Chapter 5: Problem 24

What is the formula for elasticity of savings with respect to interest rates?

Short Answer

Expert verified

The elasticity of savings with respect to interest rates can be calculated using the formula: Elasticity (E) = \(\frac{(New Savings - Initial Savings) × Initial Interest Rate}{(New Interest Rate - Initial Interest Rate) × Initial Savings}\).

Step by step solution

Understand the Variables and Formula for Elasticity

Elasticity is a concept used in economics to measure the responsiveness of one variable to changes in another variable. The formula for calculating elasticity is as follows: Elasticity (E) = (% Change in Quantity) / (% Change in Price) When discussing the elasticity of savings with respect to interest rates, we are interested in how a change in interest rates (the 'price') affects the quantity of savings.

Define the Formula for the Percentage Change in Savings

To find the percentage change in savings, we will use the following formula: % Change in Savings = \((\frac{New Savings - Initial Savings}{Initial Savings}) × 100\)

Define the Formula for the Percentage Change in Interest Rates

To find the percentage change in interest rates, we will use a similar formula: % Change in Interest Rates = \((\frac{New Interest Rate - Initial Interest Rate}{Initial Interest Rate}) × 100\)

Find the Formula for the Elasticity of Savings with Respect to Interest Rates

Now that we have the formulas for the percentage change in savings and interest rates, we can plug them into the elasticity formula: Elasticity (E) = \(\frac{(\frac{New Savings - Initial Savings}{Initial Savings}) × 100}{(\frac{New Interest Rate - Initial Interest Rate}{Initial Interest Rate}) × 100}\)

Simplify the Formula

To simplify the formula, we can remove the 100 from both the numerator and the denominator, as they will cancel each other out: Elasticity (E) = \(\frac{New Savings - Initial Savings}{Initial Savings}\) / \(\frac{New Interest Rate - Initial Interest Rate}{Initial Interest Rate}\) Now, we can further simplify by multiplying both the numerator and the denominator by \(Initial Savings × Initial Interest Rate\): Elasticity (E) = \(\frac{(New Savings - Initial Savings) × Initial Interest Rate}{(New Interest Rate - Initial Interest Rate) × Initial Savings}\) This is the final formula for the elasticity of savings with respect to interest rates.