A curve's angle is not its elasticity.
Slope compares changes in measured units; elasticity compares percentage changes. A straight demand line can have constant slope but different elasticities in different regions because price and quantity bases change. A straight supply ray through the origin has unit PES wherever positive price and quantity make the ratio defined, whatever its angle. Changing axis units changes a curve's visual angle without changing the economic relationship. Horizontal and vertical curves are limiting models, and a straight demand line is not unit elastic throughout. Always use the relationship and stated comparison, not an unlabeled steepness shortcut.
- Slope
- Slope compares changes in axis units; elasticity compares percentage changes. The same number of units can be a small percentage of a large quantity or a large percentage of a small one.
- Straight demand
- A straight demand line can have the same slope throughout but different PED values because the price and quantity bases change.
- Supply through the origin
- Qs means quantity supplied and P means price. In Qs = kP, k is a fixed positive multiplier. The line starts at the origin, where P = 0 and Qs = 0. At positive values, price and quantity change by the same percentage, so PES = 1.
Limiting demand cases
Perfectly inelastic
On a vertical demand curve, quantity demanded does not change when price changes. PED is zero in this model.
Perfectly elastic
In this limiting model, buyers will not pay more than the stated price. Quantity can vary at that price, so the curve is horizontal. This is not a normal data calculation with a zero denominator.
Constant unit elastic
A relationship such as Q = 120/P keeps P x Q at 120 for positive prices. Its curve is not a straight downward line.
Visual comparisons
Comparing flatter and steeper curves can be useful at a common point on the same axes, but an angle by itself cannot establish an elasticity category.
| Interval | Price change | Quantity change | Midpoint PED |
|---|---|---|---|
| P4 to P6; Q160 to Q140 | 40% | -13.33% | About -0.33 |
| P14 to P16; Q60 to Q40 | 13.33% | -40% | -3 |
Worked example: Two intervals on the same straight demand curve
Demand is Qd = 200 - 10P: Qd means quantity demanded and P means price. Quantity is units per week and price is dollars per unit. Use midpoint percentages for both intervals.
- At P = 4, Q = 160; at P = 6, Q = 140. The price change is 40% of the midpoint price 5, and the quantity change is about -13.33% of midpoint quantity 150. PED is about -0.33.
- At P = 14, Q = 60; at P = 16, Q = 40. Price changes by about 13.33% and quantity by -40%. PED is -3.
- Both intervals lose 20 units for a $2 rise, so the slope is identical. Yet one interval is inelastic and the other elastic.
- For supply Qs = 5P, doubling price from 2 to 4 doubles quantity from 10 to 20. Both rise by 100% using original bases, so PES = 100/100 = 1. Qs = 20P also has equal percentage changes and unit PES, despite its different angle.
Watch out for this
A flatter-looking line is always more elastic than a steeper-looking line.
Visual comparison needs common axes, units and a comparable price-quantity position. In general, calculate proportional responsiveness rather than judging the angle.
Check your understanding
Two straight supply curves are Qs = 4P and Qs = 12P, for positive P. Which statement is correct?
- The second must be more elastic because its quantity change per dollar is larger.
- Both have unit PES.
- Both have PES zero because they are straight.