The demand function for mobile applications at the Apple App

The demand function for mobile applications at the Apple App Store is QA = 1.4p-20 and the demand function at Google Play is QG=1.4p-3.7 where the quantity is in millions of apps. These demand functions are equal (cross) at one price. What are the elasticities of demand for each demand curve where they cross? Where the demand curve for the Apple App Store and the demand curve for Google Play cross, the elasticity of demand is EA- for the Apple App Store and for Google Play. (Enter your responses rounded to one decimal place,)

Solution

Demand for Apple App is Q_A = 1.4p^-2.0

Demand for Google play is Q_G = 1.4p^-3.7

They intersect where Q_G =Q_A

1.4p^-3.7 = 1.4p^-2

p^-3.7 = p^-2

p² = p^3.7

1 = p^1.7

P = 1.

Demand at P= 1 is 1.4 for both the apple and Google play store

Elasticity of demand is e = (dQ/dP)*(P/Q)

e_A = (-2.8p^-3)*(1/1.4p^-2)

e_A = -2/p = -2

Elasticity of demand for Google is

e_G = (-5.18p^-4.7)*1/(1.4p^-3.7)

e_G = -3.7