ECO2A Microeconomics Detailed Course Notes — University of Johannesburg (UJ) Economics Module Guide

Microeconomics studies how individuals and firms make decisions under scarcity and how those decisions interact through markets to determine prices, quantities, and welfare. ECO2A focuses on core analytical tools—demand and supply, consumer choice, market structures, production theory, and welfare analysis—using both graphs and algebraic reasoning. These notes are designed for exam preparation at South African institutions, especially for students following the University of Johannesburg (UJ) Economics module “ECO2A Microeconomics,” with attention to the kind of questions commonly asked in South African university midterms and finals.

Section 1: Foundations of Microeconomics and Market Analysis (ECO2A Core Framework)

Microeconomics answers questions like: Why do prices change? Who benefits from taxes? What happens to output when costs rise? ECO2A typically begins with the building blocks needed to model those answers logically. A strong command of these foundations also improves performance in later sections on elasticity, consumer theory, production decisions, and market power.

1.1 The Microeconomic Model: Assumptions and Objectives

At the micro level, we model agents—consumers, firms, and sometimes governments—who choose among alternatives to maximise benefits or minimise costs. Standard ECO2A-style assumptions include:

Rational choice: consumers maximise utility; firms maximise profit (or minimise cost).
Scarcity: resources are limited, so trade-offs matter.
Ceteris paribus reasoning: when analysing one market factor, other factors are held constant.
Opportunity cost: costs reflect the value of forgone alternatives.
Marginal thinking: decisions depend on how much changes at the margin (extra unit, extra hour, extra percent).

The objective is not to memorise definitions but to build exam-ready “chains of reasoning”:

Identify the market and relevant variables.
Determine the shock (price change, income change, technology change, tax/subsidy).
Draw or describe the shifts and the movement along curves.
Compute or explain changes in quantity, price, and welfare.

1.2 Markets, Prices, and Coordination

In competitive markets, prices coordinate decisions. If demand rises (say due to higher tastes), the price tends to rise, encouraging suppliers to expand output. If supply falls (say due to a cost shock), price rises and demand falls.

A common exam pitfall is mixing up movement along vs shift:

Movement along demand/supply curve happens when the own price changes.
Shift happens when a non-price determinant changes (income, tastes, input prices, technology, number of firms, expectations).

1.3 Demand: Determinants, Functions, and Curve Interpretation

Demand law

Quantity demanded typically falls when price rises, holding other factors constant.

Demand function examples

ECO2A questions often give a form like:

(Q_d = a – bP)
or (Q_d = a + bY – cP) where (Y) is income.

Determinants of demand (non-price)

Income (Y):
- Normal goods: demand rises with income.
- Inferior goods: demand falls with income.
Tastes and preferences (advertising, fashion, health concerns).
Prices of related goods:
- Substitutes: if the substitute’s price rises, demand for the good rises.
- Complements: if the complement’s price rises, demand for the good falls.
Expectations about future prices.
Number of buyers.

Graph skill

In exam settings, you may be asked to:

State whether a curve shifts left/right.
Predict new equilibrium price and quantity.
Explain the reasoning in words (sometimes 2–4 marks) and using graphs (often 5–8 marks).

1.4 Supply: Determinants, Cost Intuition, and Curve Interpretation

Supply law

Quantity supplied typically rises when price rises, holding other factors constant.

Supply determinants (non-price)

Input prices (wages, raw materials).
Technology (productivity improvements shift supply right).
Number of sellers (more firms increase market supply).
Taxes/subsidies affecting production.
Expectations (e.g., future selling opportunities).
Regulation impacting compliance costs.

1.5 Market Equilibrium: Solving for Price and Quantity

A standard ECO2A equilibrium setup:

Equilibrium occurs where (Q_d = Q_s).

Example (numerical equilibrium)

Suppose:

(Q_d = 100 – 2P)
(Q_s = 20 + 3P)

Set equal:
[
100 – 2P = 20 + 3P \Rightarrow 80 = 5P \Rightarrow P^* = 16
]
Then:
[
Q^* = 100 – 2(16) = 68
]
Exams often test the equilibrium logic under shocks. For example, if demand shifts right due to higher income, the equilibrium price rises and quantity rises.

1.6 Comparative Statics: Shocks and Direction of Change

Comparative statics asks: given a change in one determinant, what happens to equilibrium? Without heavy algebra, you can often infer directions:

Increase in demand → higher (P^) and higher (Q^).
Decrease in demand → lower (P^) and lower (Q^).
Increase in supply → lower (P^) and higher (Q^).
Decrease in supply → higher (P^) and lower (Q^).

However, welfare analysis requires more than directions; taxes and quotas depend on elasticities.

1.7 Elasticity: The Bridge Between Market Shifts and Welfare

Elasticity measures responsiveness. ECO2A typically introduces elasticity early and then uses it repeatedly:

to determine incidence of taxes,
to evaluate efficiency loss,
to interpret consumer and producer behaviour.

You may see:

Price elasticity of demand:
[
\varepsilon_d = \frac{dQ}{dP}\cdot \frac{P}{Q}
]
Income elasticity and cross-price elasticity for demand relationships.

A key conceptual rule:

More elastic demand means quantity changes more with price, affecting how tax burdens are shared.

Section 2: Elasticity, Taxes, and Welfare Analysis (ECO2A Analytical Applications)

Elasticity and welfare analysis are high-yield ECO2A topics because they integrate multiple earlier concepts (demand/supply, equilibrium, marginal reasoning) and they frequently appear in calculation-based exam questions. Many marks come from clear graphical explanations and correct numerical welfare computations.

2.1 Price Elasticity of Demand and Supply

Point vs arc elasticity

ECO2A may use:

Point elasticity (calculus-based):
(\varepsilon = (dQ/dP)(P/Q))
Arc elasticity (finite change):
[
\varepsilon = \frac{\Delta Q}{\Delta P}\cdot \frac{\overline{P}}{\overline{Q}}
]
where (\overline{P}) and (\overline{Q}) are averages.

In many university exams, arc elasticity is preferred since questions are numerical without calculus.

Interpretation

If (|\varepsilon_d| > 1): elastic demand (percentage quantity response larger than price response).
If (|\varepsilon_d| < 1): inelastic demand.
If (|\varepsilon_d| = 1): unit elastic.

Elasticity and slope confusion

A common misconception: “steeper demand means more elastic.” Not always. Elasticity depends on:

slope and
where you are on the curve (values of (P) and (Q)).

2.2 Determinants of Elasticity (Why it Matters)

For demand:

Availability of substitutes: more substitutes → more elastic.
Necessity vs luxury: necessities tend to be less elastic.
Time horizon: in the short run, fewer adjustments → more inelastic; in the long run → more elastic.
Share of income: goods taking larger share of income tend to be more elastic.
Definition of the market: narrowly defined products usually have more elastic demand.

For supply:

Flexibility of production: easier to ramp up production → more elastic supply.
Time horizon: short run supply is often more inelastic.
Possibility of storing output or adjusting inputs.

In exam answers, elasticity must be connected to incidence:

If demand is more inelastic than supply, consumers bear more of a per-unit tax.

2.3 Income Elasticity and Cross-Price Elasticity

Income elasticity

[
\varepsilon_Y = \frac{dQ}{dY}\cdot \frac{Y}{Q}
]

(\varepsilon_Y > 0): normal good.
(\varepsilon_Y < 0): inferior good.
Magnitude indicates whether demand responds strongly or weakly to income.

Cross-price elasticity

[
\varepsilon_{xy} = \frac{dQ_x}{dP_y}\cdot \frac{P_y}{Q_x}
]

Positive → substitutes.
Negative → complements.

ECO2A exam questions may ask for qualitative predictions like: If the price of electricity increases, what happens to demand for gas? That depends on whether the goods are substitutes.

2.4 Tax Incidence: Who Pays the Tax?

A classic ECO2A question: impose a per-unit tax (t). The wedge between consumer price (P_c) and producer price (P_p) is:
[
P_c = P_p + t
]

Even if the tax is collected from sellers, the burden splits depending on elasticities.

Graphical intuition

Tax shifts supply up by (t) (equivalently, supply moves left).
Consumers face higher price (P_c).
Producers receive lower net price (P_p).
Equilibrium quantity falls.

Price consumers pay rises from 16 to 22 (+6).
Net price producers receive falls from 16 to 12 (-4).
Quantity falls from 68 to 56.

This numerical breakdown is exam-friendly because it shows how incidence reflects elasticities.

2.5 Deadweight Loss (DWL) and Efficiency

Taxes typically cause deadweight loss due to under-consumption relative to the efficient equilibrium. DWL is the efficiency cost above and beyond revenue collected.

Welfare areas

Consumer surplus (CS): area under demand above price.
Producer surplus (PS): area above supply below price.
Tax revenue (TR): (t \times Q_{tax}).

With tax, CS and PS decline; TR is part of those losses but DWL is the remainder.

Exam computations (how to structure)

A typical approach:

Find equilibrium without tax: ((P^, Q^)).
Find equilibrium with tax: ((P_c, P_p, Q_{tax})).
Compute CS, PS, TR using triangle areas or integration if linear.
Compute DWL:
[
DWL = (CS_{before}-CS_{after}) + (PS_{before}-PS_{after}) – TR
]
Provide a clear statement: tax creates DWL because mutually beneficial trades are not completed.

2.6 Price Controls: Floors and Ceilings

ECO2A often includes price ceilings and floors.

Price ceiling

If maximum price (P_{max}) is below equilibrium:

Quantity demanded exceeds quantity supplied → shortage.
A black market may emerge; rationing occurs.

Price floor

If minimum price (P_{min}) is above equilibrium:

Quantity supplied exceeds quantity demanded → surplus.
Governments may store or buy excess.

Graphing these requires careful identification:

If the control binds (i.e., is actually above/below equilibrium), effects appear.
If it doesn’t bind, there is no shortage/surplus effect.

2.7 Subsidies and Their Welfare Effects

A subsidy of (s) to producers:

Lowers effective cost to firms.
In many cases increases equilibrium quantity.
May cause inefficiency and fiscal burden.

For per-unit subsidy, consumer price may fall and producer price rise (net to firms plus subsidy). Welfare analysis again uses CS, PS, TR (government spending), and DWL.

2.8 Elasticity and Policy Evaluation

A high-scoring ECO2A policy explanation often references:

When demand is inelastic, tax increases raise revenue but DWL may still occur.
If demand is very elastic, the same tax causes a larger reduction in quantity, possibly reducing revenue but increasing DWL proportionally.

In exam answers, link elasticities to outcomes:

Tax incidence: depends on relative elasticities.
DWL magnitude: depends on how much quantity falls.
Revenue: peaks at some intermediate elasticity; could decline with large tax if quantity collapses.

Section 3: Consumer Theory and Choice Under Constraints (Utility, Demand, and Market Implications)

Consumer theory in ECO2A provides the microfoundations for demand. Instead of taking demand as given, you derive demand behaviour from preferences, budget constraints, and optimisation. Even when exams don’t fully require calculus, the logic of marginal trade-offs is essential.

3.1 Utility: Preferences and Rational Choice

Utility representation

Utility is a numerical way to represent preferences. What matters is ordering, not absolute utility levels.

Key preference properties:

Completeness: any two bundles can be compared.
Transitivity: if A preferred to B and B preferred to C, then A preferred to C.
Non-satiation: more is better (typically).

3.2 Indifference Curves and Marginal Rate of Substitution (MRS)

Indifference curves

An indifference curve shows combinations of goods that yield equal utility. Typical assumptions in ECO2A:

downward sloping (if both goods are desirable),
convex to the origin (diminishing MRS).

Marginal Rate of Substitution

MRS indicates how much of good Y a consumer gives up to gain one unit of good X while staying at the same utility.

In many exam questions:

MRS diminishes as consumption of X rises (convexity).

3.3 Budget Constraint and Opportunity Cost

With two goods, X and Y:
[
P_x X + P_y Y = I
]
where:

(P_x, P_y) are prices,
(I) is income.

Budget line intercepts:

(Y = I/P_y) when (X=0),
(X = I/P_x) when (Y=0).

Shifts:

Income changes → parallel shifts outward/inward.
A price change → rotation of budget line around one intercept.

3.4 Utility Maximisation: Tangency Condition

The consumer maximises utility at the point where:

the indifference curve is tangent to the budget line,
meaning:
[
MRS = \frac{P_x}{P_y}
]

Corner solutions

Not all problems involve tangency. If preferences include strong “corner” behaviour, optimum may occur where:

(X=0) or (Y=0).

ECO2A may ask you to identify whether optimum is interior or corner based on curve shapes.

3.5 From Choice to Demand

ECO2A often connects consumer optimisation to demand curves:

If price of good X changes, the tangency point changes.
The chosen bundle’s X component traces a demand relationship.

This provides microfoundations:

demand is the set of utility-maximising quantities at each price, holding income and other prices constant.

3.6 Deriving Demand from a Simple Utility Function (Exam-Relevant Pattern)

Sometimes ECO2A questions include a specific utility function (often Cobb-Douglas or perfect substitutes/compliments) and ask for demand.

Cobb-Douglas example

Let:
[
U(X,Y)=X^{a}Y^{b}
]
A standard result (when (a,b>0)) is that the optimal spending shares are constant:
[
P_x X = \frac{a}{a+b}I,\quad P_y Y = \frac{b}{a+b}I
]
This implies:

demand for X is proportional to income,
demand is inversely related to its price.

Perfect substitutes

If:
[
U(X,Y)=\alpha X + \beta Y
]
then consumer buys only the higher “effective price” option:

if (\alpha) relates to value, choose the good with better utility per rand.

Perfect complements

If:
[
U(X,Y)=\min{X,Y}
]
or (U(X,Y)=\min{X, kY}), the optimum occurs at a fixed ratio.

Exam answers need to describe the qualitative pattern even if algebra is limited:

substitutes → bang-bang corner,
complements → fixed-proportion bundle.

3.7 Income and Substitution Effects

When price changes, the total change in quantity demanded can be decomposed:

Substitution effect: consumer replaces away from the relatively more expensive good.
Income effect: the price change changes purchasing power.

For a normal good:

income effect reinforces substitution (quantity falls when price rises).
For an inferior good:
income effect may oppose substitution, creating unusual outcomes.

ECO2A may test:

Whether demand is likely to be upward sloping for an inferior good (Giffen-type reasoning, though the full Giffen case usually requires deeper assumptions).

3.8 Revealed Preference and Consistency (Conceptual Tool)

Some curricula include revealed preference:

if a bundle is chosen when it is affordable, then it must be at least as preferred as other bundles that were also affordable.
This supports the idea of consistent choice behaviour.

Even if not heavily mathematical, you might be asked to explain how observed choices can reveal underlying preferences.

3.9 Welfare Link: Consumer Surplus and Demand

Once demand is derived, consumer surplus can be interpreted:

CS depends on willingness to pay relative to market price.
Taxes and price controls reduce CS.

ECO2A thus integrates consumer theory with welfare results from earlier market analysis:

The same mechanism that shifts demand changes consumer surplus and deadweight loss.

Section 4: Production, Costs, and Firm Decisions (Cost Minimisation, Profit, and Supply)

Microeconomics becomes complete in ECO2A when we understand firms: how inputs are chosen, how costs are calculated, and how output decisions produce supply. This section emphasises the logic of cost curves, optimisation, and how market behaviour changes when assumptions about competition and market structure vary.

4.1 Production Functions and Technical Efficiency

A production function shows maximum output from inputs:
[
Q = f(L,K)
]
where (L) is labour and (K) is capital.

Key properties:

Diminishing marginal product: holding one input constant, adding more of the other eventually yields smaller additional output.
Returns to scale: increasing all inputs by a factor changes output by:
- increasing (increasing returns),
- same (constant returns),
- decreasing (decreasing returns).

Exam-ready interpretation:

diminishing marginal product typically affects short-run cost curves,
scale effects affect long-run average cost patterns.

4.2 Cost Minimisation and Isocost Lines

For input costs:
[
C = wL + rK
]
where (w) is wage, (r) is rental rate of capital.

An isocost line:
[
wL + rK = \bar{C}
]
is similar in geometry to a consumer budget constraint.

Cost minimisation chooses the combination of inputs that produces a target output at minimum cost. The tangency condition often uses:

marginal rate of technical substitution (MRTS) equals input price ratio:
[
MRTS = \frac{w}{r}
]

4.3 Short-Run vs Long-Run Costs

Short run

At least one input is fixed, commonly capital (K). This generates:

fixed costs: costs that do not vary with output (e.g., rent on a building).
variable costs: costs that change with output (e.g., labour).

Long run

All inputs are variable; fixed vs variable distinction disappears in a meaningful way. Firms can adjust scale to minimise average costs.

4.4 Cost Curves: FC, VC, TC, MC, and ATC

Common definitions:

Fixed cost: (FC)
Variable cost: (VC(Q))
Total cost: (TC(Q)=FC+VC(Q))
Average total cost:
[
ATC(Q) = \frac{TC(Q)}{Q}
]
Average variable cost:
[
AVC(Q) = \frac{VC(Q)}{Q}
]
Marginal cost:
[
MC(Q)=\frac{dTC}{dQ}
]
For discrete exam models, MC often comes from incremental cost:
[
MC \approx \frac{\Delta TC}{\Delta Q}
]

Relationship between curves (graph exam focus)

(MC) intersects (ATC) at its minimum.
(MC) below (ATC) implies (ATC) decreasing; (MC) above implies (ATC) increasing.
These relationships are central in cost-curve graph questions.

4.5 Economies and Diseconomies of Scale

In long-run analysis:

Economies of scale: as output increases, average cost falls.
Diseconomies of scale: average cost rises at high output.
Minimum efficient scale: output level where average cost is minimised.

Sources:

economies of specialisation,
bulk purchasing,
learning-by-doing (potentially),
managerial complexity (can cause diseconomies),
coordination constraints.

Exam questions may ask you to interpret a given ATC curve shape.

4.6 Profit Maximisation Under Perfect Competition

In perfect competition:

firms are price takers: (P) is given.
revenue functions:
- Total revenue: (TR(Q)=P\cdot Q)
- Marginal revenue: (MR=P)

Profit:
[
\pi(Q)=TR(Q)-TC(Q)
]

Profit maximisation rule:

Choose output where (MR = MC),
i.e.,
[
P = MC(Q)
]

Shutdown decision:

In the short run, a firm may shut down if price falls below average variable cost:
- If (P < AVC), produce 0 (avoid covering variable costs).

Exam answers must connect this to:

fixed costs being unavoidable in the short run,
variable costs being avoidable if output is zero.

4.7 Supply Curve from MC

In perfect competition, the firm’s supply curve is closely related to its marginal cost curve above the shutdown price:

supply exists where (P \ge AVC),
quantity supplied corresponds to where (P = MC).

Then market supply is the horizontal sum of individual firms’ supplies.

This link is important because later sections may use elasticity of supply and tax incidence, which depend on the supply curve.

4.8 Monopolistic and Oligopolistic Intuition (Preview)

Although full market structure analysis is often in later units, ECO2A typically introduces key intuition:

In monopoly, the firm faces a downward-sloping demand and chooses where (MR=MC) but (MR<P).
In monopolistic competition, firms have some market power but still many firms exist.
In oligopoly, strategic interaction arises.

Even if exam questions are primarily competitive in focus, understanding how market power changes the (MR)-(P) relationship helps interpret graphs.

4.9 Cost and Policy: Taxes, Subsidies, and Efficiency

Production theory connects to policy analysis:

Per-unit taxes raise effective marginal costs (shift MC up).
Subsidies lower marginal costs (shift MC down).

In competitive markets, these change equilibrium quantity and prices (consumer and producer sides). Thus cost curves are the micro foundation behind earlier incidence and welfare results.

Section 5: Market Structures, Firm Behaviour, and Policy Outcomes (Efficiency, Competition, and Strategic Logic)

ECO2A’s concluding part usually ties together consumer behaviour, production, and welfare outcomes under different market structures and interventions. Students often struggle here because it requires both graph discipline and conceptual clarity about market power, equilibrium conditions, and efficiency.

5.1 Perfect Competition: Efficiency and Allocative Outcomes

In perfect competition (with no externalities and complete information), the market can achieve:

allocative efficiency: price equals marginal cost ((P=MC)).
productive efficiency: in the long run, price equals minimum average total cost under typical assumptions.

To show allocative efficiency:

For the firm: profit maximisation gives (P=MC).
For the market: supply from firms aggregates MC relationships, resulting in the efficient quantity.

Consumer and producer surplus maximisation (welfare intuition)

In a competitive equilibrium, total surplus is maximised given the demand and supply constraints. Taxes reduce surplus due to DWL.

5.2 Monopoly: Market Power, Pricing, and Welfare Loss

In monopoly:

The firm chooses price and quantity.
Demand is downward sloping, so MR is below price.
Profit maximisation: choose (Q_m) where (MR=MC), then read price from demand at that quantity.

Consequences:

Monopoly quantity is lower than competitive quantity ((Q_m < Q_c)).
Monopoly price is higher ((P_m > P_c)).
There is deadweight loss because trades between willing buyers and sellers at the margin do not occur.

Exam structure for monopoly questions

A typical marks allocation:

Identify profit-maximising condition: (MR=MC).
Determine (Q_m) and associated price (P_m) from demand.
Compare to competitive outcome using (P=MC) and/or (Q_c).
Explain welfare:
- CS decreases,
- PS may increase or decrease depending on cost and shape,
- DWL exists due to reduced output.

5.3 Monopolistic Competition: Differentiation and Long-Run Zero Economic Profit

Monopolistic competition:

many firms,
differentiated products,
downward-sloping demand for each firm.

Long-run equilibrium in standard models:

entry drives economic profit to zero,
firms still operate with some excess capacity (ATC above minimum and demand does not touch the bottom of ATC).

In exams, key points:

differentiation gives variety (consumer benefit),
inefficiency relative to perfect competition due to excess capacity (cost for variety).

5.4 Oligopoly and Strategic Behaviour (Key Concepts)

Oligopoly has:

few firms,
interdependence: each firm’s output/pricing affects others.

Even if ECO2A doesn’t require heavy game theory, you may see qualitative questions:

Why firms may not undercut prices aggressively?
Why mergers may reduce output and increase price?
How non-cooperative behaviour leads to outcomes different from monopoly or competition?

If formal game theory appears, the most common exam-level items are:

Nash equilibrium,
best-response logic,
potentially prisoners’ dilemma style comparisons between cooperation and competition.

5.5 Collusion vs Competition: Impact on Prices and Output

Collusion among firms in an oligopoly can approximate monopoly:

output reduced,
prices higher,
welfare loss similar in direction to monopoly.

If collusion breaks down, firms may compete more aggressively, raising output and reducing prices.

Even without numbers, exam answers should:

describe incentives to deviate from collusion (cheat for higher profit),
mention enforcement challenges.

5.6 Externalities and Market Failure (Policy Motivation)

If markets involve externalities, equilibrium may be inefficient:

positive externality: market underproduces.
negative externality: market overproduces.

Standard policy tools:

taxes for negative externalities (corrective taxes),
subsidies for positive externalities.

ECO2A may connect externalities to marginal social cost/benefit:

efficient condition requires (MSC = MSB),
whereas private equilibrium satisfies only (MPB = MPC) (marginal private benefit equals marginal private cost).

5.7 Taxes in Monopoly vs Competition (Comparative Insights)

Taxes operate differently depending on market power, but the welfare logic remains:

Taxes usually create DWL by reducing quantity relative to efficient levels.
Incidence depends on elasticity, but with monopoly, the demand faced by the firm already reflects its market power.

Exam-quality response includes:

show condition changes (firm’s MR and MC intersection shifts under taxes),
explain how price and quantity adjust on both consumer and firm sides.

5.8 Pricing Policies and Regulation: Anticipating Exam Questions

South African economics exams often ask policy-oriented questions grounded in welfare analysis. Even when regulations are not fully modelled, the exam expects a logic of:

regulation aims to reduce market power harm,
but can introduce compliance costs and distortions.

Examples of regulation mechanisms in micro models:

price caps,
marginal cost pricing (theoretical),
profit regulation or utility-style rate-of-return regulation (conceptual).

A strong exam answer should always connect regulation to:

efficiency (reducing DWL),
equity (who bears costs),
practicality (information and enforcement problems).

5.9 Worked Integrated Scenario: Applying ECO2A Tools to an Exam-Style Problem

To unify the course content, consider a full micro scenario commonly seen in exams: a market for a good (like basic household energy or a durable good), where costs and policy change.

Scenario

A competitive industry produces a good with the following linear demand and supply:

Demand: (Q_d = 120 – 4P)
Supply (before policy): (Q_s = -20 + 5P)

Find the competitive equilibrium.
Introduce a per-unit tax of (t = 5).
Compute the new equilibrium consumer price and producer price.
Determine the quantity change.
Interpret incidence and welfare direction (CS, PS, TR, DWL).

Step 1: Initial equilibrium

Set (Q_d = Q_s):
[
120 – 4P = -20 + 5P
\Rightarrow 140 = 9P
\Rightarrow P^* = \frac{140}{9} \approx 15.56
]
Quantity:
[
Q^* = 120 – 4\left(\frac{140}{9}\right)
= 120 – \frac{560}{9}
= \frac{1080 – 560}{9}
= \frac{520}{9}
\approx 57.78
]

Step 2: Tax and equilibrium

Tax wedge (t=5) means:
[
P_c = P_p + 5
]
Supply in terms of producer price:
[
Q_s = -20 + 5P_p = -20 + 5(P_c – 5)= -20 + 5P_c – 25 = 5P_c – 45
]
Equilibrium:
[
120 – 4P_c = 5P_c – 45
\Rightarrow 165 = 9P_c
\Rightarrow P_c = \frac{165}{9} = 18.33
]
Producer price:
[
P_p = P_c – 5 = 13.33
]
Quantity:
[
Q_{tax} = 120 – 4(18.33)=120 – 73.32=46.68 \ (\text{approx})
]

Step 3: Incidence interpretation

Consumer price rises from (15.56) to (18.33) (increase ~ (+2.77)).
Producer price falls from (15.56) to (13.33) (decrease ~ (-2.23)).
Total tax (5) is split between consumers and producers: the difference (P_c – P_p = 5) holds.

In incidence terms:

The side with more inelastic demand/supply bears relatively more.

Step 4: Welfare direction

Even without full numerical CS/PS computation, we know:

CS decreases: consumers pay higher price and buy less.
PS decreases: firms receive lower net price and sell less.
TR increases at rate (t \times Q_{tax}), partially offsetting losses.
DWL exists because quantity falls below efficient trade levels.

Step 5: Exam-quality narrative conclusion

A per-unit tax reduces quantity from approximately (57.78) to (46.68), increasing consumer prices and lowering producer net receipts. The tax burden is shared between consumers and producers depending on demand and supply elasticities. Total surplus falls by the deadweight loss, with part of the surplus lost going to government as tax revenue.

This integrated scenario reflects the exact skills ECO2A exams test: equilibrium solving, tax wedge reasoning, incidence interpretation, and welfare logic.

5.10 Summary of High-Yield ECO2A Exam Techniques

Across all sections, success in ECO2A typically depends on mastering repeatable procedures:

Equilibrium: set (Q_d = Q_s).
Tax wedge: (P_c = P_p + t).
Elasticity: interpret magnitude (|\varepsilon|) and connect to policy incidence.
Welfare: compute or explain changes in CS, PS, TR, DWL.
Consumer choice: apply tangency (MRS = P_x/P_y) or identify corner solutions.
Firm choice: apply profit maximisation and shutdown:
- competitive: (P=MC),
- shutdown: produce only if (P \ge AVC).
Market power:
- monopoly: (MR=MC) with (MR<P),
- competition: (P=MC) and efficiency properties hold under standard assumptions.

Final Checklist (What to Practise Before Your ECO2A Test/Exam)

To prepare for typical ECO2A question styles (including those common in South African university assessment patterns), practise:

Four types of shifts (demand up/down; supply up/down) and predict direction of changes.
Arc elasticity calculations with averages.
Tax problems with full wedge logic:
- compute (P_c), (P_p), and (Q_{tax}),
- state who bears more of the tax and why.
Welfare diagrams:
- identify CS/PS/TR areas,
- explain DWL with quantity reduction.
Consumer optimisation:
- budget constraint, indifference curves, tangency and corners.
Firm optimisation:
- identify short-run shutdown,
- relate (MC) and (ATC) minima.
Market structure comparison:
- perfect competition vs monopoly welfare and output differences.

With these methods, ECO2A becomes less about memorisation and more about reliable microeconomic reasoning—exactly what exams reward.