The meaning and calculation of price elasticity of supply

Price elasticity of supply (PES) measures how responsive the quantity supplied of a good or service is to a change in its price. It reflects the positive relationship between price and quantity supplied, as outlined in the law of supply, meaning PES is always a positive value.

Formula for calculating PES

$\text{PES}=\frac{\%\mathrm{\Delta }{\text{Q}}_{\text{s}}}{\%\mathrm{\Delta }\text{P}}$

Where:

• %ΔQ_s = Percentage change in quantity supplied
• %ΔP = Percentage change in price

This can also be expressed using actual values as:

$\text{PES}=\frac{({\text{Q}}_2-{\text{Q}}_1)}{({\text{P}}_2-{\text{P}}_1)}\times \frac{{\text{P}}_1}{{\text{Q}}_1}$

Where:

• Q₁ = Initial quantity supplied
• Q₂ = New quantity supplied
• P₁ = Initial price
• P₂ = New price

PES values range from zero to infinity.

Worked example - Calculating price elasticity of supply

A firm supplies 400 units of a product at a price of £20 per unit. When the price rises to £22 per unit, the quantity supplied increases to 480 units. Calculate the PES.

Step 1: Identify the values

• Q₁ = 400 units
• Q₂ = 480 units
• P₁ = £20
• P₂ = £22

Step 2: Apply the PES formula

$\text{PES}=\frac{(480-400)}{(22-20)}\times \frac{20}{400}$

Step 3: Perform the calculation

$\text{PES}=\frac{80}{2}\times \frac{20}{400}=40\times 0.05=2.0$

Step 4: Interpretation

A PES of 2.0 indicates that supply is price elastic, as the percentage change in quantity supplied is greater than the percentage change in price.

Different values of PES and their meanings

The value of PES indicates the degree of responsiveness of supply to price changes.

Categories of PES values

• Price elastic supply (PES > 1) - The percentage change in quantity supplied is greater than the percentage change in price.
• Price inelastic supply (0 < PES < 1) - The percentage change in quantity supplied is smaller than the percentage change in price.
• Unit elastic supply (PES = 1) - The percentage change in quantity supplied equals the percentage change in price.
• Perfectly elastic supply (PES → ∞) - A small change in price leads to an infinitely large change in quantity supplied.
• Perfectly inelastic supply (PES = 0) - A change in price results in no change in quantity supplied.

Shapes of supply curves based on PES

The shape of a supply curve visually represents the PES value, showing how quantity supplied changes with price.

Characteristics of supply curves by PES value

• Price elastic supply - The curve is relatively flat and must intersect the vertical axis.
• Price inelastic supply - The curve is steep and must intersect the horizontal axis.
• Unit elastic supply - The curve passes through the origin.
• Perfectly elastic supply - The curve is a straight horizontal line.
• Perfectly inelastic supply - The curve is a straight vertical line.

Time periods and their impact on PES

In economics, time is divided into distinct periods that affect how easily suppliers can adjust output, influencing PES. Supply generally becomes more elastic over longer timeframes as more adjustments become possible.

Time periods in relation to PES

• Momentary run (market period) - All factors of production are fixed, with no adjustments possible, resulting in perfectly inelastic supply (PES = 0).
• Short run - At least one factor of production is fixed (e.g., capital), but some adjustments can occur, leading to price inelastic supply (0 < PES < 1).
• Long run - All factors of production are variable, allowing full adjustments, which makes supply price elastic (PES > 1).

Factors influencing price elasticity of supply

Several factors determine how elastic supply is, affecting how quickly and easily firms can respond to price changes.

Key factors affecting PES

• Time available - Supply becomes more elastic over time as firms can make greater adjustments.
• Mobility of labour - If labour is occupationally or geographically immobile, supply is more inelastic.
• Spare capacity - Firms with unused production facilities can increase output easily when prices rise, leading to more elastic supply.
• Labour skill requirements - Industries needing unskilled labour have more elastic supply, as workers are easier to find compared to those requiring specialised skills.
• Storage capability - Goods that can be stored have more elastic supply than perishable items.
• Production time lags - Short production processes result in more elastic supply than lengthy ones.
• Cost structure - Industries where marginal costs rise quickly with increased output tend to have more inelastic supply.
• Type of product - Primary commodities generally have lower PES than manufactured products due to longer production times.