# Discounting and the representative median agent

29.09.2017

**Emmerling**(Fondazione Eni Enrico Mattei, Centro-Euro Mediterraneo per i Cambiamenti Climatici CMCC); Ben

**Groom**(Department of Geography and Environment – London School of Economics and Political Science); Tanja

**Wettingfeld**(Committee on Climate Change)

Economics Letters, Volume 161, 78-81

We derive a simple formula for the social discount rate (SDR) that uses the median, rather than average agent of the economy to reflect the consequences of consumption growth on income inequality. Under reasonable assumptions, the difference between the growth of median and mean incomes is used to adjust the wealth-effect in the standard Ramsey rule. In a plausible special case the representative agent has the median income. With inequality aversion elasticity of 2 (1.5, 1), the U.K. and U.S. SDR would be 1% (0.5%, 0.25%) lower than the standard Ramsey rule. This reflects two decades of inequality-increasing growth and implies greater weight placed on future generations in public appraisal.

We derive a simple formula for the social discount rate (SDR) that uses the median, rather than average agent of the economy to reflect the consequences of consumption growth on income inequality. Under reasonable assumptions, the difference between the growth of median and mean incomes is used to adjust the wealth-effect in the standard Ramsey rule. In a plausible special case the representative agent has the median income. With inequality aversion elasticity of 2 (1.5, 1), the U.K. and U.S. SDR would be 1% (0.5%, 0.25%) lower than the standard Ramsey rule. This reflects two decades of inequality-increasing growth and implies greater weight placed on future generations in public appraisal.