On income fluctuations and capital gains with a convex production function (Q5903470)

This work considers a one-good economy. The production function is random and not necessarily concave; the interest factor is variable and the consumer must maximize asymptotically the expected accumulated and discounted utility. One proves that the value function is concave and the limit policy is optimal and is the unique one. Furthermore, if the production function is convex, there exist two levels of capital with the property that for initial capitals below the first level the optimal sequence of capitals stays bounded with probability one; for initial capitals above the second level, the optimal sequence of capitals tends monotonically to infinity; for initial capitals between the two levels the optimal sequence of capitals leaves the interval with probability one.