1. Consider a firm which is initially 100 percent owned by a manager. The manager's wealth, W, consists only of the market value of the firm's equity. The total amount of the firm's resources is $1 million. The manager will use some of the firm's resources for his/her own perquisite consumption, F, which is completely unproductive. That is, $1 perquisite consumption by the manager would result in $1 reduction in the firm value. The manager has a utility function, U(F, W), which is increasing and concave in both F and W. The manager's utility function is publicly known, but his/her perquisite consumption is unobservable by others.

(a) Show graphically and explain in words how the owner-manager optimally chooses his/her perquisite consumption.

(b) Now, the owner-manager wants to reduce his/her ownership of the firm from 100% to 51%. The manager thus sells 49% of the firm's shares to new shareholders who are willing to purchase the shares as long as they expect to break-even at the zero riskless rate of interest. Show that if the new shareholders naively conjecture that the owner-manager remains to consume the same amount of perks as that characterized in part (a) and price the shares accordingly, they will suffer a loss.

(c) Who would bear the agency costs of outside equity? Why?