explaining accelarating economic growth

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Eric Crampton is an economist who co-wrote an essay arguing that economic growth is New Zealand's panacea. I pointed out this was Growth Porn.

I also tweeted Eric a couple of links to arguments which laid out reasons why. His response to this one was:

Eric Crampton ‏@EricCrampton  2h2 hours ago2 hours ago@punkscience Data st derivative of distance with respect to time is speed; 1st derivative of GDP wrt to time is growth. Acceleration is 2nd.

Now, Eric's gone for a technical reply here, which I'm not going to go into. If you're interested then I'm not going to bother trying to better the Wikipedia article on the subject. For simplicity's sake I will also present an image showing the first and second derivatives of the top plot:

Suffice to say, I know what a derivative is and Eric has missed the point of the blog I linked to, which is that economic growth figures, as almost universally presented, indicate an acceleration of growth and not just a steady increase. And that is fucked up because pretending something can keep accelerating forever is even more dumb than pretending something can keep growing forever at a steady rate.

Look at these two columns of numbers:

100
102	2
104	2
106	2
108	2
110	2
112	2
114	2
116	2
118	2
120	2
122	2
124	2
126	2
128	2
130	2
132	2
134	2
136	2
138	2
140	2

The first column shows a figure of 100 growing by 2 every line. The second column the difference between each figure in the first column and the previous one. By the end of 20 lines the figure has grown from 100 to 140. The reasons for this are too obvious to elaborate upon. 

Now check out this series:

100
102		2
104.04		2.04		0.04
106.1208		2.0808		0.0408
108.2432		2.122416		0.041616
110.4081		2.164864		0.042448
112.6162		2.208162		0.043297
114.8686		2.252325		0.044163
117.1659		2.297371		0.045046
119.5093		2.343319		0.045947
121.8994		2.390185		0.046866
124.3374		2.437989		0.047804
126.8242		2.486749		0.04876
129.3607		2.536484		0.049735
131.9479		2.587213		0.05073
134.5868		2.638958		0.051744
137.2786		2.691737		0.052779
140.0241		2.745571		0.053835
142.8246		2.800483		0.054911
145.6811		2.856492		0.05601
148.5947		2.913622		0.05713

Once again you have a starting figure of 100 but this time the figure is multiplied by a constant of 1.02, or 102%. This represent a rate of 2% growth. In the second column you can see that the amount by which the figure increases is itself increasing. The first iteration it increases by 2. The 20th iteration it increases by nearly 3. 

In the third column I have calculated the difference between each value in the second column, just to demonstrate unequivocally to the hard of thinking that the rate of increase is also increasing.

The same applies to economic growth figures which are almost universally presented as percentage GDP growth per time period, normally per year. However, they are rarely presented in isolation, for a single time period. Instead they are inevitably presented in the context of historical growth figures and future forecasts. Any such presentation therefore communicates not only how much the economy has grown by, as an absolute figure within the time period specified, but also whether the rate at which that absolute figure itself is changing over time.

Edited for clarity @ 22:16