Chapter 5: Problem 10

What is the formula for calculating elasticity?

Short Answer

Expert verified

The formula for calculating generic elasticity (E) is: \(E = \frac{\% \Delta Variable1}{\% \Delta Variable2}\), where \%ΔVariable1 represents the percentage change in the first variable and \%ΔVariable2 represents the percentage change in the second variable. Calculate the percentage change for both variables using the formula: Percentage Change = \( \frac{(New \; Value - Old \; Value)}{Old \; Value} \times 100 \). Then plug in the values and solve for Elasticity (E) to interpret the responsiveness of the variables.

Step by step solution

1. Understand the concept of elasticity

Elasticity measures the responsiveness of one variable (such as quantity demanded or quantity supplied) to changes in another variable (such as price, income, or the price of a related good). The larger the elasticity value, the more responsive the variable is to changes in the other variable.

2. Introduce the general formula for calculating elasticity

The general formula for elasticity is: Elasticity (E) = \( \frac{\% \Delta Variable1}{\% \Delta Variable2} \) Where: - \( \% \Delta Variable1\) represents the percentage change in the first variable - \( \% \Delta Variable2\) represents the percentage change in the second variable

3. Calculate the percentage change for both variables

To calculate the percentage change for each variable, use the following formula: Percentage Change = \( \frac{(New \; Value - Old \; Value)}{Old \; Value} \times 100 \) Determine the percentage change in both Variable1 and Variable2 using the data provided or by comparing the initial and final values of each variable.

4. Plug in the values and calculate elasticity

Once you have the percentage changes calculated for both Variable1 and Variable2, plug these values into the general elasticity formula: Elasticity (E) = \( \frac{\% \Delta Variable1}{\% \Delta Variable2} \) Now, you can solve for the value of Elasticity (E). The value of E helps to understand how much Variable1 changes in response to a change in Variable2.

5. Interpret the elasticity value

Use the calculated elasticity value to interpret the responsiveness of Variable1 to changes in Variable2. If E > 1, Variable1 is elastic, meaning it is more responsive to changes in Variable2. If E = 1, Variable1 is unit elastic, meaning the percentage changes in both variables are equal. If E < 1, Variable1 is inelastic, meaning it is less responsive to changes in Variable2. Remember that different types of elasticities will require you to plug in different variables based on the specific concept, like price elasticity of demand, price elasticity of supply, etc.