# Price Elasticity of Supply

Price elasticity of supply is the measure of responsiveness of producers and resource suppliers to the change in price of a produce or resource. The responsiveness of suppliers to price means the degree to which they change their supply when the price of a product, service or a resource changes by a certain amount. When suppliers are more responsive, they will change the quantity they supply by a greater amount in response to a small change in price.

## Formula

A simple formula to calculate price elasticity of supply Es is:

$$\text{Price Elasticity of Supply}\ (\text{E} _ \text{s}) \\= \frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}}$$

When using the above formula, the percentage changes in price and quantity supplied are calculated by dividing the difference of initial price/quantity by the difference of final price/quantity respectively. But this causes problem. For example, when price changes from $4 to$5 the percentage change in price is $1/$5 = 20% but in case of opposite change from $5 to$4, the percentage change is -$1/4 = -25%. The same problem arises when calculating the percentage change in quantity supplied. Thus the price elasticity of supply as calculated above is different for two opposite and equal changes. We can avoid the above problem by using a more accurate formula called the mid-point formula of price elasticity given below: $$\text{E} _ \text{s} = \frac{\text{Q} _ \text{f} - \text{Q} _ \text{i}}{(\text{Q} _ \text{f} + \text{Q} _ \text{i}) ÷ \text{2}} ÷ \frac{\text{P} _ \text{f} - \text{P} _ \text{i}}{(\text{P} _ \text{f} + \text{P} _ \text{i}) ÷ \text{2}}$$ Where Qi is the initial quantity supplied, Qf is final quantity supplied, Pi is the initial price and Pf is the final price. The price elasticity of supply equals the slope of supply curve. Since the supply curve has positive slope therefore the price elasticity of supply is always positive. Remember that price elasticity of demand is negative. ## Example Calculate the price elasticity of supply using the mid-point formula when the price changes from$5 to $6 and the quantity supplied changes from 20 units per supplier per week to 30 units per supplier per week. Solution Percentage change in quantity supplied = (30 − 20) ÷ {(30 + 20) ÷ 2} = 40% Percentage change in price = ($6 − $5) ÷ {($6 + \$5) ÷ 2}
≈ 18.182%

Price elasticity of supply
≈ 40% ÷ 18.182%
≈ 2.20