1. Suppose there are two firms that must decide how much clean air to consume (assume production uses up clean air). The total amount of clean air to begin with is 60. Each firm i 6 {1,2} chooses a level of air consumption k.- 2 0. thus leaving the amount of clean air remaining as 60 k1 kg. The payoff function of firm 1 is @1031, kg) = ln(k1) + ln(60 k1 kg) with the payoff function of firm 2 similarly defined. (i) What is the Nash equilibrium if both firms choose their air consumption at the same time? [5 Marks] (ii) Graph the Best Response Function of each firm, showing the Nash Equilibrium. [5 Marks] (iii) What is the Subgame Perfect Nash Equilibrium if firm 1 chooses its consumption level first, firm 2 observes this choice and then chooses his own level? [5 Marks] (iv) Plot the SPNE outcome on the graph in part (ii) ls total pollution higher in (i) or (iii)? Why? [5 Marks]