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
H utility 1500 700
M utility 1200 400
L utility 600 300
Thus, if H buys 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. Thus L would 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 and H, M buy in the first period and L in the second period, Tony's payoff is $1000+$1000+$100=$2100.
The game is as follows: Tony announces a price p1 in period 1. The consumers simultaneously 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 announces p2 in 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.)