Modeling the evolution of carbon intensity: Linking the Solow model to the transport equation

While a sustained contraction of global production could lower emissions, it would hamper economic development in poorer countries, reduce living standards for low-income households in advanced economies, and heighten the risk of social unrest. Therefore, reducing carbon intensity emissions per unit of output appears to be the most viable and sustainable path forward. We make two contributions: one empirical and one theoretical. Empirically, we show that the distribution of carbon intensities across major economies has followed a path since 1995 that is well approximated by the transport equation, a basic differential equation from physics. Theoretically, we show that in an extended Solow model with abatement capital, the distribution of carbon intensity across a continuum of economies also follows the dynamics described by the transport equation. This theoretical result remains empirically plausible under standard parameter values. Unlike its empirical counterpart, the calibrated model can provide projections of emissions and temperature increases under various policy scenarios, with results aligning closely with forecasts by leading institutions.