An entrepreneur has a venture that will make either $196 million or $0. The chance that this venture will make $196 million depends on the effort expended by the entrepreneur: If she tries hard, the chance of the $196 million outcome is 0.2. If she does not try hard, the chance of this outcome is 0.04. The entrepreneur is risk averse with utility function: u(x)=x-disutility of effort:

where the disutility of effort is 0 if the entrepreneur does not try hard and 1000 if she does.

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)?

A risk-neutral venture capitalist is prepared to support this venture. Suppose also, for now, that effort is contractable so that there is no need to write an incentive contract. Instead, the venture capitalist simply specifies a base wage, B, and an effort level (high or low) for the entrepreneur and then takes the returns of the project for themselves. Assuming this venture capitalist is the entrepreneurs only alternative to going it alone (doing whatever you determined was the answer to part a), what is the optimal contract of this sort for the venture capitalist to write? What effort level will be specified? What will be the venture capitalists net expected monetary value with this contract?

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. Specifically, the venture capitalist will pay the entrepreneur a base amount B up