Global warming

Global warming is an especially difficult policy problem because it involves a lot of uncertainty and very long spans of time. To see why, consider the following stylized example. Suppose that the following things are known:

• No one will be able to tell whether warming is occurring until 50 years from now.
• If no action is taken, warming will occur with probability w; with probability (1-w), however, the world won't warm up even if we do nothing to stop it.
• In year 50 it will be clear whether warming has happened. At that point, however, it will be too late to do anything about it. If warming occurs, it causes a loss of $1 trillion ($1000 billion, about 1/8th of current US GDP) a year forever starting in year 51.
• Warming can be prevented for certain by cutting carbon dioxide emissions substantially starting in year 1. (That is, enacting this policy would cause w to become zero.) The compensating variation for such a policy is $60 billion a year forever (starting in year 1). For the policy to be effective, it must begin right away even though the uncertainty will not be resolved until year 50.

Using this information, please answer the following questions:

1. Suppose that the interest rate is 5% and w is 10%. Would a risk neutral agent adopt the emissions-cutting policy or do nothing? Why? Is it a close decision? Explain. Show how you obtained your answer. Assume the decision is made in period 0.
2. If w is 10%, what is the maximum interest rate at which it makes sense to adopt the prevention policy? When the interest rate is 5%, what is the minimum value of w for which the prevention policy makes sense? Discuss. Be sure to show your work.

Note: This is a very stylized representation of the climate change problem. In reality, there are several important uncertainties, including the amount of warming that will occur (eg, how many degrees), and the damages that will result from that warming (eg, how bad it is for the climate to warm up a given amount). The problem collapses the all those uncertainties into one probability that represents the chance that climate-related damage will occur. A more detailed analysis would treat them all separately.

Solution