In this question you will work out a model of price competition (Bertrand competition) with differentiated products, i.e., when the two firms that compete produce slightly different products. Consider two price-setting firms, 1 and 2, each with marginal cost c, that produce goods, 1 and 2, that are imperfect substitutes. Some customers are loyal to a particular variety of the good so both firms can still have positive sales when they set different prices. Demand for firm 1's output, '31. as a function of the prices of both products, 391 and p2 , is given by q1 = 2 3331 + 3192. And the demand for firm 2's output, qz, is given by q2 = 6 2392 + p1. a. How can we tell, by looking at the demand functions above, that in the preferences of consumers the two products are substitutes? Explain your answer. [7 marks] b. Write this strategic situation as a simultaneous game between the two firms, specifying the set of players, the set of alternatives and the preferences of each firm. Write down the profit equation of each firm as a function of the price it sets and that of the other firm. [7 marks] c. For each firm, maximise the firm's profit given the price set by the other firm to find the reaction functions p1(p2) and p2 (p1)of both firms. [7 marks] d. Find the Bertrand-Nash Equilibrium prices if marginal cost c = 1. Do the firms make profits? If yes, what are their profits? [7 marks] e. How does the outcome above differ from the Bertrand competition with homogenous goods (that is both firms produce the exact same product) we studied in lectures? Explain intuitively why the outcome above differs to the Bertrand competition model we did in lectures. [7 marks]