Question

2. On the weekend days during the summer, people in a large metropolitan area like

to go to the beach. Assume the population is 100,000 Suppose that going to the

beach yields a payoff of 15 − k , where k is the number of people who choose to go 1000

to the beach. Suppose that the other option, staying at home, yields a payoff of zero. In equilibrium, how many people choose to go to the beach? If there is more than one equilibrium, report all equilibria.

Answer 1

Ans) Let k be the number of people who choose to go to the beach. Then people staying at home is 100,000-k.

Let us first try to understand the way this problem is constructed. If 1 person goes to the beach, he gets 15-1=14. While 99,999 people get zero. Since going to the beach seems to be a better option, more people would want to go to the beach unless going to the beach pays less than staying at home. And if number of people going to the beach is such that the payoff from going to the beach is negative, more and more people would start staying at home.

Based out of the dynamics as explained above, in equilibrium payoff to people from staying at home has to be equal to the payoff from staying at home.

Thus, 15-k=0 implies, k=15.

Thus, 15 people choose to go to the beach and as soon as 15 people are present on the beach already, it is optimal to stay at home.

The above question is an example of the negative externality. Since the beach is a common area, more and more people would mean resources have to be shared between the larger group, which leads to uneasiness to the ones on the beach.