Question 2: Networks and Platforms

There is a mass M = 1 of consumers uniformly distributed along a straight (Hotelling) road of length

1. A single games platform is located at one end of the road and consumer i's "willingness to pay"

from playing on the platform is given by:

u₂ (di) = 1 - di

(1)

Here, d; is the distance consumer i must travel to reach the console store. Assume that consumers

who do not participate on the platform receive zero utility.

The platform charges a price p for the access and faces costs C(x) = x², where is the proportion of

consumers using the platform. The platform sets prices to maximise profits.

a. Determine the demand curve and inverse demand curve faced by the platform.

b. What is the profit-maximising price charged by the store?

c. What price would a welfare-maximising social planner choose?

d. What is the dead-weight loss associated with the monopoly price?

Now assume that a new multi-player game is introduced that allows the platform users to gain utility

by interacting with others using the same platform, so the "willingness to pay" of each consumer is

now given by:

7

ui (di, 9) = 1 + 1/2 − di

-

8

(2)/n7

==

u,(di,q)

+1/12-di

Here, q is the proportion of consumers agent i expects to use the platform.

e. Recalculate parts b., c., and d. above for the new situation.

f. How did the introduction of the multi-player game impact on the profits of the platform?

The firm realises that there is actually a mass N of advertisers willing to advertise on the platform.

Each advertiser j expects to receive profit ; (Pa, 9) from advertising, where:

(2)

Tj (Pasq) = 2q-cj- Pa

(3)

Here, c; is a random variable drawn from a uniform distribution over [0, 1], pa is the price charged by

the console manufacturer to the advertiser, and q is the proportion of consumers expected to use the

platform.

The platform faces additional costs Ny² from adding advertisers, where y is the proportion of adver-

tisers advertising on the console.

g. Given your solutions to part e., calculate the price på the platform should charge advertisers.

h. Should the platform vary the price p charged to consumers? If so, how?

i. Compare the profit-maximising prices charged with the marginal costs for the games platform

in the two markets. Comment on your answers.

j. What prices would a social planner charge if it were able to set prices on the platform?

k. How large is the Spence distortion?