Public capital and private investment, a real option approach

In this paper, we extend the usual models of irreversible investment under uncertainty by introducing the stock of public capital as an input for the private sector. Public investment takes place in a stochastic environment. Public capital then increases the productivity of private capital which is assumed to be fully irreversible. In our model, the government has an intertemporal budget constraint, i.e. taxes are collected each period to fund the public debt. We provide a partial equilibrium analysis, as it is standard in models of irreversible investment under uncertainty. Even under uncertainty, the optimal tax rate is then constant and does not depend on the size of uncertainty, it is exactly the same as the one that would prevail in a deterministic world. We show that the government has an insurance role since it removes part of the uncertainty faced by the firm.