Regulating a monopolist with limited funds

We consider the problem of regulating a monopolist with unknown
costs when the regulator has limited funds. The optimal regulatory mechanism sat-
isfies four properties. The first property is bunching at the top, that is the more
efficient types produce the same quantity irrespective of their costs. The second
property is separability of less efficient types. The third property is full bunching of
types when the available fund is small enough. The fourth property of the mecha-
nism is that it is a third best one, that is, the output under this regulatory mechanism
is strictly lower than the second best output for any given type.