The Solow-Swan neoclassical growth model describes the process of economic growth, which depends on the production function, the neoclassical production function has several economic and mathematical assumptions. The Inada condition is a purely mathematical assumption with not economic interpretation, was introduced to ensure the existence and uniqueness of the equilibrium point in the Uzawa’s Two Sector Economic Growth Model, since then the Inada condition was adopted as an assumption in the Neoclassical Economic Growth Model. We introduce the Richard production function in the neoclassical growth model, this function not only allows to depict the three stages of the industrialization, but also we show that under some conditions of marginal productivity, the Richard’s function describes the poverty traps, exogenous shocks, and others economics features. However, the Richard function does not satisfies the Inada conditions, but explain more economic situations than the Cobb-Douglas production function.