There are two kinds of people: Safe Sallies and Risky Rachels. Safe Sallies view traffic lights as amenities and get +1 utility for each light. Risky Rachels drive like maniacs and see traffic lights as disamenities. They get -1 utility for each light.

There are two towns A & B that have identical wages, rents, etc. Each town installs S/(S+R) traffic lights where S is the number of Sallies and R is the number of Rachels. (Basically, the bigger the fraction of Sallies the more votes for traffic lights.)

At the dawn of time, two Rachels and two Sallies are born in each town.

a) Assume moving costs are 0.2. Is the current situation at the dawn of time a spatial equilibrium (meaning does anyone have incentive to move, assuming the rest stay)?

b) Assume we return to the dawn of time with two Rachels and Sallies in each town but moving costs are 0.05. What is the new spatial equilibrium?