Violation of Invariance of Measurement for GDP Growth Rate and its Consequences

The aim here is to address the origins of sustainability for the real growth rate in the United States. For over a century of observations on the real GDP per capita of the United States a sustainable two percent growth rate has been observed. To find an explanation for this observation I consider the impact of utility preferences and the effect of mobility of labor \& capital on every provided measurement. Mobility of labor results in heterogenous rates of increase in prices which is called Baumol's cost disease phenomenon. Heterogeneous rates of inflation then make it impossible to define an invariant measure for the real growth rate. Paradoxical and ambiguous results already have been observed when different measurements provided by the World Bank have been compared with the ones from the systems of national accounts (SNA). Such ambiguity is currently being discussed in economy. I define a toy model for caring out measurements in order to state that this ambiguity can be very significant. I provide examples in which GDP expands 5 folds while measurements percept an expansion around 2 folds. Violation of invariance of the measurements leads to state that it is hard to compare the growth rate of GDP for a smooth growing country such as the U.S. with a fast growing country such as China. Besides, I state that to extrapolate the time that economy of China passes the economy of the US we need to consider local metric of the central banks of both countries. Finally I conclude that it is our method of measurements that leads us to percept the sustainable growth rate.