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An optimal growth model is devised and subject to dynamic analysis. The model is a standard intertemporal utility maximization framework, with a one-dimensional constraint characterizing the pace of productivity growth. In this setting, knowledge acquisition depends not only on the investment in the adoption of existing technologies, but also on the pre-determined shape of the world’s productivity distribution. The configuration of the distribution will determine the probability of successful imitation and, therefore, the extent in which the economy might approach the world’s technology frontier. The dynamic analysis points to the formation of a saddle-path stable equilibrium. The type of distribution is decisive in defining the exact location of the stable trajectory and of the equilibrium point.
Orlando Gomes (2024) studied this question.