The Ramsey–Cass–Koopmans model (M-1) relies on the “neoclassical” dogma of declining marginal utility of consumer goods that can take place under non-realistic assumptions besides the dead abstraction of perfect foresight. This model consists of two ODEs—for private consumption and for capital intensity, both are related to labour input in efficiency units. A positive (strongly destabilizing) second-order feedback loop connects these variables. M-1 possesses a saddle stationary state. Linearized M-1 has a saddle path that is allegedly stable optimal solution gained through the Pontryagin maximum principle with an initial private consumption as a jump variable. An existence of such a non-resilient saddle path is practically excluded in M-1. This utter instability leads to typical outcomes outside a viable region: the first with complete destruction of fixed production assets, the second with usage of asymptotically 100% of net output for accumulation of fixed production assets. This unsound model should be not included in realistic models for avoiding wrong economic and climate projections as well as heavy policy risks. An alternative model R-1 with robust proportional and derivative control over private consumption with historically given initial conditions enables socially efficient extended reproduction.