Betty is looking for a job. She considers job opportunities in two cities. Bettyís utility is given by y- x, where y is the lifetime income and x is the amount spent on buying a house. The income from City 1 fluctuates although the house price is stable. On the contrary, the income from City 2 is stable while the house price fluctuates. If she moves to City 1, Betty can earn a lifetime income y1 with probability alpha and 1 + y1 with probability 1-alpha . The house price in City 1 is x1. Moving to City 2 means that Betty can earn an income of y2. However, the house price is x2 with probability gamma and 1 + x2 with probability 1-gamma . Do the following: (a) Write down the expected utilities associated with living in the two respective cities, i.e., V1 and V2. (b) Derive the condition under which Betty chooses City 1.
Betty is looking for a job. She considers job opportunities in
two cities. Bettyís utility is given by y- x, where y is the lifetime income and
x is the amount spent on buying a house. The income from City 1 fluctuates
although the house
2 is stable while the house price fluctuates. If she moves to City 1, Betty
can earn a lifetime income y1 with probability alpha and 1 + y1 with probability
1-alpha . The house price in City 1 is x1. Moving to City 2 means that Betty
can earn an income of y2. However, the house price is x2 with probability
gamma and 1 + x2 with probability 1-gamma . Do the following: (a) Write down the
expected utilities associated with living in the two respective cities, i.e., V1
and V2. (b) Derive the condition under which Betty chooses City 1.
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