An entrepreneur has a venture that will make either $100M or $0. The chance that this venture will make $100M depends on the effort level expended by the entrepreneur: If she tries hard, the chance of the $100M outcome is 0.2. If she does not try hard, the chance of this outcome is 0.05. This entrepreneur is risk averse, with utility function. √x - disutility of effort, where the disutility of effort is O if the entrepreneur does not try hard and 1000 if she does. (a) Assuming this entrepreneur bears all the risk of this venture, will she try hard or not? What will be her expected utility, net of the disutility of effort (if any)? (b) A risk-neutral venture capitalist is prepared to support this venture. Risk-neutrality means that the venture capitalist cares only about expected profit (average weighted by probabilities of net gains). Specifically, the venture capitalist will pay the entrepreneur a base amount B up front, in return for which the venture capitalist will retain X out of the $100M the venture generates, if the venture succeeds. Assuming this venture capitalist is the entrepreneur's only alternative to doing it alone (doing whatever you determined the answer was in part a), and assuming the venture capitalist can make part of his contract with the entrepreneur a specification of her effort level, what is the optimal contract of this sort for the venture capitalist to write? What will be the venture capitalist's net expected monetary value with this contract? Hint for Part (b): Notice that the venture capitalist (VC) is risk neutral, while the entrepreneur (E) is risk-averse. Thus the optimal contract will have the VC bear all the risk, with X=$100M. With the VC receiving all the profit in case of success, your task is simply to find B that makes E just willing to go through the VC instead of bearing the risk of this venture himself (without VC, as in Part (a) of the exercise). You should do this both for a contract that stipulates low effort and one that stipulates high effort, and see which is most profitable to the VC. (c) Unhappily, the venture capitalist cannot contractually specify the effort level of the entrepreneur. If the venture capitalist wishes to motivate the entrepreneur to try hard, he must do this with the terms B and X in the contract he provides. The purpose of this question and