Consider a city of 200 people (100 rich and 100 poor) and two neighborhoods (100
people in each). Both groups generally prefer to live with rich people and are willing to
pay a premium for living with a fraction of rich people that is larger than 50%. Poor
people’s premium curve is given as �!""# = 2�$, where x is the percentage of rich above
50% (e.g., if there are 52% rich, x will be 2). Rich people’s premium curve is given by
�%&'( = 60� − 0.4�$.
a) What is the equilibrium outcome (i.e., what is the share of rich and poor people,
respectively). Explain.
b) Calculate the premium to be paid at the equilibrium.
Sample Solution