Consumer Surplus, Elasticity and Production
(Exam-Ready Study Guide)
This lecture covers three main areas:
1. Consumer surplus
2. Elasticities of demand
3. Production theory
PART 1 — Consumer Surplus
Definition
Consumer Surplus is the difference between:
• the maximum price a consumer is willing to pay
• the actual price paid in the market
It measures consumer welfare (benefit consumers receive from trade).
Graphical Interpretation
Consumer surplus equals:
The area under the demand curve and above the market price.
If price falls:
• consumers pay less
• consumer surplus increases.
Formula for Change in Consumer Surplus
When price changes, the change in consumer surplus is:
Change in CS = −½ × (P₂ − P₁) × (Q₁ + Q₂)
Where:
P₁ = original price
P₂ = new price
Q₁ = original quantity
Q₂ = new quantity
The formula comes from calculating the area of a trapezoid under the demand curve.
Example
Willingness to pay = R15 000
Actual price = 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
The result is positive because price decreased, increasing consumer welfare.
, PART 2 — Price Elasticity of Demand (PED)
Definition
Price elasticity of demand measures:
How responsive quantity demanded is to a change in price.
Basic Formula
PED = (%ΔQ) / (%ΔP)
Where:
%ΔQ = percentage change in quantity demanded
%ΔP = percentage change in price
Arc Elasticity (Midpoint Formula)
Used when price changes significantly 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 to measure elasticity at a specific point on the demand curve.
PED = (dQ / dP) × (P / Q)
Interpretation of PED
Value of PED Interpretation
PED > 1 Elastic demand
PED = 1 Unitary elastic
PED < 1 Inelastic demand
PED = 0 Perfectly inelastic (vertical demand curve)
PED → ∞ Perfectly elastic (horizontal demand curve)
(Exam-Ready Study Guide)
This lecture covers three main areas:
1. Consumer surplus
2. Elasticities of demand
3. Production theory
PART 1 — Consumer Surplus
Definition
Consumer Surplus is the difference between:
• the maximum price a consumer is willing to pay
• the actual price paid in the market
It measures consumer welfare (benefit consumers receive from trade).
Graphical Interpretation
Consumer surplus equals:
The area under the demand curve and above the market price.
If price falls:
• consumers pay less
• consumer surplus increases.
Formula for Change in Consumer Surplus
When price changes, the change in consumer surplus is:
Change in CS = −½ × (P₂ − P₁) × (Q₁ + Q₂)
Where:
P₁ = original price
P₂ = new price
Q₁ = original quantity
Q₂ = new quantity
The formula comes from calculating the area of a trapezoid under the demand curve.
Example
Willingness to pay = R15 000
Actual price = 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
The result is positive because price decreased, increasing consumer welfare.
, PART 2 — Price Elasticity of Demand (PED)
Definition
Price elasticity of demand measures:
How responsive quantity demanded is to a change in price.
Basic Formula
PED = (%ΔQ) / (%ΔP)
Where:
%ΔQ = percentage change in quantity demanded
%ΔP = percentage change in price
Arc Elasticity (Midpoint Formula)
Used when price changes significantly 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 to measure elasticity at a specific point on the demand curve.
PED = (dQ / dP) × (P / Q)
Interpretation of PED
Value of PED Interpretation
PED > 1 Elastic demand
PED = 1 Unitary elastic
PED < 1 Inelastic demand
PED = 0 Perfectly inelastic (vertical demand curve)
PED → ∞ Perfectly elastic (horizontal demand curve)
