 Economists who want to advise their governments on climate policy often talk about the social cost of carbon. What is that? How is it important? How do they calculate it? And why do they fight over it? The earth is warming. Its main cause is the emission of carbon dioxide, which we produce every day when we use fossil fuels to drive our cars, to heat our homes and to produce the goods in our factories. We can stop global warming if we move away from fossil fuels to renewable energy, but how much effort should we put in? To answer that question, economists calculate the social costs of carbon. The basic idea is simple. Economists calculate the expected damages from global warming and divide these by the emissions that cause the warming. The ratio between the damage and its cause is the social cost of carbon. Economists say that this is the price that everyone should pay as a climate tax when they use fossil fuels. To put the theory into practice, economists develop models that do all the calculations. So important are these models that the Nobel Committee awarded the prize in 2018 to William Nordhaus, one of the first economists who did the calculations. How did he go about it? The first step is to calculate the damages caused by global warming. We can calculate the costs of air conditioning in summer when it becomes warmer and the prevented costs of heating in the winter. We can calculate which crops may grow when the climate changes and how much they change the value of farming. In this way, economists have found damages to be in the order of a few percentage points of our income for each degree Celsius of global warming. In this video clip, we will use the symbol delta for this damage estimate. Importantly, it is a relative damage estimate. Thus, if delta equals 0.02, that means that each degree Celsius temperature rise will cause damages that equal 2% of our income. We thus multiply that number with world income, 80 trillion euros per year, for which we use the symbol y. If we multiply the two, we find that each degree Celsius of temperature rise will cost us 1.6 trillion euros. The second step is that we find out the climate sensitivity. Economists rely on their colleagues in natural sciences who use large climate models. They predict that for each million, million tonnes of carbon dioxide, global temperatures go up by between a half and 0.7 degrees Celsius. We use the symbol sigma for this climate sensitivity estimate. Multiplying all terms, we find that each ton of carbon dioxide causes 96 euro cents of damages each year. The climate models predict that the temperature rise is almost permanent. The economist then asks for how many years we should look ahead. If we add all future damages forever, damages become infinite. But most economists say that the future weighs less than the present. When we invest our money in the economy, we receive an interest of maybe 5% on our investments. We should use the same interest to discount future damages. On the other hand, the world economy has increased by 3% a year over the past half century. Next year's damages will also be 3% larger but discounted at 5%. The year after, damages are again 3% larger and again discounted at 5%. With a smart mathematical trick, economists then find that the sum of all weighted damages is equal to 50 times the annual damages, where the 50 is equal to 1 divided by the difference between the interest and the growth rate. We are ready. We have a simple formula for the social cost of carbon. 0.02 times 80 times 0.6 divided by 0.02 gives 48 euros per tonne of CO2. Why is this important? Economists tell our governments that we should tax fossil fuels by 48 euros per tonne of CO2. Not all economists agree. Some believe that damages are much larger because ecosystems will suffer and these do not receive enough weight in the estimates. Other economists say that we should use a larger or smaller interest rate. They quarrel about the numbers. The fossil fuel industry has smartly used the disagreement to push back the call for climate policy. It is now time to overcome the differences. Almost all economists agree it is time that fossil fuels pay for the damages they cause. We need the social cost of carbon as a climate tax because we need to stop climate change.