BUSS1040 · Economics For Business Decision Making
Market Equilibrium, Welfare & Elasticity
Topic 4 solves for the competitive equilibrium (set Qd = Qs for P* and Q*), measures the welfare it generates as consumer + producer surplus, and then asks how responsive quantities are with elasticity. Elasticity is the workhorse: the point method εd = (dQ/dP)(P/Q), the arc/midpoint method, and the cross-price and income variants that classify goods. It is examined as full short-answer calculation — find P*/Q*, compute a surplus triangle, and evaluate an elasticity, often with the total-revenue interpretation.
What this chapter covers
- 011. Competitive equilibrium: set Qd = Qs (or Pd = Ps) and solve for P*, Q*
- 022. Consumer surplus (CS): area below demand, above price
- 033. Producer surplus (PS): area above supply, below price; total surplus = CS + PS
- 044. Total surplus is maximised at the competitive equilibrium
- 055. Point price-elasticity of demand: εd = (dQ/dP)(P/Q); for P = a − bQ, εd = −(1/b)(P/Q)
- 066. Arc / midpoint elasticity using average price and quantity
- 077. Elastic |ε|>1, inelastic |ε|<1, unit |ε|=1; the total-revenue test
- 088. Cross-price elasticity (substitutes/complements) and income elasticity (normal/inferior/luxury)
Equilibrium, consumer surplus and point elasticity
- 2 marksSet demand = supply: 60 − 2Q = 4Q ⇒ 60 = 6Q ⇒ Q* = 10, and P* = 4(10) = 40.
- 2 marksConsumer surplus is the triangle under demand above the price. The demand choke price (Q = 0) is 60, so CS = ½ × (60 − 40) × 10 = ½ × 20 × 10 = 100.
- 2 marksFor elasticity, invert demand: Q = (60 − P)/2 ⇒ dQ/dP = −1/2. Then εd = (dQ/dP)(P/Q) = (−1/2)(40/10) = −2.
- 1 markInterpret: |εd| = 2 > 1, so demand is elastic at the equilibrium — a 1% price rise reduces quantity demanded by about 2%, so a price cut would raise total revenue.
Key terms
- Consumer surplus (CS)
- The gain to buyers: the area below the demand curve and above the price paid, up to the quantity traded. For a linear demand it is the triangle ½ × (choke price − P) × Q.
- Producer surplus (PS)
- The gain to sellers: the area above the supply curve and below the price received, up to the quantity traded. Total surplus = CS + PS, and it is maximised at the competitive equilibrium.
- Point price elasticity of demand
- εd = (dQ/dP)(P/Q), measuring the % change in quantity demanded per % change in price at a point. For linear demand P = a − bQ, dQ/dP = −1/b, so εd = −(1/b)(P/Q).
- Arc (midpoint) elasticity
- Elasticity between two points using averages: [(Q₂ − Q₁)/((Q₁ + Q₂)/2)] ÷ [(P₂ − P₁)/((P₁ + P₂)/2)]. Used when the question gives two price-quantity pairs rather than a point.
- Total-revenue test
- If a price rise raises total revenue, demand is inelastic (|ε| < 1); if a price rise lowers total revenue, demand is elastic (|ε| > 1); if TR is unchanged, demand is unit-elastic (|ε| = 1).
- Cross-price and income elasticity
- Cross-price εxy = %ΔQx/%ΔPy: positive ⇒ substitutes, negative ⇒ complements. Income εI = %ΔQ/%ΔI: >1 luxury, between 0 and 1 normal necessity, <0 inferior good.
Market Equilibrium, Welfare & Elasticity FAQ
How do I compute consumer and producer surplus quickly?
Find the equilibrium P* and Q* first. Consumer surplus is the triangle below demand and above P*: ½ × (demand choke price − P*) × Q*. Producer surplus is the triangle above supply and below P*: ½ × (P* − supply intercept) × Q*. If a curve is not linear, the area may not be a triangle, but in BUSS1040 the curves are linear, so the ½ × base × height formula does the job. Always identify the choke price / intercept by setting Q = 0.
Point elasticity or arc elasticity — which do I use?
Use the point method when the question gives you a single price-quantity point (or a curve and a point on it): εd = (dQ/dP)(P/Q). Use the arc/midpoint method when the question gives you two distinct price-quantity pairs and asks for elasticity 'between' them — it averages the base, so you get the same answer regardless of which point you call the start. Mixing them up, or using endpoint values instead of averages in the arc formula, is a common error.
What is the link between elasticity and total revenue?
Total revenue = P × Q. If demand is elastic (|ε| > 1), quantity reacts more than proportionally, so raising price LOWERS total revenue (and cutting price raises it). If demand is inelastic (|ε| < 1), quantity barely moves, so raising price RAISES total revenue. At unit elasticity (|ε| = 1) total revenue is at its maximum and unchanged by small price moves. This is the intuition behind monopoly pricing in Topic 6.
How is Topic 4 examined?
As a multi-part short-answer: solve for equilibrium (Qd = Qs), compute a surplus area (CS, PS or total surplus), and evaluate an elasticity (point, arc, cross-price or income), usually with a one-line interpretation. Classifying goods from an elasticity sign (substitute/complement, normal/inferior/luxury) is a favourite MCQ. The surplus triangles also become the deadweight-loss measures used in Topics 6 and 9.
Exam move
Lock a fixed routine: equilibrium first (Qd = Qs → P*, Q*), then welfare (draw the curves, mark the choke prices, compute CS and PS as ½ × base × height), then elasticity (point or arc) with a one-sentence interpretation. For elasticity, memorise εd = (dQ/dP)(P/Q) and the shortcut −(1/b)(P/Q) for a linear demand, and always keep the negative sign before judging |ε| against 1. Practise the classification reflexes — sign of cross-price (substitute vs complement) and size/sign of income elasticity (inferior/normal/luxury) — because they are quick MCQ marks. Finally, connect elasticity to the total-revenue test now; it is the bridge to monopoly pricing in Topic 6 and saves you re-learning the same idea later.
