Problem 1 (50 points) Pat (principal) hires Allen (agent) to develop a new software. After one month Pat will learn whether the project is successful or not. A successful project generates revenues of 6, while the revenue is 2 if the project is unsuccessful. Success depends on Allen's high effort as well as on a random factor. Specifically, if Allen expends high effort, then success will be achieved with probability 1/2; if Allen expends low effort, then the project is unsuccessful for sure. Using the notation seen in class, xs = 6, XF = 2, Pr(xsle = 1) = 1/2, Pr (xsle = 0) = 0. Assume that the cost of high effort for Allen is 1 while the cost of low effort is zero. The parties can write a contract that specifies compensation for Allen conditional on whether the project is successful, but it cannot be conditioned directly on Allen's effort. Assume that Allen has utility function u (w) = wa, his outside option is 0 and that he is risk averse, meaning that 0