Consider a duopoly market with only two sellers selling an identical product. Market demand is given by P = 40 - 1- Q. Technology in the industry is such that the marginal (and average) cost of production is constant at MC = AC = $10. There are no fixed costs - assume the short run applies. a) If the two firms compete by setting output levels in a single period, simultaneous move, static game, find the best response functions for one of the firms. b) Use your answer from a) (along with the other firm's best response function) to compute the Nash equilibrium quantities and the market price that results in the equilibrium. c) If instead, the firms competed by setting prices in a single period, simultaneous move, static game, what is the predicted market price that will prevail in the Nash equilibrium? d) If the firms wanted to form a Cartel, how many units should the duopoly coordinate to produce collectively? At what price should the firms collude at selling these units? Explain.