1- The table below displays the profits from a price game between GM and FORD
FORD
GM Low price High Price
Low Price 100, 100 500, 0
High Price 0, 300 200, 250
Suppose this game is repeated indefinitely in each period t = 0;1;2; .... Let 0
(i) Formulate the trigger strategy of each firm under which both firms collude on setting high prices.
(ii) Compute the infinite discounted sum of the stream of profits earned by each firm assuming that both firms set the collusive price pH in each period.
(iii) Suppose GM deviates from the collusive price in period t = 0, while FORD keeps maintaining the collusive price pH. From the table what is the profit GM earns during period t = 0.
(iv) Suppose instead that FORD deviates from the collusive price in period t = 0 , while GM keeps maintaining the collusive price PH. From the table what is the profit FORD earns during period t = 0.
(v) Compute the infinite sum of the stream of profits made by GM assuming that only GM deviates from the collusive price in period t = 0, but FORD follows its trigger-price strategy from period t = 1 and on.
(vi) Compute the infinite sum of the stream of profits made by FORD assuming that only FORD deviates from the collusive price in period t = 0, but GM follows its trigger-price strategy from period t = 1 and on.
(vii) For each firm separately, compute the minimum threshold value of that would make it unprofitable for the firm to unilaterally deviate from the collusive outcome assuming that the competing firm adheres to its trigger-price strategy.