We study the mechanisms according to which social infrastructure influences the preservation of physical capital and, consequently, economic growth. The presented model considers that social infrastructure is a specific type of human capital, which acts in order to preserve already existing physical capital, by, e.g. reducing the incentive for rent seeking or corruption. Using an innovative methodology in economics, the Gröbner bases, we study the equilibrium of our model and conclude for the existence of two feasible steady-states or of unicity according to different combinations of parameters, highlighting a trade-off between consumption and production on one hand and social infrastructure and physical capital accumulation, on the other. We also present sufficient conditions for saddle-path stability. Finally, we describe transitional dynamics and calculate welfare effects from what we show that strengthening social infrastructure increases welfare.

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