Pooley-Tupy theorem

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

$Percentage\ Change\ in\ Knowledge\ Resources=\left({\frac {Time\ Price_{t}}{Population_{t}}}\right)\div \left({\frac {Time\ Price_{t+n}}{Population_{t+n}}}\right)-1$

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.

$Time\ Price={\frac {Money\ Price}{Hourly\ Income}}$

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:

$Percentage\ Change\ in\ Time\ Price={\frac {Time\ Price_{t+n}}{Time\ Price_{t}}}-1$

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

$Resource\ Multiplier={\frac {Time\ Price_{t}}{Time\ Price_{t+n}}}$

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

$Percentage\ Change\ in\ Resource\ Multiplier=Resource\ Multiplier-1$

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

$Compound\ Annual\ Growth\ Rate=Resource\ Multiplier^{1/n}-1$

References

^ Pooley, Gale L.; Tupy, Marian L. (4 December 2018). "The Simon Abundance Index: A New Way to Measure Availability of Resources". www.cato.org. Retrieved 5 September 2024.
^ Pooley, Gale and Marian Tupy (December 4, 2018). "The Simon Abundance Index: A New Way to Measure Availability of Resources". Cato Policy Analysis NO. 857.
^ Gilder, George F. (2023). Life after capitalism: the meaning of wealth, the future of the economy, and the time theory of money. Washington, D.C.: Regnery Gateway. ISBN 978-1-68451-224-9. OCLC 1346534521.
^ Sowell, Thomas (1980). Knowledge and decisions. New York: Basic Books. ISBN 978-0-465-03736-0.
^ Simon, Julian Lincoln (1998). The ultimate resource 2. Princeton paperbacks Economics (2. ed., rev. ed., 3. printing and 1. paperback printing ed.). Princeton, NJ: Princeton Univ. Press. ISBN 978-0-691-00381-8.
^ Hayek, F. A. The Use of Knowledge in Society.
^ Gilder, George F. (2013). Knowledge and power: the information theory of capitalism and how it is revolutionizing our world. Washington, DC: Regnery Publishing, Inc. ISBN 978-1-62157-027-1. OCLC 807025294.
^ Romer, Paul M. (1990). "Endogenous Technological Change". Journal of Political Economy. 98 (5): S71–S102. doi:10.1086/261725. ISSN 0022-3808. JSTOR 2937632.
^ "Superabundance: Population Growth, Innovation, and Human Flourishing". Superabundance.
^ Tupy, Marian L.; Pooley, Gale Lyle (2022). Superabundance: the story of population growth, innovation, and human flourishing on an infinitely bountiful planet. Washington, D.C.: Cato Institute. ISBN 978-1-952223-39-6.
^ "Superabundance: Population Growth, Innovation, and Human Flourishing". Superabundance. Retrieved 2024-06-11.

[1] Pooley, Gale L.; Tupy, Marian L. (4 December 2018). "The Simon Abundance Index: A New Way to Measure Availability of Resources". www.cato.org. Retrieved 5 September 2024.

[2] Pooley, Gale and Marian Tupy (December 4, 2018). "The Simon Abundance Index: A New Way to Measure Availability of Resources". Cato Policy Analysis NO. 857.

[3] Gilder, George F. (2023). Life after capitalism: the meaning of wealth, the future of the economy, and the time theory of money. Washington, D.C.: Regnery Gateway. ISBN 978-1-68451-224-9. OCLC 1346534521.

[4] Sowell, Thomas (1980). Knowledge and decisions. New York: Basic Books. ISBN 978-0-465-03736-0.

[5] Simon, Julian Lincoln (1998). The ultimate resource 2. Princeton paperbacks Economics (2. ed., rev. ed., 3. printing and 1. paperback printing ed.). Princeton, NJ: Princeton Univ. Press. ISBN 978-0-691-00381-8.

[6] Hayek, F. A. The Use of Knowledge in Society.

[7] Gilder, George F. (2013). Knowledge and power: the information theory of capitalism and how it is revolutionizing our world. Washington, DC: Regnery Publishing, Inc. ISBN 978-1-62157-027-1. OCLC 807025294.

[8] Romer, Paul M. (1990). "Endogenous Technological Change". Journal of Political Economy. 98 (5): S71–S102. doi:10.1086/261725. ISSN 0022-3808. JSTOR 2937632.

[9] "Superabundance: Population Growth, Innovation, and Human Flourishing". Superabundance.

[10] Tupy, Marian L.; Pooley, Gale Lyle (2022). Superabundance: the story of population growth, innovation, and human flourishing on an infinitely bountiful planet. Washington, D.C.: Cato Institute. ISBN 978-1-952223-39-6.

[11] "Superabundance: Population Growth, Innovation, and Human Flourishing". Superabundance. Retrieved 2024-06-11.

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