Burglary and income inequality

In a model where risk-neutral agents have differing (legal) incomes which may be supplemented by burglary, we study the effects of income distribution on the level of burglary. Assuming that a detected burglar is incarcerated for a fixed term, and assuming that burglars choose target houses using the signal of house quality, we show how increases in income inequality may increase the level of crime. In particular, increases in 'relative differential' inequality, unambiguously increase burglary crime. Corollaries are that a more regressive income tax increases the level of crime, and that richer neighborhoods may have lower crime rates.