1. One factory owner and 2 citizens lobby the government about clean water regulation. Each can choose not to lobby or devote exactly 1 hour to lobbying. One hour of lobbying costs $100. If clean water regulation is implemented, then each citizen receives payoff of 175 and the factory owner receives payoff of 0 (net of their lobbying costs). If the regulation is not implemented, then each citizen receives payoff of 0 and the factory owner receives payoff of 250 (net of their lobbying costs).

Whether the regulation is implemented depends on how much each side lobbies. Let C1 be how much citizen 1 lobbies, C2 be how much citizen 2 lobbies, and F be how much the factory owner lobbies (i.e., each of these takes value of either 0 or 1). If the citizens lobby C = C1 + C2 hours and factory owner lobbies F, then the government regulates water with probability

0.5 if C = F = 0,

C

C + F otherwise

(a) Which policy, regulation or no regulation, is the utilitarian optimum? Why?

(b) Calculate the best response of citizen 1 to all four combinations of lobbying efforts by citizen 2 and the factory owner.

(c) Based on the answer you received in part (b), does citizen 1's optimal lobbying choice depend on what others are doing? Can you explain why or why not?