Toward Sustainability: Technology Transition and Endogenous Population Growth

In order to reach the state of economic sustainability, the problem of technology transition emphasizes the possibility of substituting for the exhaustible resource with an everlasting source of energy input. This paper aims at providing an analysis of this problem in an overlapping-generation model where the population is not a datum, but endogenous in the sense that it results from fertility decisions made by economic agents. First, we provide a new proof of the existence of competitive equilibrium under infinite time horizon. Here the difficulty lies in the fact that the market size is itself endogenous, because fertility - hence the population - is an individual decision at every point in time. Second, and perhaps most interestingly, the oil stock might not be entirely depleted, and the unused part in situ may serve the role of storing value for wealth transmission over time, just as money. But in contrast with paper money, which has no intrinsic value, leaving productive oil in situ as a bubble certainly adds another dimension to the inefficiency of overlapping-generation model. In this case, there are infinitely many equilibria as well as many steady states, depending on the data that characterize the initial state of the economy. Moreover, the convergence to some steady state, far from being simply monotone, might exhibit cyclical behavior, such as damped oscillation, limit cycles, etc.