A two-sector model of economic growth with social capital accumulation

• We analyze a two-sector growth model with social capital accumulation.
• The productivity of leisure is determined by the quality of social environment.
• We show that the time evolution of social capital may exhibit an inverted-U shaped path.
• This finding can be obtained only if the balanced growth path is locally indeterminate.

In this paper we analyze a two-sector growth model in which the utility function is not additively separable in consumption and “quality leisure time”. Differently from the main body of theoretical literature on quality leisure, we assume that the “productivity” of leisure is not determined by the stock of human capital but instead by the quality of social environment, which in turn depends on the joint action of the economy-wide average leisure and of the stock of social capital. In this context we show that the time evolution of social capital may exhibit an inverted-U shaped path, according to which the stock of social capital, initially increasing, becomes definitively decreasing. This result is consistent with several empirical studies about the time evolution of social capital in industrialized economies (see e.g. Robert Putnam, 1995 and Putnam, 2000). Furthermore, we show that the inverted-U shaped evolution of the stock of social capital can be observed only if the balanced growth path is locally indeterminate.