Suppose an entrepreneur owns a firm which has two production opportunities. Technology A generates an output (net profit) of 10 in state 1, an output of 20 in state 2, and an output of 90 in state 3. All states are equally likely. Technology B generates an output of 40, 50, and 60, respectively. Because of technological constraints, the entrepreneur can only implement one technology. The entrepreneur maximizes his expected utility.
(a) Which technology should the entrepreneur implement and what is the value of the firm?
(b) Suppose the firm has debt with face value 12 outstanding. What project does the entrepreneur implement?
(c) Suppose the firm has debt with face value 50 outstanding. What project does the entrepreneur implement?
(d) Determine the utility of the entrepreneur as a function of face value D for technology A and B, respectively.
(e) What is the maximal debt level such that the entrepreneur still chooses the (socially) efficient technology?
(f) Suppose the firm only has equity and 98% of shares are owned by retailed investors and the initial entrepreneur owns 2% of the firm. What technology does he implement?