Homework questions help please? 2.Mike and Mary are considering two options for

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Homework questions help please?

2.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.

a) As utility maximizers, should the couple go to Yellowstone or Chicago?

b) What probability of rain in Chicago would leave the couple indifferent between the two honeymoon destination?

Explanation / Answer

(1)

Expected value, Lottery 1 = 0.5 x $125 - 0.5 x $100 = $62.5 - $50 = $12.5

Expected value, Lottery 2 = (2/3) x $44 - (1/3) x $64 = $29.33 - $21.33 = $8

A risk-neutral individual will choose the lottery with higher expected value, that is, lottery 1.

If U = (M + 100)0.5,

Utility from lottery 1 = (12.5 + 100)0.5 = (112.5)0.5 = 10.61

Utility from lottery 2 = (8 + 100)0.5 = (108)0.5 = 10.39

Lottry 1 (with higher utility) would be chosen.

Here, risk aversion or neutrality does not impact the decision.

(2)

(a)

Expected utility, Yellowstone = 0.6 x 100 + 0.4 x 0 = 60

Expected utility, Chicago = 0.8 x 70 + 0.2 x 40 = 56 + 8 = 64

Since expected utility is higher for Chicago, the couple would prefer Chicago.

(b)

Expected utility, Yellowstone = 0.6 x 100 + 0.4 x 0 = 60

If probability of rain in Chicago be P, then

60 = P x 40 + (1 - P) x 70

60 = 40P + 70 - 70P

30P = 10

P = (1/3)

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