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Midpoint Method Formula
E = (ΔQ / Qavg) ÷ (ΔX / Xavg)
ΔQ = Q2 − Q1 |
Qavg = (Q1 + Q2) / 2
ΔX = X2 − X1 | Xavg = (X1 + X2) / 2
ΔX = X2 − X1 | Xavg = (X1 + X2) / 2
Model Assumptions
- Demand/supply curves are locally linear between the two observed points
- All other factors held constant (ceteris paribus)
- Midpoint method gives a direction-independent elasticity estimate
- Midpoint averages prevent endpoint bias
For educational purposes. Not financial advice. Market conventions simplified.
Calculation Result
Elasticity Coefficient
−1.22
Elastic
|E| (Absolute)
1.22
Classification
Elastic
% Δ Quantity
−22.22%
% Δ Price
18.18%
Total Revenue Test
Price increase → Revenue decreases
TR1 = $1,000.00 →
TR2 = $960.00
Good Classification
Normal Good
Formula Breakdown
PED = [(Q2 − Q1) / Qavg] ÷ [(P2 − P1) / Pavg]
All four elasticity types use the midpoint method
Elasticity Classification
| Classification | |E| Value | Interpretation |
|---|---|---|
| Perfectly Inelastic | = 0 | No response to price |
| Inelastic | 0 < |E| < 1 | Weak response |
| Unit Elastic | = 1 | Proportional response |
| Elastic | |E| > 1 | Strong response |
| Perfectly Elastic | = ∞ | Infinite response |
| Inferior Good | YED < 0 | Demand falls as income rises |
| Neutral Good | YED ≈ 0 | Income has no effect on demand |
| Normal Good | 0 < YED ≤ 1 | Demand rises with income |
| Luxury Good | YED > 1 | Demand rises faster than income |
| Complements | XED < 0 | Price B↑ → Demand A↓ |
| Unrelated Goods | XED ≈ 0 | No cross-price relationship |
| Substitutes | XED > 0 | Price B↑ → Demand A↑ |
Understanding Price Elasticity of Demand
What Is Price Elasticity of Demand?
Price elasticity of demand (PED) measures how sensitive the quantity demanded of a good is to a change in its price. A higher absolute elasticity means consumers respond more strongly to price changes. The midpoint method produces a consistent elasticity value regardless of whether price rises or falls.
Midpoint Method Formula
PED = [(Q2 − Q1) / ((Q2 + Q1) / 2)] ÷ [(P2 − P1) / ((P2 + P1) / 2)]
Source: Mankiw, Principles of Microeconomics, Ch. 5
Source: Mankiw, Principles of Microeconomics, Ch. 5
The Total Revenue Test
The total revenue test reveals how a price change affects a firm's revenue depending on elasticity:
- Elastic demand (|PED| > 1): Price increase → total revenue falls; price decrease → revenue rises.
- Inelastic demand (|PED| < 1): Price increase → total revenue rises; price decrease → revenue falls.
- Unit elastic (|PED| = 1): Price changes leave total revenue unchanged.
Determinants of Elasticity
Several factors determine whether demand is elastic or inelastic:
- Availability of substitutes: More substitutes → more elastic.
- Necessities vs. luxuries: Necessities tend to be inelastic; luxuries elastic.
- Time horizon: Demand becomes more elastic over longer time periods as consumers adjust.
- Share of budget: Goods taking a larger share of income tend to be more elastic.
Mankiw Verification Example: Ice cream priced at $2.00 (Q = 10) rises to $2.20 (Q = 8).
PED = (−2/9) ÷ (0.20/2.10) = −22.2% ÷ 9.52% = −2.33 (Elastic)
PED = (−2/9) ÷ (0.20/2.10) = −22.2% ÷ 9.52% = −2.33 (Elastic)
Key Assumptions
- Demand/supply curves are locally linear between two observed data points
- All other factors (income, preferences, related goods) held constant (ceteris paribus)
- Midpoint method removes directional bias in arc elasticity calculations
- Results are point estimates for the arc between two price–quantity pairs
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Frequently Asked Questions
Price elasticity of demand (PED) measures how sensitive the quantity demanded of a good is to a change in its price. Specifically, it is the percentage change in quantity demanded divided by the percentage change in price. It matters because it tells businesses how a price change will affect their revenue: if demand is elastic (|PED| > 1), raising the price reduces revenue; if inelastic (|PED| < 1), raising the price increases revenue. Governments also use PED to predict the impact of taxes on consumption.
The midpoint method formula is: PED = [(Q2 − Q1) / ((Q2 + Q1) / 2)] ÷ [(P2 − P1) / ((P2 + P1) / 2)]. It uses the average of the two quantities and prices as the base, making the result the same regardless of the direction of the change. For example, using Mankiw's ice cream example: price rises from $2.00 to $2.20 and quantity falls from 10 to 8 cones. PED = (−22.2%) / (9.52%) = −2.33, which is elastic.
Demand is elastic when |PED| > 1, meaning consumers are highly responsive to price changes — a 1% price increase leads to more than a 1% drop in quantity demanded. Demand is inelastic when |PED| < 1, meaning consumers are less responsive — a 1% price increase leads to less than a 1% drop in quantity. Unit elastic demand (|PED| = 1) means the percentage changes are exactly equal. Goods with many close substitutes and luxury items tend to be elastic; necessities and goods with few substitutes tend to be inelastic.
The total revenue test shows how a price change affects total revenue (TR = P × Q) depending on the price elasticity of demand. If demand is elastic (|PED| > 1): a price increase reduces TR because the percentage drop in quantity exceeds the percentage rise in price. If demand is inelastic (|PED| < 1): a price increase raises TR. If demand is unit elastic (|PED| = 1): TR remains unchanged. This test is a practical shortcut for firms deciding whether to raise or lower prices.
Cross-price elasticity of demand (XED) measures how the quantity demanded of one good (Good A) responds to a change in the price of another good (Good B). XED = % change in Qty of A ÷ % change in Price of B. A positive XED means the goods are substitutes (e.g., butter and margarine): as the price of B rises, consumers switch to A. A negative XED means the goods are complements (e.g., cars and gasoline): as the price of B rises, demand for A also falls. An XED near zero indicates the goods are unrelated.
Income elasticity of demand (YED) measures how the quantity demanded of a good changes as consumer income changes, calculated as % change in Quantity ÷ % change in Income. Normal goods have YED > 0 (demand rises with income). Luxury goods have YED > 1 (demand rises faster than income — e.g., vacations, fine dining). Inferior goods have YED < 0 (demand falls as income rises — e.g., generic brands when consumers switch to premium ones). Normal necessities fall between 0 and 1.
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Disclaimer
This calculator is for educational purposes only. Results are based on the midpoint arc elasticity formula between two observed price-quantity pairs. Real-world demand and supply relationships may be nonlinear and are influenced by many factors not captured here. This tool should not be used for business, investment, or policy decisions.
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