Dynamic efficiency of tradable license system with time-flexible quantities.

Tradable license system (TLS) is a fundamental policy instrument for environmental management or resource development. We construct a muti-periods dynamic model with respect to a general TLS with three time-flexible quantity mechanisms: fixed quantity, solely banking, and banking and borrowing, in which the firm maximizes its discounted net benefits over the horizon by selecting an optimal license usage by license trading across agents or transferring across periods. The dynamic efficiency performance and price dynamics in TLS are respectively examined. The decentralized equilibrium in TLS with fixed quantity cannot achieve benefit-maximum unless initial license allocation is efficient. The decentralized behaviors in TLS with solely banking lead to benefit-maximum and price dynamics follows the Hotelling rule, if and only if the cumulative initial license allocation in each period is not less than the optimum, while TLS with banking and borrowing can achieve the optimal outcome and price dynamics follows Hotelling rule regardless of the initial allocation. The findings highlight the synergistic effects between the initial allocation of licenses and time-flexible quantity mechanisms in TLS design.

Na/Mo co-doped PbTiO3 for photocatalytic water oxidation and Z-scheme overall water splitting under visible light.

Herein, we demonstrate a sodium/molybdenum (Na/Mo) co-doped ferroelectric PbTiO3 for efficient photocatalysis under visible light. Doped with a high concentration of Mo6+, quasi-continuous new energy levels are successfully introduced below the conduction band minimum of PbTiO3, giving rise to a band-to-band redshift of the absorption edge. The valence state difference of Mo6+ and Ti4+ in the doped PbTiO3 is compensated by the Na dopant, thus effectively suppressing the formation of the recombination centres caused by Mo4+. Combined with the intrinsic built-in electric field in PbTiO3, this Na/Mo co-doping strategy enables PbTiO3 to exhibit superior water oxidation activity under visible light with threshold wavelength up to 550 nm, which also promotes overall water splitting under visible light in a Z-scheme photocatalytic system. This strategy provides a generally applicable solution to extend the visible light absorption spectrum and engineer electronic structures of ferroelectric materials for photocatalysis and other energy conversion applications.