The 130 campers at Bear Creek Campground love their own campfires but hate the smoke from their neighbors’ campfires. Each camper’s utility function is U = 22f – f 2 – s, where f is the number of hours her own campfire burns per day and where s is the amount of smoke in the air. It happens that s is 10 times the average amount of hours that campers use their fires. The campground authority could make all campers better off by limiting the number of hours of campfire per day for everyone. How many hours of campfire per day should the authority allow each camper in order to make the typical camper as well off as possible?
