  The results of R^2 dynamical random surface model (2-dimensional quantum
gravity with a $R^2$ term) are applied to explain the personal income
distribution. A scale invariance exists if there is not the $R^2$ term in the
action. The R^2 term provides a typical scale and breaks the scale invariance
explicitly in the low and middle income range. A new distribution, Weibull
distribution, is deduced from the action analytically in the low income range,
and a consistent fitting is obtained in the whole income range. Also, we show
that the lognormal distribution in the middle income range can be understood in
this framework.

Statistical Mechanics;High Energy Physics - Theory;General Finance