Using Calculus To Calculate Income Elasticity of Demand

Using Calculus To Calculate Income Elasticity of Demand

By
Mike Moffatt
Mike Moffatt
Professor of Business, Economics, and Public Policy
  • Ph.D., Business Administration, Richard Ivey School of Business
  • M.A., Economics, University of Rochester
  • B.A., Economics and Political Science, University of Western Ontario
Mike Moffatt, Ph.D., is an economist and professor. He teaches at the Richard Ivey School of Business and serves as a research fellow at the Lawrence National Centre for Policy and Management.
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Updated on April 03, 2017

Suppose you're given the following question:

Demand is Q = -110P +0.32I, where P is the price of the good and I is the consumers income. What is the income elasticity of demand when income is 20,000 and price is $5?

We saw that we can calculate any elasticity by the formula:

  • Price elasticity of income: = (dQ / dI)*(I/Q)
demand equation
  • dQ/dI = 0.32
  • Income elasticity of demand: = (dQ / dI)*(I/Q)
    Income elasticity of demand: = (0.32)*(I/(-110P +0.32I))
    Income elasticity of demand: = 0.32I/(-110P +0.32I)
  • Income elasticity of demand: = 0.32I/(-110P +0.32I)
    Income elasticity of demand: = 6400/(-550 + 6400)
    Income elasticity of demand: = 6400/5850
    Income elasticity of demand: = 1.094
Demand is Income Elastic

Next: Using Calculus To Calculate Cross-Price Elasticity of Demand

Other Price Elasticity Equations

  1. Using Calculus To Calculate Price Elasticity of Demand
  2. Using Calculus To Calculate Income Elasticity of Demand
  3. Using Calculus To Calculate Cross-Price Elasticity of Demand
  4. Using Calculus To Calculate Price Elasticity of Supply
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Moffatt, Mike. "Using Calculus To Calculate Income Elasticity of Demand." ThoughtCo, Apr. 5, 2023, thoughtco.com/calculate-income-elasticity-of-demand-1146249. Moffatt, Mike. (2023, April 5). Using Calculus To Calculate Income Elasticity of Demand. Retrieved from https://www.thoughtco.com/calculate-income-elasticity-of-demand-1146249 Moffatt, Mike. "Using Calculus To Calculate Income Elasticity of Demand." ThoughtCo. https://www.thoughtco.com/calculate-income-elasticity-of-demand-1146249 (accessed June 1, 2023).
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