What is the Price of Carbon? Five definitions

What is the value of a tonne of CO2 that has not been emitted into the atmosphere, or in other words, the carbon price? It all depends on what you mean by value! The purpose of this note is to elucidate and illustrate five frequently used definitions of the carbon price for one tonne of carbon (as in carbon dioxide) avoided: 1. The expected mitigation of climate-change damage, 2. The cost of reducing CO2 emissions, 3. The social cost of carbon, 4. The politically negotiated value and 5. CO2 market prices.