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Homework answers / question archive / Segregation vs
Segregation vs. Integration 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 Ppoor = 2x2, 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 Prich = 60x -0.4x2 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.
Solution :
P(poor) = p (rich)
2x2 = 60x - 0.4x2
2.4x2 = 60x
x = 25
x is the percentage of rich above 50%, thus there are 25% rich people above 50%.
P (poor) = 1,250
P (rich) = 1,250
The equilibrium premium is $1,250.
