Optimal taxation with endogenous fertility and health-damaging emissions

Abstract

Output is produced from labor and capital by technologies that differ in their emission intensity and relative capital intensity. Aggregate emissions decrease every individual’s health, but each individual can invest its own health. Population grows by the difference of fertility and exogenous mortality. Labor is used in production or child rearing. I construct a differential game where the benevolent government is a leader that determines taxes and subsidies, while the representative family is a follower that saves in capital and decides on its number of children. The main results are as follows. Without government intervention, population increases or decreases indefinitely. Capital should be taxed, if dirty technology, and subsidized, if clean technology is relatively capital intensive. Child rearing should be taxed, if dirty technology is relatively capital intensive or mildly labor intensive.