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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 P(poor)= 0.9x^2, where x is the percentage ofrich above 50% (e.g., if there are 52% rich, x will be 2). Rich people’s premium curve is given by P(rich)= 35x-0.1x^2. What is the equilibrium outcome? Explain.

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Answer:

Explanation:

Step 1. Given information.

  • City of 200 people
  • 100 rich, 100 poor.

Step 2. Formulas needed to solve the exercise.

  • P(poor) = 0.9x^2
  • P(rich)= 35x-0.1x^2

Step 3. Calculation and step 4. Solution.

P(poor) = p (rich)

0.9x2 = 35x - 0.1x2

1x2 = 35x

x = 35

x is the percentage of rich above 50%, thus there are 35% rich people above 50%.

P (poor) = 1102.5

P (rich) = 1102.5

The equilibrium premium is $1,102.5

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