We study the equilibrium effects of innovation subsidies that reduce firms' innovation costs in a monopolistic competition model with firm heterogeneity in innovation capabilities and an industry-level resource constraint. Subsidies change product market competition and resource price, and further affect firms' innovation. We show a counterintuitive result: though subsidies lower innovation costs, high-capability firms may reduce their innovation. This finding implies that the demand curve for innovation investments of certain firms in equilibrium can be locally upward-sloping. We show that at the industry level, both average innovation input and output demonstrate inverted-U shaped responses to increasing subsidies but with differing turning points. Notably, an increase in average innovation input may be accompanied by a decrease in average innovation output. These findings cast doubts on the interpretation of existing empirical evidences on firm and industry responses to innovation subsidies, most of which assume away treatment effect heterogeneity and equilibrium feedbacks.
Owing to their capability to produce reactive oxygen species (ROS) under solar irradiation, covalent organic frameworks (COFs) with pre-designable structure and unique architectures show great potentials for water purification. However, the sluggish charge separation, inefficient oxygen activation and poor structure stability in COFs restrict their practical applications to decontaminate water. Herein, via a facile one-pot synthetic strategy, we show the direct conversion of reversible imine linkage into rigid thiazole linkage can adjust the $π$-conjugation and local charge polarization of skeleton to boost the exciton dissociation on COFs. The rigid linkage can also improve the robustness of skeleton and the stability of COFs during the consecutive utilization process. More importantly, the thiazole linkage in COFs with optimal C 2p states (COF-S) effectively increases the activities of neighboring benzene unit to directly modulate the O2-adsorption energy barrier and improve the ROS production efficiency, resulting in the excellent photocatalytic degradation efficiency of seven toxic emerging contaminants (e.g. degrading \textasciitilde99% of 5þinspace}mgþinspace}L−1 paracetamol in only 7þinspace}min) and effective bacterial/algal inactivation performance. Besides, COF-S can be immobilized in continuous-flow reactor and in enlarged reactor to efficiently eliminate pollutants under natural sunlight irradiation, demonstrating the feasibility for practical application.
