Free · Elasticity and market changes

Income Elasticity: Base-Period & Midpoint Methods

Compare the proportional change in demand with the proportional change in income, using either initial-value or midpoint denominators.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

Income rising from 1,000 to 1,200 and quantity from 100 to 140 gives base-period income elasticity of 2: quantity increases 40% while income increases 20%.

Elasticity = relative quantity change / relative income change; base-period change = (new − old) / old; midpoint change = 2(new − old) / (new + old)

Worked example

Enter these known values and leave the other values blank.

Initial income
1000 USD
Final income
1200 USD
Initial quantity demanded
100
Final quantity demanded
140
Income change by chosen method
20 %
Quantity change by chosen method
40 %
Signed income elasticity
2

Assumptions and limitations

  • Initial quantity and both incomes must be positive; final quantity can be zero. Income change must be nonzero.
  • Base-period percentages depend on the direction of comparison. Midpoint percentages use the average of the two endpoints.
  • This is an arithmetic comparison of two observations. Interpreting it as an economic response requires other relevant influences to be controlled.
  • Use matching periods, currency and quantity units. Currency selectors use captured fixed exchange rates, not live rates.

Common questions

Why do the methods give different answers?

They use different denominators for a percentage change. Use one method consistently for both income and quantity.

Can I recover a missing endpoint?

Yes. Enter an endpoint and a feasible percentage change under the selected method. Both forward and reverse calculations use that method.

References

Use separate base-period and midpoint inverse formulas so midpoint endpoints do not divide by the zero base-period coefficient. Require feasible positive-income and nonnegative-quantity endpoints, nonzero income change and exact elasticity classifications.

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