²The results do not change if we permit differences in the levels of wealth across households, but this is because we are assuming CRRA utility, perfect certainty, perfect capital markets, and various other things. When any of these assumptions is relaxed, the distribution of assets does matter. For exploration of this more complex and realistic framework, see Carroll (1992), Aiyagari (1994), Krusell and Smith (1998), Carroll (2000).