Climate, technology, family size; on the crossroad between two ultimate externalities

We extend the Brock-Mirman model with endogenous growth through variety expansion, temperature rise affecting both the level and build up of TFP, human capital, and endogenous fertility. We derive closed-form solutions for capital investments, research, and the Social Cost of Carbon. Calibration of the fundamentals show that the social costs of carbon associated with reduced TFP growth are very large (median: 161 euro/tCO2) compared to previous SCC estimates based on climate change TFP-level effects. We also compare the contribution of population growth to welfare through its effects on knowledge creation versus its effect on accelerated climate change. We find in most cases a net positive externality of children on average welfare for other dynasties (median: 22 keuro/child).