A phase diagram analysis on "The environment and directed technical change"

Analyzing a dynamic general equilibrium model that incorporates endogenous and directed technical change and environmental constraints, Acemoglu et al. (2012) present thought-provoking discussions on green growth and environmental disaster. For the clarity of argument, they place a restriction on the initial technology levels (Assumption 1). By means of the phase diagram, this note shows that without the assumption the same arguments can be extended. In other words, their results remain valid in the wide range of the initial technology levels. Also, it is shown that there exists a threshold of the relative technology level, which determines the future of the environment: Disaster or restoration.