Recent discussions on the future of metropolitan cities underscore the pivotal role of (social) equity, driven by demographic and economic trends. More equal policies can foster and contribute to a city's economic success and social stability. In this work, we focus on identifying metropolitan areas with distinct economic and social levels in the greater Los Angeles area, one of the most diverse yet unequal areas in the United States. Utilizing American Community Survey data, we propose a Bayesian model for boundary detection based on income distributions. The model identifies areas with significant income disparities, offering actionable insights for policymakers to address social and economic inequalities. Our approach formalized as a Bayesian structural learning framework, models areal densities through finite mixture models. Efficient posterior computation is facilitated by a transdimensional Markov Chain Monte Carlo sampler. The methodology is validated via extensive simulations and applied to the income distributions in the greater Los Angeles area. We identify several boundaries in the income distributions which can be explained in light of other social dynamics such as crime rates and healthcare, showing the usefulness of such an analysis to policymakers.

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