Recent research on climate change predicts that extreme
weather will increase the risk of severe and mild flooding in the next two
years. The study also finds that if any flooding event happens this year, there
will be no risk of flooding occurring in the following year.
The research suggested a 40 percent chance of severe
flooding at the end of this year (𝑃𝐹1​) and a 20 percent chance of
mild flooding (𝑃𝑀F1​). Otherwise, there will be no flooding (𝑃NF1​). If there is no flooding this
year, there is still a 30 percent chance of severe flooding and a 10 percent
probability of mild flooding in the next year (𝑃𝑀F2​).
In response, the NSW government is considering two
strategies:
S1:
Investing in an early warning system – or the system (E)
S2:
Not investing in the new system, remaining in the status quo (NE).
To install the system, the NSW Government must spend
$1,350,000 on the system’s development (𝐶𝑅​) and $200,000 on the
installation cost (𝐶C). Once installed, the system would
last for 20 years. Note that the government may also install the system next
year if they decide not to install it this year.
Economists hired by the government estimated the social cost
of the floods. Without an early warning system, the cost of severe and mild
flooding to society is estimated at $4.5 million (𝐶𝑆𝐹|𝑁𝐸​) and $2.5 million (𝐶𝑀𝐹|𝑁𝐸),
respectively. The government can respond swiftly and evacuate earlier using the
early warning system. Given that, severe flooding and mild flooding would only
cost the economy $1.5 million (𝐶𝑆𝐹|𝐸​) and $50,000 (𝐶𝑀𝐹|𝐸​), respectively.
(a) Construct the decision tree with all the relevant
nodes. Label each branch with corresponding probabilities and outcomes. Use a
rectangular shape to represent the decision node and a circle shape to
represent the chance node.
(b) Discuss your decision tree. Explain what your
decision rule is according to the graph.
(c) Suppose the social discount rate is 6%; which
policy should the government undertake at the beginning of this year?