Question 5 (10 points) Suppose that two firms are situated next to a lake. It costs each firm $1,500 per period to use filters that avoid polluting the lake. However, each firm must use the lake's water in production, so it is also costly to have a polluted lake. The cost to each firm of dealing with water from a polluted lake is $1,000 times the number of polluting firms. The possible outcomes for one period are illustrated by the payoff matrix below. The first number of each pair of payoffs is Lago's payoff and the second is Nessie's payoff. Assume that the firms are able to collude or cooperate with each other. Nessie, Corp. Pollute Don't Pollute Lago, Inc. Pollute -$2.000. -$2.000 -$1.000, -$2.500 Don't Pollute -$2.500. -$1.000 -$1.500. -$1.500 a. (6 points) Assume that both firms know that they are going to play the game for 10 periods. In the last period (period 10), what is the equilibrium of the game? Explain your answer. b. (4 points) Assume that the game is repeated forever over an infinite horizon, what will be the most likely observed behavior of the firms? Explain your