Lets make fun of Obama while he is still relevant.

[Mikebert]

(12-07-2016, 01:13 AM)Warren Dew Wrote:

(12-06-2016, 04:06 PM)Mikebert Wrote:

Warren Dew Wrote:d(population)/dt / population > 0 (percentage population increases as old people have retired but not died yet)
 
d(GDP/population)/dt = population * d(GDP)/dt + GDP * d(population)/dt

Using more compact notation you are saying:
 
d(GDP/N)dt = N * dGDP/dt + GDP dN/dt
 
this is the differentiation of the product of GDP and N, done correctly you would have
 
d[GDP * (1/N)]/dt = (1/N) dGDP/dt - GDP (1/N)^2 (dN/dt)
 
I'm still confused

Sorry, yes, messed up on that intermediate line.  The conclusion is still the same, though.  Derivation with the corrected equation below.

d(GDP/worker)/dt / (GDP/worker) > 0 (percentage individual worker productivity increases)

d(workers)/dt / workers < - d(GDP/worker)/dt / (GDP/worker)
    (percentage worker population decreases faster than percentage worker productivity increases)

d(GDP)/dt / GDP = d(workers*GDP/worker)/dt / (workers*GDP/worker)
    = (GDP/worker * d(workers)/dt + workers * d(GDP/worker)/dt) / (workers*GDP/worker)
    = d(workers)dt / workers + d(GDP/worker)/dt / GDP/worker < 0 (GDP decreases)

d(population)/dt / population > 0 (percentage population increases as old people have retired but not died yet)

d(GDP/population)/dt = d(GDP)/dt / population - GDP * d(population)/dt / population^2
    = (GDP/population) * (d(GDP)/dt / GDP - d(population)/dt / population) < 0
    (average living standard for the economy cannot keep up)

You already have negative  GDP growth (or at least assumed it).  Until population also falls per capita GDP then must also fall. There is no need for the math which only reiterate the initial assumptions.

So far per capita GDP appears to have been rising slowing (through 2013)
http://www.indexmundi.com/g/g.aspx?v=67&c=ja&l=en

So I looked t the GDP trend and so the same thing:

http://www.indexmundi.com/g/g.aspx?c=ja&v=65

So what is you point? You make and assertion that if true would predict both of these things would be going down.  You point out that your assertions are supported by the data.  But your own math shows that it this were so then it would also be supported by the data about trends in GDP and GDP per cap, which it is not.  So what is the problem. Its the productivity figure. You are making the same mistake Turchin did.  You are assuming that productivity is an independent measure that you can then manipulation to make a prediction abut GDP.  It's not.  What you are doing is going around in circles thinking there is something there when there is not.  I've been there.