# Principles of Economics/Elasticity

Elasticity refers to the degree, to which one value changes when another does. For example, how quantity supplied and demanded change with respect to price; how investment and savings change with respect to interest rate. The higher (lower) the elasticity, the higher (lower) the degree of change.

Let's use these notations for the following formulas.

• $P$ is price
• $Q_{s}$ is quantity supplied
• $Q_{d}$ is quantity demanded
• $\Delta$ is 'change in'

Price elasticity of demand

$=-{\frac {\%\Delta Q_{d}}{\%\Delta P}}$ Price elasticity of supply

$={\frac {\%\Delta Q_{s}}{\%\Delta P}}$ The higher the absolute value of the elasticity, the higher the degree of change. We use absolute value of elasticity here because the price elasticity of demand is always negative by law of demand. Therefore, the degree of change is higher when the price elasticity of demand is more negative, but it means that it is low in numerical value. Thus, we take the absolute value, so that 'the higher the value of elasticity, the higher the degree of change' holds.

For example, if the price elasticity of demand is more negative, say it equals -5, then if price increases by 10%, the quantity demanded will decrease by 50%. On the other hand, if the elasticity is less negative, say it equals 0.1, then if price increases by 10%, the quantity demanded will only decrease by 1%.

## Cross elasticities

The elasticities mentioned above refer to one object (e.g. the price elasticity of demand refer to the price and quantity demanded of one object). Cross elasticities refer to the effects of something's price, interest, etc. on something else. This comes into play with substitute and complementary goods and services for the consumer. For example, one type of cross elasticity refers to the degree to which the quantity demanded of good A changes when price of good B changes.