The price elasticity of demand measures the responsiveness of the quantity demanded of a product to a change in its price. In simpler terms, it determines how sensitive the demand for a product is to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.
Mathematically, the price elasticity of demand ( E_d ) is given by:
E_d = \frac{{\%\text{ change in quantity demanded}}}{{\%\text{ change in price}}} = \frac{{\Delta Q/Q}}{{\Delta P/P}}
The price elasticity of supply, on the other hand, measures the responsiveness of the quantity supplied of a product to a change in its price. It determines how sensitive the supply of a product is to a change in its price. It is also calculated as the percentage change in quantity supplied divided by the percentage change in price.
Mathematically, the price elasticity of supply ( E_s ) is given by:
E_s = \frac{{\%\text{ change in quantity supplied}}}{{\%\text{ change in price}}} = \frac{{\Delta Q/Q}}{{\Delta P/P}}
Now, in terms of the relationship between price elasticity and position on the demand curve, we observe the following pattern: as we move up the demand curve to higher prices and lower quantities, the measured elasticity tends to be more elastic (greater than 1). This means that for relatively small changes in price, the quantity demanded changes significantly.
The rationale behind this is that as the price increases, consumers tend to be more sensitive to the change and their demand becomes more responsive. At higher prices, consumers may have more alternatives or substitutes available, making it easier for them to switch to other products or reduce their overall consumption.
In summary, as we move up the demand curve to higher prices and lower quantities, the measured elasticity becomes more elastic (greater than 1). This implies that the change in quantity demanded is relatively greater compared to the change in price.