We consider model of adaptation of pure time preference in the closed economy with three assets and non-uniform households. We were studying that the households are trying to imitate the currently optimal one. Such adaptive behavior leads to the convergence of the pure time preference rates and wealth redistribution. We have shown that the system possesses the equifinality property: regardless on the criterion of the determination of the most prosperous household the final distribution is defined solely by the value of R_i=w_i exp{-delta_i T/beta} in the initial distribution of welath w_i and time prefernce rates delta_i. The criterion R_i shows the existing relationship between wealth and pure time preference rate. The higher delta is the more wealth is required to ensure the high consumption level in future. The higher the beta is the less wealth w is required to compensate too high level of the pure time preference.