Stealing is costly and the manager expects to lose C(S)=(S2/2k) when he steals because, for example, other people need to be paid off and there is some probability that the manager will be caught and punished. A higher value of k – representing, in this case, weaker corporate governance rules or a weaker legal system or both – means that it is less costly to steal. Thus, the value of stealing, S−C(S), is concave in S. The marginal value of stealing falls as the amount stolen increases because it becomes harder to steal as the absolute amount of theft increases; the stealing becomes more obvious and easier for a court to stop.1
The manager invests what he does not steal in a project that earns a gross rate of return R, which is greater than one, and from which he obtains the share α of profits. The manager's optimization problem is given by