ECON 601 - Microeconomics: Theory and Applications - Final Exam - Question 2: Evolutionary dynamics
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?
Show your work.
2.2. For what values of δ would a law integrating segregated neighborhoods be Pareto-improving?
Draw two figures representing pb(f) and pr(f) over f, one where integrated (f = 1⁄2) neighborhoods are preferred to perfectly segregated ones and one where they are not. Circle all equilibria and indicate which are stable.
2.3. A key difference between this model and most instances of housing segregation is that real world groups tend to have asymmetric preferences and power. Imagine that reds have the same preferences as above with p = 1 and δ = 0.1, but high-income blues are agnostic about neighborhood composition and value all homes based on housing quality at the slightly elevated rate of pr(f) = 1.1. Draw the figure representing these two price dynamics, identify all equilibria, and discuss their stability.
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