Pooley-Tupy theorem explained

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

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.

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

and .

Examples

If knowledge resources were being evaluated at the individual level and the time price was 60 minutes at

and 45 minutes at , the percentage change in knowledge resources would be:

If population at

was 100 and 200 at , the percentage change in knowledge resources would be:

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:

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

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

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

References

1. Web site: The Simon Abundance Index: A New Way to Measure Availability of Resources . Pooley . Gale L. . Tupy . Marian L. . 4 December 2018 . www.cato.org . 5 September 2024 .
2. Web site: 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. Book: Gilder, George F. . Life after capitalism: the meaning of wealth, the future of the economy, and the time theory of money . 2023 . Regnery Gateway . 978-1-68451-224-9 . Washington, D.C. . on1346534521.
4. Book: Sowell, Thomas . Knowledge and decisions . 1980 . Basic Books . 978-0-465-03736-0 . New York.
5. Book: Simon, Julian Lincoln . The ultimate resource 2 . 1998 . Princeton Univ. Press . 978-0-691-00381-8 . 2. ed., rev. ed., 3. printing and 1. paperback printing . Princeton paperbacks Economics . Princeton, NJ.
6. Book: Hayek, F. A. . .
7. Book: Gilder, George F. . Knowledge and power: the information theory of capitalism and how it is revolutionizing our world . 2013 . Regnery Publishing, Inc . 978-1-62157-027-1 . Washington, DC . 807025294.
8. Romer . Paul M. . 1990 . Endogenous Technological Change . Journal of Political Economy . 98 . 5 . S71–S102 . 10.1086/261725 . 2937632 . 0022-3808.
9. Web site: Superabundance: Population Growth, Innovation, and Human Flourishing. Superabundance.
10. Book: Tupy . Marian L. . Superabundance: the story of population growth, innovation, and human flourishing on an infinitely bountiful planet . Pooley . Gale Lyle . 2022 . Cato Institute . 978-1-952223-39-6 . Washington, D.C..
11. Web site: Superabundance: Population Growth, Innovation, and Human Flourishing . 2024-06-11 . Superabundance . en.