  By its nature, the so-called social cost of carbon (SCC(t)) will likely not
cover the cost induced by climate change (damage cost and abatement cost) if it
is used as a CO$_2$-price. It is a marginal price only. We define an implied
CO$_2$-price that covers the climate change-induced costs. The price can be
interpreted as a \textit{polluter pays principle}. A numerical analysis using a
classical DICE model reveals that the cost-implied CO$_2$ price is around 500
\$/tCO$_2$, while the corresponding price associated with the SCC is about 50
\$/tCO$_2$. In addition, we define the internal rate of return of carbon
abatement and calculate it for the classical DICE model. This rate is much
higher than the model's discount rate, which may suggest the advantage of
financing abatement by loans.
