2. duopoly revisited recall the dell and hewlett-packard problem, in which the two competitors chose between producing 10 3 units per period and producing 2.5 units per period. the latter represented the cartel output and the former the cournot output. you solved for the nash equilibrium in the single period “game” and found it consisted of both firms producing 10 3 . profit per period per firm hp cournot cartel dell cournot 546, 546 511, 684 cartel 684, 511 615, 615 if the game lasts many periods, having a strategy becomes much more complex, and you can wonder whether cournot is still the equilibrium. a. to narrow the strategies down, write an expression for the expected (present and future) profit if both firms begin and continue playing “cartel” perpetually. each period has a probability “p” of the laptop computer becoming obsolete, but the market could continue indefinitely in principle. b. write another expression for the expected profit of beginning and continuing to play “cournot” perpetually, but the opposing firm plays cartel in the present and then cournot perpetually thereafter. c. comparing your answers to parts (a) and (b), you can say whether it is optimal to deviate from the cartel in the present or not. which is more profitable if = 0.9? which is more profitable if = 0.2? d. what value of p will make the firms indifferent to the 2 strategies of deviating immediately and not deviating immediately?