Robustness of results under general production and utility functions

Establish that the qualitative results derived under linear production technologies (G_t = a^g μ_t l_t^g and B_t = a^b μ_t l_t^b) and linear utility u^i(g_t, b_t) = λ_t γ(i) g_t + b_t—specifically, the local stability of the green steady-state equilibrium and the feasibility of achieving a green transition via lower or temporary taxation on the brown good due to positive social-preference externalities—remain valid when the production and utility functions are replaced by general, standard non-linear functional forms commonly used in macroeconomic analysis.

Background

The paper studies an economy with two consumption goods (green and brown) where household utility combines an intrinsic individual preference for the green good γ(i) and a social preference component λ_t that increases with the past ratio of green to brown consumption. Brown-good consumption is taxed at rate τ and tax revenue funds public healthcare H_t, while labour productivity μ_t depends on past brown output and healthcare levels.

Under linear production functions and linear utility, the authors characterize equilibrium dynamics, show conditions for local stability of a green steady-state equilibrium (with zero brown consumption), and demonstrate that the social-norm externality permits a lower, potentially temporary tax on the brown good to achieve the green transition. The conjecture asks whether these qualitative results persist under more general, standard assumptions for production and utility, which would strengthen the robustness and policy relevance of the model’s conclusions.