A theory of average growth rate indices

•An axiomatic approach to average rate of growth (change) measurement is developed.•Average growth rates measure utility growth of an agent associated with the problem.•Average growth rate has a representation by means of a family of time preferences.

This paper develops an axiomatic theory of an economic variable average growth rate (average rate of change) measurement. The obtained structures generalize the conventional measures for average rate of growth (such as the difference quotient, and the continuously compounded growth rate) to an arbitrary domain of the underlying variable and comprise various models of growth. These structures can be described with the help of intertemporal choice theory by means of parametric families of time preference relations on the “prize-time” space with a parameter representing the subjective discount rate.