Optimal firm behavior underenvironmental constraints

The paper examines the Porter and induced-innovation hypotheses in a firm model where: (i) the firmhas a vintage capital technology with two complementary factors, energy and capital ; (ii) scrappingis endogenous; (iii) technological progress is energy-saving and endogenous through purposive R&Dinvestment; (iv) the innovation rate increases with R&D investment and decreases with complexity;(v) the firm is subject to emission quotas which put an upper bound on its energy consumption at anydate; (vi) energy and capital prices are exogenous. Balanced growth paths are first characterized, and acomparative static analysis is performed to study a kind of long-term Porter and induced-innovationhypotheses. In particular, it is shown that tighter emission quotas do not prevent firms to grow in thelong-run, thanks to endogenous innovation, but they have an inverse effect on the growth rate ofprofits. Some short-term dynamics are also produced, particularly, to analyze the role of initialconditions and energy prices in optimal firm behavior subject to environmental regulation. Amongnumerous results, we show that (i) firms which are historically “small” polluters find it optimal tomassively pollute in the short run: during the transition, new and clean machines will co-exist with oldand dirty machines in the productive sectors, implying an unambiguously dirty transition; (ii) higherenergy prices induce a shorter lifetime for capital goods but they depress investment in both newcapital and R&D, featuring a kind of reverse Hicksian mechanism....