Please any help on this would be appreciated

3. Consider the following numerical example: Assume a duopoly where firms 1 and 2 produce homogeneous outputs q, and q2 respectively. The inverse market demand function is P = 70 -Q, and the firms have identical cost curves MC=AC=10 and zero fixed costs. (a) In a simultaneous one period game, what are the outputs and profits of each firm at the Cournot-Nash equilibrium? (b) If the firms collude to maximize their joint profit and each firm undertakes to produce one-half of the joint profit-maximizing output, how much would each firm produce? Provide the numerical value of these output levels. (c) What would the profit of each firm be if they collude to maximize joint profit which they divide equally? (d) If we assume that the duopoly firms are engaged in an infinitely repeated game and that they agree that each firm will produce one-half of theindustry output level that maximizes their joint profit which they share equally, how much profit would each firm gain by complying with the agreement rather than by producing their Cournot equilibrium output? (e) Suppose that each firm adopts a trigger (or grim) strategy to incentivize compliance with the collusive agreement. Describe what is meant by a "trigger strategy". (f) If only one firm breaks the collusive agreement, what output would it produce to maximize its profit in the period in which it breaks the agreement? (g) How much extra profit would the firm that breaks the agreement earn in that period, assuming that the other firm is complying with the agreement? (h) Calculate the critical value of the rate of interest, r, where r > 0, for which the present value of the future losses (the punishment under the trigger strategy, beginning next period and continuing in perpetuity), would be greater than the present value of the profit gained by breaking the agreement, so that the trigger strategy would give the firms an incentive to comply with the agreement