X and Y are working on a group project. They put in x and y hours...

 

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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 U_X=6(x+y)^0.5-x and Y's utility from the grade is given by UY=5(x+0.5y)^0.5-y. 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? 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 U_X=6(x+y)^0.5-x and Y's utility from the grade is given by UY=5(x+0.5y)^0.5-y. 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?

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