English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Discrete choice models with social interactions or spillovers may exhibitmultiple equilibria. This paper provides a systematic approach to enumeratingthem for a quantitative spatial model with discrete locations, socialinteractions, and elastic housing supply. The approach relies on twohomotopies. A homotopy is a smooth function that transforms the solutions of asimpler city where solutions are known, to a city with heterogeneous locationsand finite supply elasticity. The first homotopy is that, in the set of citieswith perfectly elastic floor surface supply, an economy with heterogeneouslocations is homotopic to an economy with homogeneous locations, whosesolutions can be comprehensively enumerated. Such an economy is epsilon closeto an economy whose equilibria are the zeros of a system of polynomials. Thisis a well-studied area of mathematics where the enumeration of equilibria canbe guaranteed. The second homotopy is that a city with perfectly elastichousing supply is homotopic to a city with an arbitrary supply elasticity. In asmall number of cases, the path may bifurcate and a single path yields two ormore equilibria. By running the method on thousands of cities, we obtain alarge number of equilibria. Each equilibrium has different populationdistributions. We provide a method that is computationally feasible foreconomies with a large number of locations choices, with an empiricalapplication to the City of Chicago. There exist multiple ``counterfactualChicagos'' consistent with the estimated parameters. Population distribution,prices, and welfare are not uniquely pinned down by amenities. The paper'smethod can be applied to models in trade and IO. Further applications ofalgebraic geometry are suggested.

Equilibrium Multiplicity: A Systematic Approach using Homotopies, with an Application to Chicago