Question . Sony Interactive Entertainment oversees Playstation sales, generating profits both from console sales and from game licensing. Users need a console to play games. Assuming the marginal cost of producing a console is 100 and the cost of making games available to additional users is zero, this question asks you to work through Sony's optimal two-part tariff.1

a) Suppose there is a single consumer with inverse demand: () = 30 , where is the number of games purchased. Calculate Sony's optimal two-part. Does the outcome maximize total surplus? [Hint: Recall that Sony's cost of providing a console is 100 and its cost of providing access to each game is zero.]

Now suppose there are two different consumers. Consumer 1 has a low willingness to pay, with inverse demand function () = 28 , where is the number of games purchased by

consumer 1. Consumer 2 has a high willingness to pay, with inverse demand function () = "

32.

b) Suppose Sony sells games at the same price as calculated in (a). What is the highest console price that Sony can charge and still sell consoles to both consumers?

c) Note that the two consumers considered in (b) have the same average demand as the single consumer from part (a). Comparing parts (a) and (b), briefly discuss the effect of dispersion of willingness to pay on Sony's profitability?

In the questions below, suppose Sony charges a per-game price of 2. We will calculate the optimal console price.

c) Assuming all customers have purchased consoles, calculate how many games each consumer purchases when the per-game price is 2. Calculate each consumer's surplus.

d) Use the results from part (c) to obtain the highest price that Sony can charge per console and still sell consoles to both consumers.

e) How do Sony's profits in parts (b) and (d) compare? f) How does the deadweight loss in parts (b) and (d) compare?