  We report the proof that the extension of Gibrat's law in the middle scale
region is unique and the probability distribution function (pdf) is also
uniquely derived from the extended Gibrat's law and the law of detailed
balance. In the proof, two approximations are employed. The pdf of growth rate
is described as tent-shaped exponential functions and the value of the origin
of the growth rate distribution is constant. These approximations are confirmed
in profits data of Japanese companies 2003 and 2004. The resultant profits pdf
fits with the empirical data with high accuracy. This guarantees the validity
of the approximations.
