Chapter 5: Problem 10

What is the formula for calculating elasticity?

Short Answer

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The formula for calculating elasticity (E) between two variables (A and B) is given by: \( E = \frac{\% \Delta A}{\% \Delta B} \), where \( \% \Delta A \) represents the percentage change in variable A and \( \% \Delta B \) represents the percentage change in variable B. The percentage change in a variable can be calculated using the formula: \( \% \Delta X = \frac{X_{1} - X_{0}}{X_{0}} \times 100 \), with \( X_{0} \) as the initial value of variable X and \( X_{1} \) as the final value of variable X.

Step by step solution

Understand the Concept of Elasticity

Elasticity is a measure of how much one variable changes in response to a change in another variable. In this context, we are interested in calculating the elasticity between two variables, which is a ratio that tells us the percentage change in one variable when there is a one percent change in another variable.

General Formula for Elasticity

The general formula for calculating elasticity (E) between two variables (A and B) is given by: \( E = \frac{\% \Delta A}{\% \Delta B} \) Here, \( \% \Delta A \) represents the percentage change in variable A, and \( \% \Delta B \) represents the percentage change in variable B.

Calculating the Percentage Change

To use this formula, we need to calculate the percentage changes in variables A and B. The percentage change in a variable can be calculated using the following formula: \( \% \Delta X = \frac{X_{1} - X_{0}}{X_{0}} \times 100 \) Here, \( \% \Delta X \) represents the percentage change in variable X, \( X_{0} \) is the initial value of variable X, and \( X_{1} \) is the final value of variable X.

Applying the Formula to Calculate Elasticity

Once we have calculated the percentage changes in variables A and B, we can plug these values into the general formula for elasticity. This will give us the elasticity between the two variables, which tells us how one variable responds to changes in the other variable.

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