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# ECON 601 - Microeconomics: Theory and Applications - Final Exam - Question 2: Evolutionary dynamics

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Economics 601 -Microeconomics: Theory and Applications

Final Exam

Please answer all questions below. Answers are due as a single document (pdf preferred) on Canvas. Feel free to scan / take photos of hand-drawn answers for math, figures, or diagrams, just make sure to embed them in your answers. Email me if you have any clarifying or similar questions, and good luck!

2.     Evolutionary dynamics (30 points) Suppose that two cultural groups, red and blue, have housing preferences that vary as a function of the fraction f ∈ [0,1] of red households in the neighborhood, with each group’s relative valuation / price being given as:

pb(f)=1⁄2(f+δ)–1⁄2(f+δ)2 +p pr(f)=1⁄2(f-δ)–1⁄2(f-δ)2 +p with replicator equation:

Δf = αf(1 - f)β(pr - pb)

where α is the fraction of movers from either side who consider selling their house, β is the probability a sale occurs given a positive gap in valuation, p = 1 is the intrinsic value of these otherwise identical homes.

2.1.  For what value of own-group discriminatory preference δ will red households value living in a

perfectly red neighborhood equally with living in an equally integrated (f = 1⁄2) neighborhood?