Optimal transition to greener production in a pro-environmental society

Orlov, S. & Rovenskaya, E. ORCID: https://orcid.org/0000-0002-2761-3443 (2021). Optimal transition to greener production in a pro-environmental society. Journal of Mathematical Economics 98 e102554. 10.1016/j.jmateco.2021.102554.

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Abstract

Achieving sustainable development requires a transition from the current production fashion that leads to the environmental degradation to a cleaner production. Such a substitution can be costly if the new technology is less productive. In this paper, we present a two-sector endogenous growth model that analyzes the potential of a transition from a more productive brown sector to a less productive green sector. The representative agent maximizes the weighted sum of the present value of the utility of consumption and the amenity value of green production. We derive a closed-form optimal solution using a suitable version of the Pontryagin Maximum Principle. For an economy, in which the brown sector dominates initially, we obtain that as long as the preference towards green production is positive, the optimal solution always has a single switching point and the following structure. Initially, the representative agent distributes the output between investment in the green sector and consumption, making no investment in the brown sector. This allows attaining a particular critical ratio between green and brown capital stocks in the fastest way. Once this ratio has been reached, the optimal solution switches to that, which allows both capitals to grow at the same rate. The representative agent has to sacrifice his/her consumption to invest in the green sector, especially in the initial period, which is due to the amenity that this sector provides. Under constant productivities, a full substitution of brown production by green production is not possible; rather, they co-exist and evolve proportionally. Three parameters are positively related to the ratio of the green capital stock: the social discount rate, the (augmented) productivity of the green capital, and a representative agent’s preference towards the green production amenity.

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