Question

The government is contemplating to implement actions to prevent climate change. If no action is taken then climate change will happen with a probability of 10%. There is a probability of 100%-10% that there will be no climate change. We will not be able to tell if there is climate change until 30 years from today. In 30 years, we will know if there is climate change but it would be too late to do anything about it if climate change takes place. If there is climate change then the world will suffer a loss of $71 million a year forever starting in year 30 +1. Scientists say that we can prevent climate change for sure by reducing emissions of CO2 today. The cost of reducing emissions is $28, 000 every year forever. Assuming the interest rate is 17.7%, what is the expected value doing nothing against climate change minus the expected value of preventing climate change?

Answer 1

Expected value of preventing climate change:
It is given that each year it would cost $28,000 to prevent climate change.
And the interest rate is 17.7%
Therefore, interest rate on that money after 1 year would be 28,000 [1 + 0.177]
Interest rate on that money after 2 year would be 28,000 [1 + 0.177 + 0.177^2]
Let r be the interest rate then we can write it's value as 28,000 [1+r+r2+r3+r4+.. .]
This is a geometric series and since 0<r<1 so it's value would be = 28,000/(1-r)
= 28,000/(1- 0.017)
= $28,884.23
This sum will be added every year.

Therefore, expected value of preventing climate change = $28,884.23 + $28,884.23 + ......

Expected value of doing nothing about climate change:
After 30+1 year it will cost $71000000 with a probability of 10%
Its value would be = 10/100 * [71000000/(1-0.177)] = $5843300
And this sum will be added every year after 30 years.
1-0.056
Therefore, expected value of doing nothing about climate change = $5843300 + $5843300 + ...
Therefore, (Expected value of doing nothing about climate change - Expected value of preventing climate change) = (5843300 - 31*28,884.23) + (5843300 - 28,884.23) + (5843300 - 28,884.23) + ....

Therefore, this sum will be a positive value.

Don't forget to upvote if you find the solution useful. Thank you!