The paper presents a model of wealth distribution that makes use of Gibrat's lawof proportionate effect to explain the way wealth is distributed and how the distribution changes over time. The stochastic factor in each period is shown tobe the result of deliberate choices by individual decision makers regarding their savings, investment, and bequests, given their inherited wealth and natural ability. The source of randomness is two-fold: uncertainty about the rates of return and randomness of the distribution of natural skills. Also studied is the impact of government tax parameters on the inequality of wealth. Two categories of taxes are distinguished: taxes on flows, such as those on income, portfolio returns, and earnings, and those on the stock, such as wealth or estate taxes.