Please help with the following question:

1. [26] Imagine that you wake up from a night of too much studying and find yourself in an alternate universe. It's the year 2007. The Latin-crossover sensation Despacito has hit the airwaves in a big way, it is destined to become the number 1 selling ring-tone of all time. Demand for this wonderful melody is given by Q = 360 - 3p. There are only two firms that produce this coveted product, they both have cost function c = 60 + q,2, where j = 1,2 denotes the firm. Total production of Despacito ring-tones is equal to the output from the two firms.a. [6] Suppose the two firms compete on quantities. Find the Cournot-Nash equilibrium price and output of each firm. How much profit does each firm make? b. [8] Suppose that the two firms decide to form a cartel. What will the firms' profits be under a collusive arrangement? Are their profits different than in part(a)? Explain the intuition behind your finding. c. [4] Is the cartel is a stable arrangement in a one period interaction? Show supporting calculations. d. [8] Suppose instead that firm 2 has more foresight and gets the ring-tone to market faster, becoming the market leader, and that the firms continue to engage in quantity competition. i. [6] How much profit does each firm make? ii. [2] Are consumers better off under this market structure than under a simultaneous quantity setting duopoly? Explain your reasoning without calculating consumer surplus explicitly