1. [10 pts] Betty is looking for a job. She considers job opportunities in two cities. Betty's utility is given by y w, where y is the lifetime income and m is the amount spent on buying a house. The income from City 1 uctuates although the house price is stable. On the contrary, the income from City 2 is stable while the house price uctuates. If she moves to City 1, Betty can earn a lifetime income yl with probability a: and 1 + yl with probability 1 a. The house price in City 1 is ac]. Moving to City 2 means that Betty can earn an income of y2. However, the house price is 2:2 with probability '7 and 1 + $2 with probability 1 7. Do the following: (a) Write down the expected utilities associated with living in the two respective cities, 216., V1 and V2. (b) Derive the condition under which Betty chooses City 1