A Golden Formula in Neoclassical-Growth Models with Brownian-Motion Shocks

type="main" xml:id="sjpe12042-abs-0001"> <title type="main">Abstract</title> <p>In the paper, a Golden Formula, which does not depend on the specification of production and preference functions, is established to reveal that time-average of the growth rate of optimal capital accumulation will converge to a constant, which is endogenously determined by relevant parameters, almost surely. The Golden Formula naturally implies surprisingly interesting and also intrinsic economic relations between some important macroeconomic variables; for example, it serves as a direct bridge between the modified Golden Rule and the modified Ramsey Rule. Furthermore, it indeed subsumes and hence substantially extends the classical Golden Rule in deterministic theory.