Please Answer this question and all its parts with full explanations.

1. [25] Imagine that you wake up from a night of too much studying and nd yourself in an alternate universe. It's the year ZDDI The Latin-crossover sensation Despoclto 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 = 35o 3p. There are only two rms that produce this coveted product, they both have cost function or = l} + of, wherej = 1,2 denotes the firm. Total production of Despocfto ring-tones is equal to the output from the two rms. a. [6] Suppose the two firms compete on quantities. Find the Cournot-Nash equilibrium price and output of each rm. How much profit does each rm make? b. [3] Suppose that the two rms decide to form a cartel. What will the firms' prots be under a collusive arrangement? Are their profits different than in partlal? Explain the intuition behind your finding. c. [4] Is the cartel is a stable arrangement in a one period interaction? Show sup porting calculation s. d. [3] 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