##### 6. Ethel is trying to decide whether to have 0 cars, 1 car, or 2-(Answered)

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**Question**

6. Ethel is trying to decide whether to have 0 cars, 1 car, or 2 cars. If x is the number of cars she has and y is the amount of money she has per year to spend on other stuff, Ethel's utility function is U(x, y), where U(0, y) = y^{1/2}, U(1, y) = (15/14)y^{1/2}, and U(2, y) = (10/9)y^{1/2}. Suppose that it costs $2,000 a year to have 1 car and $4,000 a year to have 2 cars. Ethel finds that the right thing to do depends on her income.

a. What is her willingness to pay for 1 car if her income is M?

b. What is the lowest income at which she would have a car?

c. What is the lowest income at which she would have 2 cars?

a. Her willingness to pay for 1 car is about 0.129M, where M is her income.

b. The lowest income at which she would get a car is $15,504.

c. If we solve the equation U(1, y - 2,000) = U(2, y - 4,000), we find $55,143. At incomes above that she prefers 2 cars; below that she would be better off to have 1 car.

Paper#9256758 | Written in 27-Jul-2016

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