Newton's Second Law
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Let's set F equal to the ability of a society to exist. An arbitrary value will be assigned to denote "adequate" societal performance,
Lets set M as the population of the society
Let's set A as the product of the money supply and the velocity of that money.
Thus, when a nation's population increases, in order to maintain F at a constant, the money supply or the velocity of the money must increase. Since there is an inverse relationship of mass to acceleration, these must increase more rapidly than the rate of growth.
If money is leaving the country in external trade imbalances, the product of the money supply and velocity is made smaller and F drops below "adequate" societal performance.
Just a thought...I'll work on it more later.