Several people are have published work on compulsory voting and income inequality. In a broad cross-national paper (Chong and Olivera, 2008. "Does Compulsory Voting Help Equalize Incomes? Economics and Politics 20.3. "), enforceable compulsory voting is associated with greater income equality as measured by the GINI coefficient.
"Enforceable" is an important caveat - many countries with compulsory voting policies don't enforce them well. This page shows countries, their voting requirements, and voter turnout figures. Countries with compulsory voting range from about 70% - 80% voter turnout. The possible penalties for not voting range from nothing at all to imprisonment or losing the right to vote altogether.