# 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
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