Please help with some questions from econ homework? Suppose we have utility of w

Question

Please help with some questions from econ homework?

Suppose we have utility of wealth function U(W) = 5 + 5 W + 10 W^2. Calculate the absolute risk aversion? Are they increasing in wealth? You are given the opportunity to play two different lotteries at no cost. The first lottery is a 50/50 chance of winning $125 or losing $100. With the second one, you win $44 with probability 2/3, and lose $64 with probability 1/3. Which lottery should you choose if you are risk neutral? What if you are risk averse and your utility function is U(M) = root M + 100? In this example, does your attitude towards risk affect your decision? Mike and Mary are considering two options for a March honeymoon. They can visit Yellowstone National Park, which has spectacular scenery and great hiking when the weather is clear. When it rains, however, viewing is minimal and hiking is difficult. They have agreed that their utility is 100 if the weather is clear, and 0 if it rains. Based on historic data, the chance of rain in Yellowstone is 0.4. The alternative is a trip to Chicago, which is not spectacular, but offers more to do regardless of weather. Chicago is worth 70 if the weather is clear and 40 if the weather is rainy. The chance of rain in Chicago is 0.2. As utility maximizes, should the couple go to Yellowstone or Chicago? What probability of rain in Chicago would leave the couple indifferent between the two honeymoon destination?

Explanation / Answer

For the given utilioty of wealth function,

U'(W) = 5 + 10 (2W) = 5 + 20W

U''(W) = 20

Absolute risk aversion = U''(W)/U''(W) = 20/(5+20W)

The absolute risk aversion expression "20/(5+20W)" is decreasing in wealth.

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