Question

X and Y are working on a group project. They put in x and y hours respectively. They both get the same grade, but X's utility from the grade is given by ?_?=6(?+?)^0.5 −? and Y's utility from the grade is given by ?_?=5(?+0.5?)^0.5−?. They choose the number of hours to work on the project simultaneously.

X thinks Y is not doing his fair share so threatens that she will put in zero hours. In this case how many hours does X end up working?

Answer 1

X assume that y = 0

Not X will end up working that many hours where she gets maximum utility.

UX = 6(?+?)0.5−?

Ux = 6(x + 0)0.5 - x

To maximize Ux,

d(Ux)/dx = 6*0.5(x)-0.5 - 1

3x-0.5 - 1 = 0

3x-0.5 = 1

x-0.5 = 1/3

x0.5 = 3

(x0.5)2 = (3)2

x = 9

So X will end up working 9 hours.