The demand for voice mail is Q = 1,000 - 150P + 20I. Assume that per capita disposable income I is $900. At a price P of $40, the income elasticity of demand is

Question

Quizplus · Accepted Answer

The formula for income elasticity of demand is:

Income Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Income)

Since we are given that per capita disposable income I is $900, there is no percentage change in income. Therefore, income elasticity of demand will simply equal the coefficient on income in the demand equation, which is 20.

Next, we need to find the percentage change in quantity demanded when the price changes from P = $40 to P = $50. Using the demand equation:

Q = 1,000 - 150P + 20I

When P = $40 and I = $900,

Q = 1,000 - 150($40) + 20($900) = 16,000

When P = $50 and I = $900,

Q = 1,000 - 150($50) + 20($900) = 14,500

Therefore, the percentage change in quantity demanded is:

(% Change in Quantity Demanded) = [(14,500 - 16,000) / ((14,500 + 16,000) / 2)] x 100%

= (-1,500 / 15,250) x 100%

= -9.84%

Putting it all together:

Income Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Income)

= (-9.84%) / 0%

= undefined

Therefore, we cannot calculate the income elasticity of demand when there is no change in income.

The Demand for Voice Mail Is Q = 1,000 -