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30. There are 101 people working together. Each person’s utility function is u(x, y) = x...

30. There are 101 people working together. Each person’s utility function is u(x, y) = x + 0.5y − (x^2)/2 where x is the number of hours she works, and y is the number of hours everyone else (not including herself) works. If people are choosing individually how much to work, how much would each person work?

(a) 1

(b) 50

(c) 100

(d) 51

31. (Continued from the previous problem.) What is the socially optimal number of hours each person should work?

(a) 1

(b) 50

(c) 100

(d) 51

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