2. (20 pts) Two students, Alex and Bob, are working on their senior thesis, supervised by the same instructor. Each can choose a level of effort, ea or es, to put into the paper, which causes disutility of per unit of effort. Their grade will be assigned partly on a curve and partly on an absolute standard, giving them the following payoff function: Ua(easeb) = (a +7(ea - eb)) - ea, and similarly for Bob. (The square root term represents Alex's grade.) y is a parameter for the degree of curving. 2 (a) Solve for Alex's best response function. It should be a function of 7 and e. (Bob's will be the same (except as a function ea), since they have the same payoffs). (b) If there is no curve (y=0), how much effort will Alex choose in equilibrium? (c) Solve for the Nash Equilibrium of this game when y> 0. Also compute the resulting equilibrium payoff. Hint: The same hint applies as in question 1. After taking first-order con- ditions, you may assume that ea = e, in equilibrium. (d) As the instructor applies a stronger curve, will the equilibrium effort of the students rise or fall? Does the equilibrium grade rise or fall? Does equilibrium. utility rise or fall?