Two companies in the pencil market sell differentiated but substitute products: DIXON and MIRADO, their demand functions are: D = 12 D + 0.5D and M = 14 M + 0.5D. The production costs of both companies are equal to (i) = 2, = , (2.0 points). a. Determine the Nash equilibrium price assuming that the firms simultaneously decide the price of their products. Obtain the level of production and profits of the companies. b. Now suppose that the demand function of the DIXON company changes and becomes the following: D = 14 D + 0.5M . Obtain the prices, equilibrium output, and profit if the firms simultaneously decide on prices. c. If the companies form a collusion and charge a price higher than the one in the previous section by 5 units, how much do they produce and what are their profits? d. What happens if the company MIRADO decides to charge the price of subsection c and not that of d? What would happen if the DIXON company decides to charge the price of part c and not the one of d? and. Construct a payoff matrix and find the Nash equilibrium.