A remark on the form of accumulation functions in economic growth models

This study is a short note designed to underline the importance of using the theoretically required form of accumulation functions. It is now a common knowledge that a growth model must rely on non-diminishing returns to a factor of production in order to generate endogenous growth. In Lucas (1988), for example, there is no diminishing-returns to the accumulation of human capital, which is the source of endogenous growth in the model. This rule, however, can lead to the following potentially misleading assumption: diminishing marginal productivity to each factor of production - given that there is no other source of long run growth - is sufficient for generating steady state equilibrium at levels. In this short note, we make two points. First, diminishing marginal productivity alone is not necessarily sufficient for generating steady state equilibrium at levels. Second, the inclusion of a theoretically required counter-force in the accumulation function together with diminishing returns is sufficient for generating steady state equilibrium. In conclusion, we heuristically argue that an accumulation function with no theoretically required counter-moving force, with or without diminishing returns, may bias the results of the model. -- Accumulation function ; Stationary state ; Steady state ; Differential equations ; Economic Growth ; Long-run Equilibrium