The price elasticity of demand measures the responsiveness of the quantity demanded of a good or service to a change in its price. It is a crucial concept in economics because it helps firms and policy makers understand how changes in price will affect the quantity of a product that is demanded and the total revenue that a firm will earn. There are several methods for finding the price elasticity of demand, including the midpoint method and the arc elasticity method.

The midpoint method is a simple and commonly used method for calculating the price elasticity of demand. It involves finding the percentage change in the quantity demanded of a good or service and the percentage change in its price, and then dividing the former by the latter. The midpoint method is preferred because it takes into account the absolute change in both the quantity demanded and the price, rather than just the change in one variable or the other.

To use the midpoint method, we need to start by finding the initial and final quantities demanded of the good or service in question, as well as the initial and final prices. For example, let's say that the initial quantity demanded of a certain good is 1000 units, and the final quantity demanded is 800 units. At the same time, the initial price of the good is $10 per unit, and the final price is $12 per unit.

To find the percentage change in the quantity demanded, we first need to find the difference between the initial and final quantities demanded. In this case, the difference is 200 units (1000 - 800 = 200). We then divide this difference by the initial quantity demanded and multiply the result by 100 to express it as a percentage. This gives us a percentage change in the quantity demanded of 20% (200 / 1000 * 100 = 20).

To find the percentage change in the price, we follow the same process. The difference between the initial and final prices is $2 per unit, and the initial price is $10 per unit. Dividing the difference by the initial price and multiplying the result by 100 gives us a percentage change in the price of 20% ($2 / $10 * 100 = 20%).

Finally, we can divide the percentage change in the quantity demanded by the percentage change in the price to find the price elasticity of demand. In this case, the price elasticity of demand is equal to 1 (20% / 20% = 1). This means that the quantity demanded of the good is perfectly elastic, meaning that a change in the price will result in an equal percentage change in the quantity demanded.

There are other methods for finding the price elasticity of demand, such as the arc elasticity method, which involves calculating the elasticity over a range of prices rather than just at a single point. However, the midpoint method is a simple and reliable method that is commonly used in economics.