Please solve the below question

2 Principal - Agent Games Pat owns a. software design rm and proposes to hire Allen. If Allen works for Pat, he can exert high effort or low effort and this will affect the outcome of the project in a probabilistic manner. There are only two possible outcomes for Allen's work1 the program can either succeed, leading to revenue of r, = 6 or it can tail, :7 = 2. If Allen expands high e'ort, success occurs with probability of .5 and if low effort is expended there is 0 probability,r of success. The cost to Allen of high effort in monetary terms is 1 while the cost of low eil'ort is 0. Allen's utility function is going to be assumed to be U (rt-,8) = (a: e)' where e is the cost of effort, a: is total compensation and 0 measures the degree to which Allen is risk averse. (1 2 a > 0, a: = 1 implies risk neutral, and o-