Summary Consumer Surplus, Elasticity & Production EXAM NOTES | Cost Curves & Profit Maximisation

Consumer Surplus, Elasticity & Production
Exam-Ready Study Guide
This lecture combines consumer theory and firm theory.
You must understand three main areas:
Consumer surplus
Elasticities of demand
Production and profit maximization


PART 1 — Consumer Surplus
Definition
Consumer surplus is the extra benefit consumers receive when they pay less than what they were
willing to pay.
Consumer surplus =
• willingness to pay
• minus actual price paid
It measures consumer welfare.


Graphical Meaning
Consumer surplus equals:
Area under the demand curve and above the market price
If price decreases:
• more units are bought
• consumers pay less
• consumer surplus increases


Formula for Change in Consumer Surplus
When price changes:

Change in CS = −½ × (P₂ − P₁) × (Q₁ + Q₂)
Where:

P₁ = original price
P₂ = new price
Q₁ = original quantity
Q₂ = new quantity


Example
Price falls from R15 000 to R10 000
Quantity increases:
Q₁ = 10
Q₂ = 20
Calculation:
Change in CS = −½ × (10 000 − 15 000) × (10 + 20)
Change in CS = −½ × (−5000) × 30
Change in CS = 75 000
Consumer surplus increased by R75 000.

, PART 2 — Price Elasticity of Demand (PED)
Definition
Price elasticity measures:
how responsive quantity demanded is to price changes


Basic Formula
PED = (%ΔQ) / (%ΔP)
Where:

%ΔQ = percentage change in quantity
%ΔP = percentage change in price


Arc Elasticity (Midpoint Formula)
Used when price changes between two points.

PED = (ΔQ / ΔP) × (P̄ / Q̄ )
Where:

ΔQ = Q₂ − Q₁
ΔP = P₂ − P₁
P̄ = (P₂ + P₁) / 2
Q̄ = (Q₂ + Q₁) / 2


Point Elasticity
Used when measuring elasticity at a specific point on the demand curve.

PED = (dQ / dP) × (P / Q)


Interpretation of PED
PED Value Meaning
PED > 1 Elastic demand
PED = 1 Unitary elasticity
PED < 1 Inelastic demand
Special cases:
Perfectly inelastic → vertical demand curve
Perfectly elastic → horizontal demand curve