You have produced an independent movie, and are trying to decide the optimal channel for distribution. You have two mutually exclusive choices:

Choice 1: You sell the movie to Netflix. Netflix will agree to pay you a fee that depends on your movie hitting various thresholds of total viewing hours. Your close friend who works in analytics for DreamWorks has drawn up the following projections, which you believe:

30% chance that you reach 12,000 viewing-hours; Netflix will pay you $2/viewing-hour

55% chance that you reach 100,000 viewing-hours; Netflix will pay you $3.50/viewing-hour

15% chance that you reach 1,000,000 viewing-hours; Netflix will pay you $4/viewing-hour1

Choice 2: Apple will offer the movie for sale via iTunes. It will retail for $4.99, and iTunes will keep $1.49 of each sale. By advertising on You-Tube and TikTok, you can drive sales through iTunes. You know that each additional customer you attract will cost more than the last one. You model the total cost of acquiring customers as: Total cost = .5 + ^2/300,000. You recognize that this implies the marginal cost of customer acquisition is: C = .5 + /150,000.

a) From an expected value standpoint, what is your optimal choice and what is your expected net revenue? (By net revenue I mean payment received if you sell to Netflix, and revenue received advertising costs if you choose iTunes.)

b) Youre aware that Netflix acquires a lot of movies and uses a complicated black-box algorithm to present content to users. Youve heard that sometimes movies will fall into an algorithmic black hole, and essentially never appear as an option for viewers. In this outcome, the movie receives zero viewing hours, and Netflix pays nothing. In all other states of the world, your original projections hold. What probability do you have to project for this adverse outcome to make you indifferent between choosing Netflix and iTunes? (Feel free to write answer as a fraction, or round to nearest .1%.) c)

Ignore the scenario presented in 4b. What is the most you would pay to learn with certainty which of the 3 Netflix outcomes would happen?