Decision Theory and Stochastic Growth

This paper examines connections between stochastic growth and decision problems. We use tools from the theory of large deviations to show that wishful thinking decision problems are equivalent to utility maximization problems, both of which are equivalent to growth max-imization under idiosyncratic risk. Rational inattention problems are equivalent to growth-optimal portfolio problems, both of which are equivalent to growth maximization under aggregate risk. Stochastic growth generates extreme inequality, with nearly all wealth eventu-ally held by those who happen to have faced empirical distributions that match the solution to the wishful thinking or rational inattention problem. (JEL D31, D81, D82, D83, G51, O41)