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.

[math]\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) }[/math]

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

Reference Material

Papers

Books

Lectures

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

Outlet Title Link Air Date
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

Interviews

Outlet Title Link Air Date
Institute for New Economic Thinking Economic Thinking In A Fallible World Watch 2014-06-22
Institute for New Economic Thinking What Math and Physics Can Do for New Economic Thinking Watch 2013-10-30

Other Sources