Why do we always insert a negative sign in front of demand elasticity?

Demand elasticity measures the responsiveness of the quantity demanded of a good or service to changes in its price. In simple terms, it shows how sensitive customers are to price changes - whether they will buy less or more of a product when the price changes.

Demand elasticity (Ed) is calculated using the following formula: \(Ed = \frac{\% \textrm{ Change in Quantity Demanded}}{\% \textrm{ Change in Price}}\) Expressed differently: \(Ed = \frac{(\Delta QD / QD_1)}{(\Delta P / P_1)}\) Where: - \(Ed\) is the demand elasticity - \(\Delta QD\) is the change in quantity demanded - \(QD_1\) is the initial quantity demanded - \(\Delta P\) is the change in price - \(P_1\) is the initial price

Demand elasticity is usually negative because of the law of demand, which states that as the price of a good or service increases, the quantity demanded decreases, all else being equal. It is an inverse relationship between price and quantity demanded, meaning that when the price goes up, demand goes down, and vice versa.

Introducing a negative sign in front of demand elasticity ensures that the value of elasticity is always positive. This is important because it makes it easier to understand and compare elasticity values between different goods or services. A positive elasticity value indicates the presence of an inverse relationship between price and demand, while a zero or negative elasticity would suggest either a constant or a direct relationship between the two, which is not typically the case for most goods and services. By convention, we attach a negative sign to the demand elasticity value to make it positive and facilitate interpretation. In this context, the absolute value of the demand elasticity is usually considered, meaning that larger elasticity values correspond to higher sensitivity to price changes. In conclusion, we always insert a negative sign to demand elasticity because it emphasizes the inverse relationship between price and demand, which is consistent with the law of demand, and makes it easier to compare elasticities between different goods or services.