The demand function for mobile applications at the Apple App

The demand function for mobile applications at the Apple App Store is :14p-20 and the demand function at Google Play is 3.7 QG 1.4p where the quantity is in millons of apps. These demand functions are equal (cross) at one price, What are the elasticties of demand for each Where the demand curve for the Apple App Store and the demand curve for Google Play cross, the elasticity of demand is for the Apple App Store and for Google Play (Enter your responses rounded to one decimal place) Enteryour answer in the edit fields and then click Check Answer All parts showing crear All ay

Solution

QA = 1.4 p^-2.0

Elasticity of apply store = (change in QA/change in p) (p/QA)

To calculate elasticity for apple store, firstly calculate (change in QA/ change in p) by taking the first derivative of QA , we get:

= (-2.0)(1.4)p^-3 = -2.8 p^-3

Elasticity = -2.8 p^-3 (p/ 1.4 p^-2 )

= -2.8 p^-3+1 / 1.4 p^-2

= -2.8 p^-2 / 1.4 p^-2

= -2.8 /1.4

= -2. (Elasticity of demand for apple store)

QG = 1.4 p^-3.7

Elasticity for Google play = (change in QG / change in p) (p/ QG)

To calculate elasticity firstly calculate (change in QG/change in p) by taking the first derivative of QG, we get:

= (-3.7)(1.4)p^-4.7 = (-5.18)p^-4.7

Elasticity = (-5.18) p^-4.7 (p / 1.4 p^-3.7)

= (-5.18) p^-3.7 / 1.4 ^p-3.7

   = -5.18/ 1.4

= -3.7. (Elasticity of demand for Google play)