(impact of entrepreneurial risk aversion). Consider the fixed-investment model developed in this chapter: an entrepreneur has cash amount A and wants to invest 1>A into a project. The project yields R > 0 with probability p and 0 with probability 1 - p. The probability of success is pH if the entrepreneur works and pL = pH - ?p (?p > 0) if she shirks. The entrepreneur obtains private benefit B if she shirks and 0 otherwise. Assume that
(Suppose that pLR + B so the project is not financed if the entrepreneur shirks.)
(i) In contrast with the risk-neutrality assumption of this chapter, assume that the entrepreneur has utility for consumption c:
(Assume that A ≥c0 to ensure that the entrepreneur is not in the "-∞ range" in the absence of financing.) Compute the minimum equity level A for which the project is financed by risk-neutral investors when the market rate of interest is 0. Discuss the difference between pH = 1 and pH
(ii) Generalize the analysis to risk aversion. Let u(c) denote the entrepreneur's utility from consumption with u> 0, u.