Tuesday, November 13, 2018

Accelerating economy

Suppose an object is at position X. The velocity can be defined as the rate of change of the position with respect to time. We can write that as: \[V=\frac{dX}{dt} \] and we can differentiate that again to get the acceleration, which is the rate of change of velocity. \[A=\frac{dV}{dt}=\frac{d^2X}{dt^2} \] That is the second derivative of position with respect to time.
When the object is static, the position X is constant, the velocity is zero and so is the acceleration.
Now consider an economy. Economic activity can be considered to be a flow of money. Mathematically we could consider it to be the rate of change of ownership of money with respect to time.
Above we stated that acceleration is the rate of change of velocity which is the second derivative of position. Now in an economy, we can again take the second derivative of ownership of money. It is the rate of change of the flow of money. This is known as economic growth, which can of course be negative or zero. So, economic growth is the acceleration in the flow of money.
If you are trying to make long-term economic plans with the aim of maximising human welbeing, then what sort of economic growth do we want? Or to put it another way, for an optimal economy what sort of acceleration in the flow of money do we need? I would posit that at the optimal there won't be acceleration or in other words there won't be economic growth.
And that is a slightly wordy mathematical argument ( but not proof ) that, for an optimal society, there won't be economic growth.
Here's an easy question: is an accelerating object slowing down?
The answer is of course: no.
Is an economy that is growing slowing down?
Again the answer is: no.
In China, if growth goes from 6% to 4%, then is the economy slowing down?
Of course not.
When economic growth is positive, economic activity is increasing.