Please help with parts A-D of the attached practice question, thank you!

Consider a Cournot duopoly game, where the two firms have the same costs of production. Firm 1 selects quantity q1 and pays the production cost of 4q1. Firm 2 selects quantity 92 and pays the production cost 4q2. The market price is given by p = 20 - q1 - 92. Thus, the payoff functions are u1 (91, q2) = (20 - q1 - q2)q1 - 4q1 and u2(91, q2) = (20 - q1 - q2)q2 - 492. a.) * Find the profit of each firm at the Cournot Nash equilibrium quantity. (5points) b.) * Assume that the two firms form a cartel (merger) and decide to unite their production process. Find the joint-profit-maximizing quantity, price, and profit for each firm. (5points) (Part c and d continued on next page)c.) * The merged rms are enjoying high prots with lesser quantity produced than the Cournot Nash equilibrium. However, Firm 1 realizes that given that Firm2 produces at half of the joint-prot-maximizing quantity, Firm 1 has an incentive to deviate and produce more and get higher prot. How many quantities will Firm 1 produce when it deviates? What is the price and prot of Firm 1 when it does this? (15points) *Assume that the two rms play multiple stage games where in each stage they can either collude and produce the jointprotmaximizing quantity or deviate by choosing to produce more quantities. They decide to employ the Grim-trigger strategy to induce cooperation. The rst rm to deviate gets a high prot (the same as in part c), but afterwards they will both deviate and thereby get the Cournot equilibrium prot (As in part a). How patient do the rms need to be in order for couperation to continue. In other words what is the 6? The answer will be in fractions or decimals. (15points)