There are three firms i=1,2,3 producing a homogeneous good and competing in quantities. Each firm produces the quantity q, 20 and has marginal costs of production of 0. There are no fixed costs nor production constraints. The inverse market demand function is p-A- KQ. where Q-91 +92 +93 and 4>K>0 holds. (a) (15 points) Find the (pure strategy) production quantity of each firm in the subgame perfect Nash equilibrium for the case that firm 1 moves first and then firm 2 second and then firm 3 third. What is the corresponding market price? (b) (15 points) Find the (pure strategy) production quantity of each firm in the subgame perfect Nash equilibrium for the case that firm 1 moves first and then firm 2 and firm 3 simultaneously. What is the corresponding market price?