Two companies in the pencil market sell differentiated but substitute products: DIXON and MIRADO, their demand functions

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Two companies in the pencil market sell differentiated butsubstitute products: DIXON and MIRADO, their demand functions are:𝑞D = 12 − 𝑝D + 0.5𝑝D and 𝑞M = 14 − 𝑝M + 0.5𝑝D. The production costsof both companies are equal to 𝐶𝑇(𝑞i) = 2, ∀ 𝑖 = 𝐷, 𝑀 (2.0points).a. Determine the Nash equilibrium price assuming that the firmssimultaneously decide the price of their products. Obtain the levelof production and profits of the companies.b. Now suppose that the demand function of the DIXON companychanges and becomes the following: 𝑞D = 14 − 𝑝D + 0.5𝑝M . Obtainthe prices, equilibrium output, and profit if the firmssimultaneously decide on prices.c. If the companies form a collusion and charge a price higher thanthe one in the previous section by 5 units, how much do theyproduce and what are their profits?d. What happens if the company MIRADO decides to charge the priceof subsection c and not that of d? What would happen if the DIXONcompany decides to charge the price of part c and not the one ofd?and. Construct a payoff matrix and find the Nash equilibrium.