Technological progress produces both positive and negative economy wide externalities. Although positive spillovers seem to prevail most of the times, there is evidence and logical arguments revealing that investment in R&D can exceed the corresponding socially optimal level. Taking on board the assumption that the two kinds of externalities are possible and that, therefore, one is able to define the pace of technical progress required to maximize social welfare, we develop a standard two-sector optimal growth model with externalities in the production of technology. The added assumption allows for introducing endogenous business cycles in the Walrasian growth setup. The undertaken stability analysis discusses the local properties of a difference equation two-dimensional system, identifying the occurrence of a flip bifurcation, and looks at global dynamics, through a numerical example, in order to better illustrate and describe the non linear nature of the system.

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• Physical Sciences - Natural Sciences