The Stationary Distributions of Wealth with Random Shocks

A convergence model with wealth accumulation subject to i.i.d. random shocks is examined. The transfer function shows what k_{t+1} - wealth at t+1 - would be, given k_t, with no shock: It has a positive slope, but its concavity/convexity is indeterminate. The stationary distribution of wealth satisfies a Fredholm integral equation. This distribution can be examined by direct analysis of the wealth-accumulation stochastic process and via the Fredholm equation. The analysis resembles some econometric theory of time series. Economic theory forces consideration of a broad range of cases, including some which violate B-convergence. Twin peaks in the stationary distribution cannot be excluded.