Using Calculus To Calculate Income Elasticity of Demand

Using Calculus To Calculate Income Elasticity of Demand

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, Aug. 27, 2020, thoughtco.com/calculate-income-elasticity-of-demand-1146249. Moffatt, Mike. (2020, August 27). 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 December 3, 2021).