Justine is a smartphone developer, her free app currently has 500 000 users. She is thinking...

Justine is a smartphone developer, her free app currently has 500 000 users. She is thinking of making a premium version. She assumes that for each 5$ increase in price the number of paying customers decreases by a factor of 1/2, i.e. half of her current paying customers will stop paying for her app.

(a) If pp is the price in dollars and CC is the number of paying customers, find the exponential function

C=f(p)

that models this situation.

(b) Her total revenue

R

is given by the number of paying customers times the price of the app, or

R=p⋅f(p).

Give the formula for dR/dp.

(c) Suppose that Justine is selling her app for 10$$. Compute dR/dp|p=10. Given this result, should Justine increase or decrease the price to get more revenue. Give a brief justification involving units.

Expert Solution

Rahul Sunny answered 3 years ago

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