Question

What is the formula for calculating elasticity?

Short answer

The formula for calculating elasticity is \(E = \frac{\% \Delta Y}{\% \Delta X}\), where \(E\) represents the elasticity, \(\% \Delta Y\) is the percentage change in variable Y (such as quantity demanded), and \(\% \Delta X\) is the percentage change in variable X (such as price). To calculate the percentage changes, use the formula \(\% \Delta X = \frac{X_{new} - X_{old}}{X_{old}} \times 100\) and \(\% \Delta Y = \frac{Y_{new} - Y_{old}}{Y_{old}} \times 100\). Substitute these values into the elasticity formula to find the elasticity value (E) for the given variables.

Step-by-step solution

1. Understand the elasticity concept

Elasticity measures how sensitive one variable (such as quantity demanded) is to changes in another variable (such as price). The most common elasticities in economics are price elasticity of demand and price elasticity of supply. However, the basic formula for calculating elasticity can be used for other types of elasticities as well.

2. Introduce the formula for calculating elasticity

The formula for calculating elasticity is: \[ E = \frac{\% \Delta Y}{\% \Delta X} \] where: - \(E\) represents the elasticity - \(\% \Delta Y\) is the percentage change in variable Y (such as quantity demanded) - \(\% \Delta X\) is the percentage change in variable X (such as price)

3. Calculate the percentage changes

To calculate the percentage change in the variables, we can use the following formula: \[ \% \Delta X = \frac{X_{new} - X_{old}}{X_{old}} \times 100 \] Similarly, for the percentage change in variable Y: \[ \% \Delta Y = \frac{Y_{new} - Y_{old}}{Y_{old}} \times 100 \] Remember to use the absolute values when calculating percentage changes for elasticity.

4. Apply the formula to find the elasticity

Once you have calculated the percentage changes, substitute these values into the elasticity formula: \[ E = \frac{\% \Delta Y}{\% \Delta X} \] This will give us the elasticity value (E) for the given variables.