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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.
Expert Solution
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.
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