Jane is trying to decide whether or not to build a dam or a nuclear plant in NYC
ID: 1201831 • Letter: J
Question
Jane is trying to decide whether or not to build a dam or a nuclear plant in NYC as a way to provide cleaner electricity to the surrounding area. If she builds a dam, she has a 40% chance of earning $2500 off electricity produced by the dam and a remaining chance of earning $1600. If on the other hand, she builds a nuclear plant, she has a 25% chance of earning $5000 and a residual chance of earning $1000 off the electricity produced by the plant. Jane’s utility function is as follows: U(Y)= Y^0.5 Where Y is the income generated.
a. What is the expected income Jane expects to earn from building the dam vs the nuclear plant?
b. Which option- the dam or the nuclear plant, does Jane prefer to build? Build option which gives her greater expected utility.
Consider another investor, Mena. Mena would like to build a dam in the Grand Canyon of Western US to provide electricity to the nearby urban area of Las Vegas. Suppose the dam costs $800 million to build and is expected to generate $150 million of annual electricity production forever. The annual discount rate is 5%. There is the possibility of environmental damage from flooding the Canyon. In fact, there is a 50% chance that the environmental damages from building the dam will be as high as $100 million per year and a 50% chance that there will be no damages from building the dam.
a. Without taking into account the expected environmental damage, is the dam a good idea?
b. Taking into account the expected environmental damage, is the dam a good idea (assuming we build it today)?
Explanation / Answer
1.
(a) Expected income form building the damn = 40% of $ 2500 + 60% of $ 1600 = 1,000 + 960 = 1,960
Expected income from building the nuclear plant = 25% of $ 5,000 + 75% of $ 1,000 = 1,250 + 750 = 1,200
(b) Utility from building damn = (1960)0.5 = 44.27
Utility from nuclear plant = (1200)0.5 = 34.64
Jane get more utility from building the damn. So, Jane prefer to build the damn.
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