Gauge Theory of Economics

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Gauge theory of economics is the application of differential geometric methods to economic problems. This was first developed by Pia Malaney and Eric Weinstein in Malaney's 1996 doctoral thesis The Index Number Problem: A Differential Geometric Approach.

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.

$\displaystyle{ q = \frac{ {p_0}\cdot{q} }{ {p_0}\cdot{q_0} } q_0 + (q - \frac{ {p_0}\cdot{q} }{ {p_0}\cdot{q_0} } q_0) }$

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 $\displaystyle{ {1}\times{3} }$ row vector $\displaystyle{ p }$. On the other hand, we buy different quantities of each item and so a $\displaystyle{ {3}\times{1} }$ column vector $\displaystyle{ q }$ 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.

Inflation

(Video and text from Pull that up, Jamie)

Here is shown a red curve/function, possibly representing the inflation of a currency as time progresses to the right along with a blue function representing the notion of âconstant wage.â The concept at play is that the definition of constant depends on the faded horizontal ticks in the background space, and in the example of a wage, it makes conceptual sense to set such a notion of constant against the inflation curve rather than the axis. This represents one spirit of what is done in the âcalculus of gauges,â and in reality we tend not to see god-given coordinate grids sprawling over space thus encouraging us to adopt a different language of geometry/calculus.

Reference Material

Lectures

Lectures, presentations, and panels by Pia Malaney and Eric Weinstein on the topic.

University of Chicago Money and Banking Workshop Gauge Theory, Inflation and Geometric Marginalism: Are our Inflation, Productivity and Trade Indicators All Off Because The Marginal Revolution Was Based on the Wrong Version of The differential Calculus? Abstract 2021-11-10
Fields Institute Towards a Mathematics of New Economic Thinking for Reflexive Markets Watch 2013-11-02
Institute for New Economic Thinking What Math and Physics Can Do for New Economic Thinking Watch 2013-10-30
Stanford University Systems Architecture, Kabuki Capitalism, and the Economic Manhattan Project Watch 2013-06-21
Perimeter Institute for Theoretical Physics A Science Less Dismal: Welcome to the Economic Manhattan Project Watch 2009-01-05
Perimeter Institute for Theoretical Physics Sheldon Glashow Owes me a Dollar (and 17 years of interest) Watch 2008-09-11
Perimeter Institute for Theoretical Physics Gauge Theory and Inflation: Enlarging the Wu-Yang Dictionary Watch 2006-05-24