• adjustment costs
• AK model
• leontief production
• nash bargaining
• economic growth
• multi-sectorial model
• dynamic optimization
• economic modelling
• tax credits
• subsidies
• fiscal policy
• public finance
• public debt

The aim of this work is to present and investigate a model that departs from three considerations. First, fiscal policy and debt sustainability are two sides of the same coin: the former is the policy instrument that government manages in the present time to achieve its social objectives, whereas, the latter is the repercussion of the former in the long run. Second, fiscal policy has a direct impact on industries capital accumulation because it affects the available income and, therefore, their savings; such an impact can be evaluated through the intertemporal optimization of industries saving decisions. Finally, fiscal policy has to be characterized on both the revenue and the spending side: revenues are determined through a unique tax rate, while spending is represented as an industry-based subsidy with a fixed fraction, Φ, that must be re-invested in capital. The production function in each industry is assumed AK and investment is subjected to quadratic adjustment costs.
The consequences of assuming a convex adjustment cost function are twofold: the model does not display growth in the long run and the invested capital due to the public incentivization program hyper-crowds out private saving, consequently the optimal Φ is 0. Another advantage, due to the simplicity of the framework, is that the notion of debt sustainability, contrary to the majority of literature on fiscal policy sustainability, is defined unambiguously therefore it is always possible to determine whether a certain public debt can be sustained. In section 4, the model is solved as a Nash bargaining problem by assuming an explicit welfare function and it is found that the optimal government size results undetermined whenever the optimal Φ is 0. However, in the conclusions, it is proposed a way to modify slightly the model in order to overcome the problem of the hyper-crowding-out and letting the designed public program of capital incentivization work effectively.