Public Capital Stocks in Dynamic Fiscal Competition

We study dynamic fiscal competition when mobile capital responds to the stock of
public infrastructure, not contemporaneous expenditure flows. Two governments
choose taxes and public investment in a differential game with gradual accumulation
and investment frictions. In the unique Nash equilibrium, long-run dynamics
depend on discounting, erosion of advantages, the share of public investment that
effectively adds to infrastructure, the private productivity effects of infrastructure,
and adjustment/acquisition costs on public investment. The model delivers convergence
to a symmetric steady state, and moderate acquisition frictions generate
“invest–then–stop” equilibria; lowering acquisition costs or accelerating diffusion
prevents premature exit from infrastructure competition. Large initial gaps can
rationally delay the laggard’s investment, generating distinct transition paths and
persistent asymmetries.