  We consider a simple theoretical model to investigate the impact of
inheritances on the wealth distribution. Wealth is described as a finite
resource, which remains constant over different generations and is divided
equally among offspring. All other sources of wealth are neglected. We consider
different societies characterized by a different offspring probability
distribution. We find that, if the population remains constant, the society
reaches a stationary wealth distribution. We show that inequality emerges every
time the number of children per family is not always the same. For realistic
offspring distributions from developed countries, the model predicts a Gini
coefficient of $G\approx 0.3$. If we divide the society into wealth classes and
set the probability of getting married to depend on the distance between
classes, the stationary wealth distribution crosses over from an exponential to
a power-law regime as the number of wealth classes and the level of class
distinction increase.
