Problem
This is a question about Tony, the seller of durable goods, whom we have met before in HW4. 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, then she obtains utility only in period 2.
The utilities, which are in equivalent dollar units, of each consumer is given in the table below:
Period → 1 2
H utility 3000 1400
M utility 2400 800
L utility 1200 600
Thus, if H buys in period 1 at a price of $1000, he gets a payoff of 3000 + 1400 - 1000 = 3400. 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 o? not buying than paying a price of $2000. You can assume that consumers who are indifferent will go ahead and buy.
If Tony charges a price of $1000 in the ?rst round and $100 in the second round while H and M buy in the ?rst period and L buys in the second period, then Tony's payoff is $1000 + $1000 + $100 = $2100.
The game is as follows: Tony announces a price p1 in round 1. The consumers simultaneously and independently decide whether or not to buy in round 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 round 2.
Task
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. Record your answers on paper, then scan and upload them.