Dirty money needs somewhere to go. Every district sells every kind of property, from a rented room or a slum shack up to the finer addresses, one of each per district, and you buy where you stand.
Live in one: a better home raises your happiness. Businesses pay you an income every day, after their upkeep. The rest you can rent out to other players, with a rent book that keeps track of who pays.
Money moves between players too. Buy and sell on the Bazaar, keep your savings in the bank, and watch the stock exchange, where prices rise and fall with the city.
Owning property gives you a stake in a district. Prices and upkeep are part of the city's economy, so a property empire takes planning as much as cash.
Everyone starts in a rented room; a better address says you have made it. As you climb you can own more than one property and spread across the districts, from the docks to Capitol Hill. A good business keeps paying while you are busy elsewhere: income you don't have to commit a crime for.