Revenue vs Costs and Transfers

At monopoly:

• profit is ((P_m – AC(q_m))\cdot q_m) on a standard diagram.
• Consumer surplus is partially transferred to the firm as monopoly profits, but not all CS becomes profit—some becomes deadweight loss.

An exam writing strategy:

1. Identify monopoly output (q_m).
2. Identify monopoly price (P_m).
3. Compute profits using cost at (q_m) if AC provided.
4. Identify welfare areas: CS loss, PS gain, DWL.

Price Discrimination: First, Second, Third Degree

Price discrimination means charging different prices for different consumers or units.

1. First-degree (perfect) discrimination:

   • the monopolist captures all consumer surplus if it can perfectly observe willingness to pay.
   • output is typically at efficient level if perfectly discriminating (depending on model).

2. Second-degree discrimination:

   • nonlinear pricing (e.g., quantity discounts, menus).
   • depends on consumer self-selection.
   • can increase efficiency relative to uniform monopoly price but still may create distortion.

3. Third-degree discrimination:

   • different prices across groups with different elasticities (e.g., students vs workers).
   • key rule: price is set lower in the group with higher elasticity.

A classic elasticity pricing rule for group (i) (under simplifying assumptions):
[
\frac{P_i – MC}{P_i} = \frac{1}{\varepsilon_i}
]
where (\varepsilon_i) is the price elasticity in segment (i).

Exam use: If one segment demand is more elastic, monopolist sets a lower markup there.

Natural Monopoly and Scale-Based Market Power

Natural monopoly occurs when:

• average costs are declining over the relevant output range, so one firm can supply at lower average cost than multiple firms.

In such cases:

• government intervention is considered to prevent excessive markups and reduce DWL.
• regulation may set price equal to marginal cost (though that can create losses if fixed costs are large) or set prices to ensure fair return.

If your course includes regulation:

• explain trade-off between efficiency (MC pricing) and cost recovery (average cost pricing).

Dynamic Considerations: Threats, Commitment, and Rational Expectations (If Included)

Some ECON2000 IIA syllabi may extend into basic strategic interaction:

• commitment problems: a firm cannot credibly commit to a future action unless it can bind itself.
• credible threats depend on incentives and rationality.

Even when full game theory is not required, some exam questions use:

• “credible vs non-credible threat” reasoning,
• “if the firm cannot commit, outcomes differ.”

You should link credibility to incentive constraints.

Monopoly and Regulation: Efficiency vs Equity

When regulators set a regulated price, they often attempt to balance:

• economic efficiency (reduce DWL by expanding output),
• fiscal feasibility (ensure the firm can cover costs),
• equity/distribution (affordability constraints).

Typical regulated price:

• Marginal cost pricing yields allocative efficiency but may not cover fixed costs.
• Average cost pricing covers costs but can sustain DWL similar to monopoly (or at least reduces it relative to unregulated monopoly, depending on assumptions).

In SA policy discussions (as referenced in course materials), utilities are often the canonical example.

Section 5: Oligopoly, Game-Theoretic Intuition, and Exam-Ready Problem Solving

Microeconomics IIA typically culminates by extending market power to oligopoly: firms recognize that their outcomes depend on rivals’ decisions. Even if the course doesn’t demand full formal game theory, the strategic logic is often essential for exam marks.

Cournot vs Bertrand: Competing on Quantity vs Price

Two foundational models:

Cournot (quantity competition)

• Each firm chooses quantity simultaneously.
• Price determined by total output.

Equilibrium occurs where each firm’s quantity is best response to rivals’ quantities.

Bertrand (price competition)

• Each firm chooses price simultaneously.
• The firm with the lower price captures more demand (in basic models).
• With identical products and constant marginal cost, Bertrand competition can drive prices to marginal cost (the “Bertrand paradox”).

Exam-style reasoning:

• Ask which model fits which scenario:
  • If firms can choose production levels and adjust output slowly: Cournot intuition.
  • If firms are pricing close substitutes with fast price adjustments: Bertrand intuition.

Nash Equilibrium: The Unifying Concept

A Nash equilibrium is a strategy profile where no player can improve by unilaterally changing their action.

In oligopoly:

• each firm’s strategy is a best response to the other’s.

To solve many exam oligopoly problems:

1. write best response functions,
2. set them equal,
3. solve for equilibrium quantities/prices,
4. interpret.

Your marks often depend on whether you justify best responses logically, not just compute.

Dominant Strategies and Subgame Logic (If Covered)

Some courses briefly cover dominant strategies:

• A strategy is dominant if it is optimal regardless of what the rival does.

Subgame perfection:

• requires equilibrium to be credible at every subgame (for sequential games).

If the course includes sequential games, typical exam reasoning requires:

• backward induction,
• ensuring threats are credible.

Collusion, Cartels, and Incentive Compatibility

A cartel attempts to behave like a monopoly (high prices, low output). But collusion must be stable against deviation.

Key incentive:

• cheating (undercutting the cartel price) can yield higher short-run profits.
• stability depends on punishment mechanisms and whether repeated-game incentives deter deviation.

If repeated games are in the syllabus:

• focus on conditions involving discount factors and incentive constraints.

If repeated games are not formal in the course:

• still discuss qualitatively: collusion is harder when firms can profit from cheating and cannot be punished.

Market Power, Welfare, and Consumer Impact in Oligopoly

Oligopoly typically produces:

• outcomes between perfect competition and monopoly,
• DWL smaller than monopoly but larger than perfect competition (in many standard models).

Exam questions may ask to rank welfare outcomes:

• Perfect competition yields highest total surplus,
• Monopoly yields lowest,
• oligopoly in between.

Make sure you tie welfare losses to reduced output relative to efficient levels.

Strategic Substitution vs Complementarities (A Key Comparative Static)

In some advanced treatments, firms’ actions may be:

• strategic substitutes: if rival increases quantity/price, best response is to decrease.
• strategic complements: if rival increases, your best response is to increase.

Cournot usually yields strategic substitutes (depending on assumptions). Bertrand can yield different patterns depending on model details.

Even if not asked explicitly, knowing the sign helps interpret equilibrium comparisons.

Exam Problem-Solving Toolkit (How to Score High)

Most students lose marks due to missing steps, not lack of understanding. A consistent toolkit:

Step 1: Identify the model

• Consumer choice? (budget + utility maximization)
• Competitive firm? (price equals MC or shutdown rule)
• Monopoly? (MR equals MC)
• Oligopoly? (best responses + Nash equilibrium)

Step 2: Write the relevant condition

Examples:

• Consumer interior optimum:
  [
  MRS = \frac{p_x}{p_y}
  ]
• Competitive firm:
  [
  P = MC \quad \text{and} \quad P \ge AVC \text{ for production}
  ]
• Monopoly:
  [
  MR = MC
  ]
• Price discrimination (segment):
  apply elasticity-markup logic if provided.

Step 3: Use the demand or cost data correctly

• If the question provides inverse demand (P(Q)), compute (TR) and (MR).
• If it provides demand (Q(P)), convert carefully to avoid derivative mistakes.

Step 4: Interpret economically

A fully correct numerical answer without interpretation may lose marks. Always include:

• “output is reduced compared to competition, so DWL appears”
• “elasticity determines incidence”
• “normal goods respond with substitution and income effects reinforcing”

Worked Mini-Example: Monopoly with Linear Demand (Template)

If an exam asks:

• demand: (P(Q) = a – bQ),
• cost: (C(Q)) given (say (C(Q)=F + cQ)).

Then:

1. revenue:
   [
   TR = (a – bQ)Q = aQ – bQ^2
   ]
2. marginal revenue:
   [
   MR = a – 2bQ
   ]
3. monopoly condition:
   [
   a – 2bQ = MC = c
   \Rightarrow Q_m = \frac{a-c}{2b}
   ]
4. monopoly price:
   [
   P_m = a – bQ_m
   ]
5. compare to competitive:
   competitive quantity solves:
   [
   P = MC \Rightarrow a – bQ_c = c \Rightarrow Q_c = \frac{a-c}{b}
   ]
   so (Q_m = \frac{1}{2}Q_c) under linear demand and constant MC.

This is a common pattern and often appears in exam form (sometimes with different numbers).

South African University Exam Style Notes: What Examiners Look For

In Wits-style microeconomics assessments, you’re typically rewarded for:

• correct use of equilibrium conditions,
• correct sign reasoning (e.g., elasticity and incidence),
• explicit linking between graphs and written logic,
• clean algebra, and
• consistent interpretation of welfare changes.

Common pitfalls to avoid:

• using monopoly condition (P=MC) (incorrect; monopoly uses (MR=MC)),
• confusing shutdown price with fixed costs,
• forgetting that Hicksian demand holds utility constant (compensated),
• ignoring substitution vs income effect decomposition when asked for both.

Consolidated Quick-Reference Summary (For Revision)

Consumer Theory

• Optimize:
  [
  \max U(x,y) \text{ s.t. } p_x x + p_y y = m
  ]
• Interior optimum:
  [
  MRS = \frac{p_x}{p_y} \quad \text{or} \quad \frac{MU_x}{MU_y}=\frac{p_x}{p_y}
  ]
• Decomposition:
  • substitution effect only in Hicksian demand,
  • Slutsky connects uncompensated and compensated responses.

Elasticity & Welfare

• Price elasticity:
  [
  \varepsilon = \frac{\partial x}{\partial p}\cdot \frac{p}{x}
  ]
• Tax incidence depends on relative elasticities.
• Deadweight loss = efficiency loss from reduced mutually beneficial trades.

Production & Costs

• Firm costs from cost minimization:
  [
  C(q) = \min_{K,L} ; wL+rK ; \text{s.t. } f(K,L)\ge q
  ]
• Competitive firm:
  [
  P=MC \text{ and produce if } P\ge AVC
  ]
• Long run: LRAC is envelope of SRAC.

Monopoly & Oligopoly

• Monopoly:
  [
  MR=MC, \quad \text{price from demand at } Q_m
  ]
• Oligopoly: Nash equilibrium via best responses.
• Welfare: competitive highest, monopoly lowest, oligopoly intermediate (model-dependent).

Course-Completion Check: Master These Exam Competencies

1. Derive demand using utility maximization and interpret substitution vs income effects.
2. Compute and interpret elasticity (including how it affects total revenue and tax incidence).
3. Link consumer welfare to CS and DWL through correct area reasoning.
4. Build cost curves conceptually from production choices.
5. Apply competitive firm shutdown rule correctly.
6. Use monopoly MR=MC with correct calculation of MR from demand.
7. Solve oligopoly equilibrium problems with best responses and Nash logic.
8. Write coherent exam explanations: not only equations, but economic interpretation.

End of ECON2000 Microeconomics IIA Full Course Notes (Wits).