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Gauge Theory of Economics: Difference between revisions
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'''Gauge theory of economics''' is the application of differential geometric methods to economic problems. This was first developed by [https://twitter.com/PiaMalaney Pia Malaney] and [[Eric Weinstein]] in Malaney's 1996 doctoral thesis [https://pdfs.semanticscholar.org/eb74/898337415912a12d5b6642e5c2e6950f637c.pdf The Index Number Problem: A Differential Geometric Approach]. | |||
'''Gauge theory of economics''' is the application of differential geometric methods to economic problems. This was first developed by [ | |||
== Examples == | == Examples == | ||
Gauge theory is all you need to break out of the economics flatland. The following is an equation that Eric Weinstein talked about. We are going to break it down together and picture the meaning of each part in a geometrical and intuitive way. The results of this work will be interesting for the present economics community. | Gauge theory is all you need to break out of the economics flatland. The following is an equation that Eric Weinstein talked about. We are going to break it down together and picture the meaning of each part in a geometrical and intuitive way. The results of this work will be interesting for the present economics community. | ||
<math> q = \frac{ {p_0}\cdot{q} }{ {p_0}\cdot{q_0} } q_0 + (q - \frac{ {p_0}\cdot{q} }{ {p_0}\cdot{q_0} } q_0) </math> | |||
where we label the first term as Reference Basket and the second one as Barter. | where we label the first term as Reference Basket and the second one as Barter. | ||
Suppose that we live in a world where there are only 3 different types of items for sale: apples, berries and cherries (A, B and C respectively.) Say today we pick up our basket and go to the market. At the market, the price of each item is posted up as a number on the wall where we can see. So, we represent the prices by a | Suppose that we live in a world where there are only 3 different types of items for sale: apples, berries and cherries (A, B and C respectively.) Say today we pick up our basket and go to the market. At the market, the price of each item is posted up as a number on the wall where we can see. So, we represent the prices by a <math>{1}\times{3}</math> row vector <math>p</math>. On the other hand, we buy different quantities of each item and so a <math>{3}\times{1}</math> column vector <math>q</math> denotes the list of 3 quantities for items A, B and C. | ||
The next day, we go back to the market and now we are interested in measuring price changes. | The next day, we go back to the market and now we are interested in measuring price changes. | ||
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* [https://pdfs.semanticscholar.org/eb74/898337415912a12d5b6642e5c2e6950f637c.pdf The Index Number Problem: A Differential Geometric Approach] by Pia Malaney. | * [https://pdfs.semanticscholar.org/eb74/898337415912a12d5b6642e5c2e6950f637c.pdf The Index Number Problem: A Differential Geometric Approach] by Pia Malaney. | ||
* [https://economics.uchicago.edu/sites/economics.uchicago.edu/files/Welfare_Chicago_Draft.pdf An Extension of Intertemporal Ordinal Welfare to Changing Tastes: Economics as Gauge Theory (Draft for University of Chicago Money and Banking Workshop. In preparation.)] by Pia Malaney and Eric Weinstein | * [https://web.archive.org/web/20230223205927/https://economics.uchicago.edu/sites/economics.uchicago.edu/files/Welfare_Chicago_Draft.pdf An Extension of Intertemporal Ordinal Welfare to Changing Tastes: Economics as Gauge Theory (Draft for University of Chicago Money and Banking Workshop. In preparation.)] by Pia Malaney and Eric Weinstein | ||
* [https://web.archive.org/web/20220607064236/https://economics.uchicago.edu/sites/economics.uchicago.edu/files/Chicago_Trade_Index_Draft.pdf Tracking Changes in Bilateral Trading Patterns in the Absence of PPP] by Eric Weinstein | |||
* [https://arxiv.org/abs/0902.4274 Time and symmetry in models of economic markets] by Lee Smolin. | * [https://arxiv.org/abs/0902.4274 Time and symmetry in models of economic markets] by Lee Smolin. | ||
* [https://arxiv.org/pdf/0908.3043.pdf Gauge Invariance, Geometry and Arbitrage] by Samuel Vázquez and Simone Farinelli | * [https://arxiv.org/pdf/0908.3043.pdf Gauge Invariance, Geometry and Arbitrage] by Samuel Vázquez and Simone Farinelli | ||