Resources | Subject Notes | Economics
This section explores how the price elasticity of demand (PED) changes along a straight-line demand curve. Understanding this variation is crucial for analyzing the impact of price changes on quantity demanded.
Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. It is calculated as:
$$PED = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}$$
The value of PED indicates the degree of responsiveness:
The elasticity of demand is not constant across all points on a demand curve. On a straight-line demand curve, the elasticity changes as you move up or down the curve.
Consider a typical straight-line demand curve with a negative slope. At lower price levels, the quantity demanded is relatively sensitive to price changes, indicating elastic demand. As the price falls to lower levels, the quantity demanded becomes less sensitive, indicating inelastic demand. Conversely, at higher price levels, a price change has a smaller impact on quantity demanded, again indicating inelastic demand.
A linear demand curve is often represented by the equation:
$$Q = a - bP$$
where:
The price elasticity of demand at a specific point on the curve can be calculated using the following formula:
$$PED = \frac{dQ/Q}{dP/P} = \frac{dQ/dP}{P/Q}$$
Substituting the demand equation into this formula gives:
$$PED = \frac{-b}{a - bP} \times \frac{dP}{dQ}$$
Since $dQ/dP = -\frac{a}{b}$, we can substitute this back:
$$PED = \frac{-b}{a - bP} \times \left(-\frac{a}{b}\right) = \frac{a}{a - bP}$$
This formula shows that the elasticity of demand at any point on the linear demand curve depends on the current price (P) and the intercept (a) and slope (b) of the curve.
Let's consider a linear demand curve with the equation $Q = 100 - 2P$:
| Price (P) | Quantity Demanded (Q) | PED |
|---|---|---|
| 0 | 100 | $$ \frac{100}{100} = 1 $$ |
| 10 | 80 | $$ \frac{20}{80} = 0.25 $$ |
| 20 | 60 | $$ \frac{40}{60} = 0.67 $$ |
| 30 | 40 | $$ \frac{60}{40} = 1.5 $$ |
As the price increases from £0 to £10, the elasticity of demand is relatively inelastic (0.25). However, as the price increases further to £20 and £30, the elasticity becomes more elastic (0.67 and 1.5 respectively). This demonstrates the variation in PED along the straight-line demand curve.
The price elasticity of demand is not constant but varies along a straight-line demand curve. It is generally more elastic at lower price levels and more inelastic at higher price levels. This variation is a fundamental concept in microeconomics and has significant implications for businesses when making pricing decisions.