2 Contract Design Pat owns a software design firm and proposes to hire Allen. If Allen works for Pat, he can exert high effort or low effort and this will effect the outcome of the project in a probabilistic manner. There are only two possible outcomes for Allen's work, the program can either succeed, leading to revenue of rs = 6 or it can fail, ry = 2. If Allen expends high effort, success occurs with probability of .5 and if low effort is expended there is 0 probability of success. The cost to Allen of high effort in monetary terms is 1 while the cost of low effort is 0. Allen's utility function is going to be assumed to be U(x, e) = (x-e)" where e is the cost of effort, x is total compensation and a measures the degree to which Allen is risk averse. (1 2 a > 0, a = 1 implies risk neutral, and a