This is a question about Tony, the seller of durable goods, whom we have met before.
This time he is selling to three potential consumers,H, M, L:Remember, since the good is durable, if a consumer buys it in period 1, she
obtains utility from it for two periods; if she buys in period 2, she only obtains the utility from period 2.
The utilities, which are in equivalent dollar units, of the various consumers are given in the table below:
Period?1 2
Hutility 1500 700
Mutility 1200 400
Lutility 600 300
Thus, ifHbuys in period 1 at a price of $1000, he gets a payoff of 1500+700-1000=1200.
Similar calculations can be done for the other consumers. If any consumer does not buy, she gets a payoff of 0. ThusLwould be better off not buying than paying a price of $1000. If Tony charges a price of $1000 in the first period and $100 in the second period andH,
Mbuy in the first period andLin the second period, Tony's payoff is $1000+$1000+$100=$2100.
The game is as follows: Tony announces a pricep1in period 1. The consumers simulta-
neously and independently decide whether or not to buy in period 1. Whoever buys leaves the game. Those who do not buy remain. Who remains is observable to everyone involved. Given this observation, Tony announcesp2in period 2.
What is the subgame perfect pricing policy for Tony? (Please make sure you write down
the strategies for all players and show why it is subgame perfect.)