A privatecompany boss and two ordinary people both lobby local government to regulate the water supply to make it clean.Each side (either the boss or the citizens) can pick whether they lobby or not. If they pick yes, they invest 1 hour. If no, 0 hours

One hour of their time is worth $100. If the water is regulated then citizens each get benefits of 175 while the private company boss gets 0, which is the net of their efforts. If no regulation is imposed, then citizens each 0 benefit and the boss gets 250, which is the net of their efforts. The regulation being imposed depends on how much each side puts into their efforts to petition the government.Let k1 and k2 be the efforts by citizens, and g is the effort by the boss. Each can take a value of 0 or 1.

If the citizens put in effort, kis the sum ofk1 andk2 hours and boss has g.The government regulates water with a probability

there is a chance of0.5 if k = g = 0

if there is effort then k/(k+g)

a. Write down the Nash equilibrium. Which is the result for the water regulation? Which result, regulation yes or no, is the optimal utilitarianresult? Why?

b. What is the best response of person 1to all four combinations of petitions by person 2 and the boss.

c. Considering the previous answer, does person 1's optimal action choice depend on what others are doing? Explain why or why not?

d. If both persons do not take action. What is the boss's best response to this situation?

e. If transfers couldhappen and everyone values money the same way, which result would be Pareto efficient?