Pollution Effects on Public Capital and Social Capital Accumulation

The interactions between the accumulation of public capital, the formation and environmental degradation are largely unexplored in the literature on growth. Each of these dimensions has recieved considerable attention in isolation, but no existing model treats them a state variables evolving jointly within a unified intertemporal framework. This paper fills this gap by developing a theoretical model, in which public capital, social capital and a stock of pollution accumulate simultaneously beside private capital. Social capital formation is endogenised via a meeting opportunity parameter linked to the availability of public infrastructure, whilst pollution appears as a by-product of productive activity, without entering into household utility. Firstly, the model admits a unique internal steady state. Secondly, a Hopf bifurcation occurs near this state, allowing the rise of a stable limit cycle and ensuring that the economy converges towards a regime of persistent endogenous oscillations. These results are established analytically and confirmed by numerical simulations.