We have proposed and studied a new model of economic growth in
which individuals differ only in their current productivity, and the state
of the economy is fully described by the probability distribution of productivities.
The necessary conditions for equilibrium in the model take
the form of a Bellman equation describing individual decisions on the
way to allocate time between producing and searching for new ideas
and a law of motion for the economywide productivity distribution. With
the right kind of initial conditions, these forces can interact to generate
sustained growth. We show that among these possibilities is a balanced
growth path, characterized by a constant growth rate and a stable Lorenz
curve describing relative incomes. We provide an algorithm for calculating
solutions along this path.
This solution is the outcome of a decentralized system in which each
agent acts in his own interest. But the new knowledge obtained by any