Energy saving technical progress and optimal capital stock: the role of embodiment

We study optimal capital accumulation at the firm level when technical progress is energy saving. Energy and capital are complementary. First we solve a benchmark case with disembodied technical progress. Then, we turn to the model with embodiment. We characterize the optimal replacement of obsolete capital, and the optimal capital stock. The latter is shown to be lower under embodiment compared to the benchmark case. Moreover, we demonstrate that a rising energy price has two opposite effects on the optimal capital stock under embodiment: the traditional direct negative effects, but also an indirect positive effect via the optimal scrapping rule. Nevertheless, the optimal capital stock is shown to remain a decreasing function of the energy cost