Exploring Simulated Residential Spending Dynamics in Relation to Income Equality with the Entropy Trace of the Schelling Model

The Schelling model of segregation has provided researchers with a simple model to explore residential dynamics and their implications upon the spatial distribution of resident identities. Due to the simplicity of the model, many modifications and extensions have been produced to capture different aspects of the decision process taken when residents change locations. Research has also involved examining different metrics for track segregation along the trace of the simulation states. Recent work has investigated monitoring the simulation by estimating the entropy of the states along the simulation, which offers a macroscopic perspective. Drawing inspiration from empirical studies which indicate that financial status can affect segregation, a dual dynamic for movements based on identity and financial capital has been produced so that the expenditure of a monetary value occurs during residential movements. Previous work has only considered a single approach for this dynamic and the results for different approaches are explored. The results show that the definition of the expenditure dynamic has a large effect on the entropy traces and financial homogeneity. The design choice provides insight for how the housing market can drive inequality or equality.