5 Durable Goods (30 points) Tony is a seller of goods that last at most two periods. There are three potential customers, H and L1 and L2, each of whom wants at most one good. The respective utilities (in money units) they get are in the table below. Period 1 Period 2 H 1200 500 L1 , L2 500 200 So if H, say, buys in the rst round, she gets a total utility 0f 1200+500-the price she pays, 121. If she waits until the second round, she gets 500132, the price in the second period. The game is: Tony announces 121. H, L1, L2, simultaneously and independently, decide whether to buy or not. Tony observes who has bought and who is left to buy and then chooses p2. Tony's payoff is the sum of (pricex quantities sold) over the two periods. The consumers get 0 if they don't buy anything; otherwise their payoff is calculated by subtracting price paid from total utility obtained. a) (15 points) What is the subgame perfect Nash equilibrium pricing policy for Tony (convince me that it's SPNE)? What is Tony's payoff? Be sure to list all the reasonable options that Tony has for pricing and what his related payoffs would be. b) (15 points) Tony suddenly nds out at the beginning of period one that he has only two items to sell. He is able to convince H, L1 and L2 of this. What is the subgame perfect equilibrium pricing strategy for Tony now? Is he better off or worse off than in (a)