A physico-economic model of space debris management

We solve a stylized physico-economic model of orbital environment and space activity, in order to analyse the externality caused by the accumulation of space debris. In line with Gordon (1954) and Schaefer (1957), we focus on the long-term equilibrium of the orbit, induced by a constant rate of satellite launches forever. We show that if, in the long run, the risk of satellite destruction by collision is increasing and convex with the launch rate and becomes arbitrarily large for sufficiently large values of the latter, then the curve representing the long-term expected population of functioning satellites, as a function of the launch rate, has an inverted-U shape. Classically, we then define and compare typical ways of managing the orbital environment (maximum carrying capacity, open-access, social optimum). The maximum carrying capacity is defined as the maximum expected population of satellites that the space sector can sustain in the long run. The physico-economic equilibrium launch rate, that would presumably emerge under conditions of open-access to the orbit, is defined as the launch rate such that the space sector makes no profit. The socially optimal launch rate is the one that maximizes the present value profit of the space sector per launch campaign. Finally, we discus the use standard economic instruments (command-and-control, tax and market) to regulate space activity in order to achieve an optimal outcome. A numerical application based on a realistic calibration is also proposed to illustrate all results.