Problem 4: [exam id #887] [20 points] Suppose Apple and Samsung are the only two firms selling smart phones. Suppose Apple faces the following demand function for their product: QA = 100 - 2PA + PSwhere PA is the price charged by Apple, Ps is the price charged by Samsung, and QA is the quantity of Apple iphones demanded by consumers. Suppose Apple has constant marginal and average costs of production of $30. Samsung faces the following demand function: Qs = 100 - 2Ps + PA where Qs is the quantity of Samsung phones demanded by consumers. Suppose Samsung faces constant marginal and average costs of production of $10. (a) [8 points] Suppose Apple and Samsung engage in strategic price competi- tion. Find the equilibrium prices PA, Ps, and industry output Q. Determine the profits for each firm in equilibrium. b) [7 points] Suppose the Apple and Samsung decide to collude, setting prices to maximize joint profit, and then dividing any additional profit so that they have the same percentage share of total industry profit as in the equilibrium in (a). What prices will they set? What will their respective profits be? (c) [5 points] Suppose Apple and Samsung agree to collude. Assume that Samsung will definitely follow the agreement. In this scenario, could Apple do better by not following the agreement? If so, how would Apple's quantity and profits compare to those in (a) and (b)