Pooley-Tupy theorem

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The Pooley-Tupy theorem is an economics theorem which measures the growth in knowledge resources over time at individual and population levels.

$P e r c e n t a g e C h a n g e i n K n o w l e d g e R e s o u r c e s = (\frac{T i m e P r i c e_{t}}{P o p u l a t i o n_{t}}) \div (\frac{T i m e P r i c e_{t + n}}{P o p u l a t i o n_{t + n}}) - 1$

The theorem was formulated by Gale Pooley and Marian Tupy who developed the approach in 2018 in their paper: The Simon Abundance Index: A New Way to Measure Availability of Resources.^[1]^[2]

The theorem is informed by the work of Julian Simon, George Gilder, Thomas Sowell, F. A. Hayek, Paul Romer, and others.^[3]^[4]^[5]^[6]^[7]^[8]

Gilder offers three axioms; wealth is knowledge, growth is learning, and money is time. From these propositions a theorem can be derived: The growth in knowledge can be measured with time.

While money prices are expressed in dollar and cents, time prices are expressed in hours and minutes. A time price is equal to the money price divided by an hourly income rate.

$T i m e P r i c e = \frac{M o n e y P r i c e}{H o u r l y I n c o m e}$

The Pooley-Tupy theorem adds changes in population as an additional variable in their formulation. In the case of an individual, population is equal to 1 at $t$ and $t + n$ .

Examples

If knowledge resources were being evaluated at the individual level and the time price was 60 minutes at $t$ and 45 minutes at $t + n$ , the percentage change in knowledge resources would be:

$= (60 \div 45) - 1$

$= 1.33 - 1$

$= 0.33 = 33 %$

If population at $t$ was 100 and 200 at $t + n$ , the percentage change in knowledge resources would be:

$= (60 \div 100) \div (45 \div 200) - 1$

$= (. 6) \div (. 225) - 1$

$= 2.666 - 1$

$= 1.666 = 166.6 %$

Other equations

The Pooley-Tupy Theorem is part of an analytical framework that uses several other equations for analysis. This framework is described in their book, Superabundance: The story of population growth, innovation, and human flourishing on an infinitely bountiful planet.^[9]^[10]^[11]

The percentage change in a time price over time can be expresses as:

$P e r c e n t a g e C h a n g e i n T i m e P r i c e = \frac{T i m e P r i c e_{t + n}}{T i m e P r i c e_{t}} - 1$

The resource multiplier indicates how much more or less of a resource the same amount of time can buy at two points in time.

$R e s o u r c e M u l t i p l i e r = \frac{T i m e P r i c e_{t}}{T i m e P r i c e_{t + n}}$

The percentage change in the resource multiplier is just the resource multiplier minus one.

$P e r c e n t a g e C h a n g e i n R e s o u r c e M u l t i p l i e r = R e s o u r c e M u l t i p l i e r - 1$

The compound annual growth rate or CAGR can be calculated as:

$C o m p o u n d A n n u a l G r o w t h R a t e = R e s o u r c e M u l t i p l i e r^{1 / n} - 1$

References

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Pooley-Tupy theorem

Examples

Other equations

References

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