A risk-neutral entrepreneur has come up with a project that requires capital of 1 to initiate. The project will either succeed, in which case it generates profit of 5 , or it will fail, in which case it generates a profit of 0 . He needs to hire a worker to run the project. The probability of success is equal to the worker's effort level e[0,1] and the worker's effort cost is 3e2. Notice that unlike the lecture, output (success or failure) is now imperfectly correlated with effort; hence, it is not actually possible to contract on effort if it is not observable. Let us consider a contract where a risk neutral worker receives a repayment r from the entrepreneur if the project is successful and 0 otherwise. Therefore, the entrepreneur's and the worker's expected profit is E=e(5r)1 and W=er3e2, respectively. The worker has an outside option of 0 . (a) Assume that effort level is observable and is thus contractible. What will be the entrepreneur's choice of e and r ? What are the expected profits of the worker and the entrepreneur? (Hint: maximise the entrepreneurs expected profits subject to the worker's participation constraint) (b) What is the socially efficient level of effort? (Hint: consider the sum of the entrepreneurs and the workers payoffs from the project.) (c) Now suppose that effort is not contractible. What will be the entrepreneur's choice of r and the resultant worker's choice of e. (Hint: maximise the entrepreneurs expected profits subject to the worker's participation constraint and incentive constraint. First solve the incentive constraint and substitute e into the participation constraint. You should be able to see that the participation constraint doesn't matter.) (d) Suppose now, the entrepreneur can punish the worker if the project fails. Le. if the project fails, the worker gets a payment of l