<p><strong>UPDATE 19-9-2017</strong></p>

<p>I just received word from the author that the book is now freely downloadable <strong>in English</strong>, <a href="https://www.centralbank.cy/en/publications/books/euclidean-economics-a-mathematical-method-for-construction-and-application-of-economics-models" rel="nofollow noreferrer"><strong>at this link</strong></a>.</p>

<hr>

<p>Got it. I remember browsing the pages of this book. But it was in Greek, and it does not appear to have been published also in English:</p>

<p><strong><a href="http://www.centralbank.gov.cy/nqcontent.cfm?a_id=12483&amp;lang=en" rel="nofollow noreferrer">Euclidean Economics: A Mathematical Method for Construction and Application of Economics Models</a></strong></p>

<blockquote>
  <p>"<em>The book establishes that economics can be studied and utilised on
  the basis of a minimum of fundamental hypotheses and the general laws
  of mathematics. Starting from 12 major propositions, it proves that
  closed exchange networks are replicated by systems of 2n first-order
  non-homogeneous linear differential equations, which simulate
  household, business, bank and government receipts and payments. Such
  networks are defined in the (R2n, t) vector space, where n is the
  number of sectors or markets and countries or currencies, while t is
  the elapsed time. Uniqueness, stability and controllability of the
  steady state as well as takings and outgoings are functions of
  behaviour coefficients and policy parameters. Annual sales of
  services, products and securities divided by average salaries, prices
  and values yield the man hours, output items and liquidity units
  traded. Demanded quantities do not coincide with available quantities.
  Potential inflation or deflation is proportional to the weighted
  deficit or surplus of market goods. Digital animation of the
  endogenous variables is possible on the basis of historical, projected
  or hypothetical data about the exogenous variables.</em>"</p>
</blockquote>

<p>Author: <strong>Sophocles Michaelides</strong><br>
Language: Greek<br>
Publisher: Mesogios Publications – Ellinika Grammata<br>
ISBN: 9963-9176-0-7<br>
Year: 2006</p>

<p>The summary does not state it clearly, but the "12 major propositions" are Euclidean, as I recall.</p>

CC BY-SA 3.0
2017-09-20T04:04:25.713Z
Wow this is really cool.
EconJohn
CC BY-SA 3.0
2015-06-26T20:23:27.773Z
2017-09-19T10:33:27.760Z
2017-09-19T10:33:27.760Z
Alecos Papadopoulos
<p>There are some papers of Stefan Behringer from University of Bonn. </p>

<p><a href="http://www.stefanbehringer.com/1219997.pdf" rel="nofollow">Optimal Harvesting of a Spatial Renewable Resource</a> published in Journal of Economic Dynamics and Control</p>

<p>As the title indicates, there is a geometrical application, at least there is the notion of space. </p>

<p>Another paper that I remember is "Spatial dynamics and convergence: the spatial AK model" by Boucekkine et al. published in Journal of Economic Theory.</p>

<p>I think you can reach another strand of literature on space and mainly on geometric technics used in economics.</p>

CC BY-SA 3.0
2016-01-07T14:06:59.903Z
2016-01-07T14:06:59.903Z
optimal control
<p>Harry Johnson frequently applied euclidean geometry to trade theory and growth theory.  Have a look at his many papers and books.   For a more or less randomly chosen starting point, try his "Trade and Growth:  A Geometrical Exposition".  </p>

CC BY-SA 3.0
2015-06-26T23:51:38.630Z
2015-06-26T23:51:38.630Z
Steven Landsburg
<p>Here are two problems (not papers, though the results are probably used in many papers)</p>

<ol>
<li>In the case of a three asset <a href="https://en.wikipedia.org/wiki/Modern_portfolio_theory" rel="nofollow">Markowitz portfolio optimization problem</a> the feasible set of portfolios in $\mu$ / $\sigma$ space can be shown to be an ellipse. </li>
<li>When a <a href="http://www.economics.utoronto.ca/jfloyd/modules/eltr.html" rel="nofollow">demand curve is a straight line the marginal revenue curve bisects the demand curve</a>. </li>
</ol>

CC BY-SA 3.0
2015-06-26T15:28:42.130Z
2015-06-26T17:43:57.910Z
2015-06-26T17:43:57.910Z
BKay
<p>Another example is <a href="http://onlinelibrary.wiley.com/doi/10.1111/1097-3923.00006/abstract" rel="nofollow noreferrer">Economies with Public Goods: An Elementary Geometric Exposition</a> by William Thomson, which relies extensively on the geometry of equilateral triangles. </p>

<p>In general, William Thomson is known for making a heavy and interesting usage of geometry in his papers. See for instance a recent working paper of his : <a href="http://rcer.econ.rochester.edu/RCERPAPERS/rcer_584.pdf" rel="nofollow noreferrer">Compromising between the proportional and constrained equal awards rules</a> (although this one might be further from basic high-school euclidean geometry than what you're looking for). </p>

<p>Other somewhat similar examples include papers relying on the geometry of simplices. An example I came across recently is</p>

<ul>
<li><a href="http://www.jstor.org.proxy.library.vanderbilt.edu/stable/41106883?seq=3#page_scan_tab_contents" rel="nofollow noreferrer">A graphical analysis of some basic results in social choice,  Estelle Cantillon and Antonio Rangel, Social Choice and Welfare Vol. 19, No. 3 (2002), pp. 587-611</a> </li>
</ul>

<p>but there are many others, starting with the exposition of the expected utility theorem in Mas-Collel, Whinston and Green.</p>

<p>I am also tempted to point at the following recent paper, although it definitely uses geometric tools which go far beyond high-school euclidean geometry:</p>

<ul>
<li><a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1974922" rel="nofollow noreferrer">A Geometric Approach to Mechanism Design,   Jacob K. Goeree and  Alexey I. Kushnir Carnegie Mellon University Tepper Business School, 2013,  University of Zurich Department of Economics Working Paper No. 56</a></li>
</ul>

<p>I don't have a specific paper for it (any intro to econ textbook would do), but I would also add the classical graphical measure of consumer and producer surpluses in ECON 101. (Especially for linear demand and consumer curves where is simplifies to measuring the area of a triangle. Can't do much more "measurement of land" than that)</p>

CC BY-SA 3.0
2015-09-14T21:38:24.950Z
2017-09-20T14:31:15.057Z
2017-09-20T14:31:15.057Z
Martin Van der Linden
<p>I am looking for economics papers which use concepts, techniques and theorems from geometry. I am mainly interested in Euclidean geometry, the kind of material that is taught on high-schools (e.g. proving theorems about triangles, squares, circles, etc.). But, other kinds of geometry are also interesting.</p>

<p>I looked at some papers about land economics, thinking that it geometry can be useful there (after all, the word "geometry" means "measurement of land"). But, the papers I found used mostly advanced measure theory and topology. I am looking for more basic geometric methods. </p>

CC BY-SA 3.0
2017-09-21T12:46:08.497Z
There a paper by Lee Smolin (a physicist) that applies gauge theory to economics; gauge theory is geometric, but its advanced geometry, so doesn't fit the 'basic geometric methods' requirement.
Mozibur Ullah
CC BY-SA 3.0
2015-06-26T20:08:09.640Z
There is an academic economist from Cyprus that has mapped basic aspects of Euclidean Geometry to some of the foundations of Economics theory. For the moment I cannot remember a specific reference but I will look it up.
Alecos Papadopoulos
CC BY-SA 3.0
2015-06-27T14:07:51.313Z
There is a theory of spatial voting with Euclidean preferences. See [here](http://authors.library.caltech.edu/43893/1/a%20notion%20of%20equilibrium.pdf) for the paper that started it all. Some of the literature gets rathert echnical though.
Michael Greinecker
<reference-request>
Economics and Euclidean geometry
Erel Segal-Halevi
# Economics and Euclidean geometry

(Asked by: username_0 on 2015-06-26)

I am looking for economics papers which use concepts, techniques and theorems from geometry. I am mainly interested in Euclidean geometry, the kind of material that is taught on high-schools (e.g. proving theorems about triangles, squares, circles, etc.). But, other kinds of geometry are also interesting.

I looked at some papers about land economics, thinking that it geometry can be useful there (after all, the word "geometry" means "measurement of land"). But, the papers I found used mostly advanced measure theory and topology. I am looking for more basic geometric methods.

**Tags:** reference-request
> **Comments:**
> **username_2**: There is an academic economist from Cyprus that has mapped basic aspects of Euclidean Geometry to some of the foundations of Economics theory. For the moment I cannot remember a specific reference but I will look it up.  
> **username_3**: There is a theory of spatial voting with Euclidean preferences. See [here](http://authors.library.caltech.edu/43893/1/a%20notion%20of%20equilibrium.pdf) for the paper that started it all. Some of the literature gets rathert echnical though.  
> **username_1**: There a paper by Lee Smolin (a physicist) that applies gauge theory to economics; gauge theory is geometric, but its advanced geometry, so doesn't fit the 'basic geometric methods' requirement.  

---

## 5 answers

### Answer by username_8 on 2015-09-14. Score: 5 | Accepted answer

Another example is [Economies with Public Goods: An Elementary Geometric Exposition](http://onlinelibrary.wiley.com/doi/10.1111/1097-3923.00006/abstract) by William Thomson, which relies extensively on the geometry of equilateral triangles.

In general, William Thomson is known for making a heavy and interesting usage of geometry in his papers. See for instance a recent working paper of his : [Compromising between the proportional and constrained equal awards rules](http://rcer.econ.rochester.edu/RCERPAPERS/rcer_584.pdf) (although this one might be further from basic high-school euclidean geometry than what you're looking for).

Other somewhat similar examples include papers relying on the geometry of simplices. An example I came across recently is

* [A graphical analysis of some basic results in social choice, Estelle Cantillon and Antonio Rangel, Social Choice and Welfare Vol. 19, No. 3 (2002), pp. 587-611](http://www.jstor.org.proxy.library.vanderbilt.edu/stable/41106883?seq=3#page_scan_tab_contents)

but there are many others, starting with the exposition of the expected utility theorem in Mas-Collel, Whinston and Green.

I am also tempted to point at the following recent paper, although it definitely uses geometric tools which go far beyond high-school euclidean geometry:

* [A Geometric Approach to Mechanism Design, Jacob K. Goeree and Alexey I. Kushnir Carnegie Mellon University Tepper Business School, 2013, University of Zurich Department of Economics Working Paper No. 56](http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1974922)

I don't have a specific paper for it (any intro to econ textbook would do), but I would also add the classical graphical measure of consumer and producer surpluses in ECON 101. (Especially for linear demand and consumer curves where is simplifies to measuring the area of a triangle. Can't do much more "measurement of land" than that)


---

### Answer by username_2 on 2015-06-26. Score: 8

**UPDATE 19-9-2017**

I just received word from the author that the book is now freely downloadable **in English**, [**at this link**](https://www.centralbank.cy/en/publications/books/euclidean-economics-a-mathematical-method-for-construction-and-application-of-economics-models).

---

Got it. I remember browsing the pages of this book. But it was in Greek, and it does not appear to have been published also in English:

**[Euclidean Economics: A Mathematical Method for Construction and Application of Economics Models](http://www.centralbank.gov.cy/nqcontent.cfm?a_id=12483&lang=en)**

> "*The book establishes that economics can be studied and utilised on
> the basis of a minimum of fundamental hypotheses and the general laws
> of mathematics. Starting from 12 major propositions, it proves that
> closed exchange networks are replicated by systems of 2n first-order
> non-homogeneous linear differential equations, which simulate
> household, business, bank and government receipts and payments. Such
> networks are defined in the (R2n, t) vector space, where n is the
> number of sectors or markets and countries or currencies, while t is
> the elapsed time. Uniqueness, stability and controllability of the
> steady state as well as takings and outgoings are functions of
> behaviour coefficients and policy parameters. Annual sales of
> services, products and securities divided by average salaries, prices
> and values yield the man hours, output items and liquidity units
> traded. Demanded quantities do not coincide with available quantities.
> Potential inflation or deflation is proportional to the weighted
> deficit or surplus of market goods. Digital animation of the
> endogenous variables is possible on the basis of historical, projected
> or hypothetical data about the exogenous variables.*"

Author: **Sophocles Michaelides**  
Language: Greek  
Publisher: Mesogios Publications – Ellinika Grammata  
ISBN: 9963-9176-0-7  
Year: 2006

The summary does not state it clearly, but the "12 major propositions" are Euclidean, as I recall.

> **Comments:**
> **username_4**: Wow this is really cool.  

---

### Answer by username_5 on 2016-01-07. Score: 2

There are some papers of Stefan Behringer from University of Bonn.

[Optimal Harvesting of a Spatial Renewable Resource](http://www.stefanbehringer.com/1219997.pdf) published in Journal of Economic Dynamics and Control

As the title indicates, there is a geometrical application, at least there is the notion of space.

Another paper that I remember is "Spatial dynamics and convergence: the spatial AK model" by Boucekkine et al. published in Journal of Economic Theory.

I think you can reach another strand of literature on space and mainly on geometric technics used in economics.


---

### Answer by username_6 on 2015-06-26. Score: 2

Harry Johnson frequently applied euclidean geometry to trade theory and growth theory. Have a look at his many papers and books. For a more or less randomly chosen starting point, try his "Trade and Growth: A Geometrical Exposition".


---

### Answer by username_7 on 2015-06-26. Score: 1

Here are two problems (not papers, though the results are probably used in many papers)

1. In the case of a three asset [Markowitz portfolio optimization problem](https://en.wikipedia.org/wiki/Modern_portfolio_theory) the feasible set of portfolios in $\mu$ / $\sigma$ space can be shown to be an ellipse.
2. When a [demand curve is a straight line the marginal revenue curve bisects the demand curve](http://www.economics.utoronto.ca/jfloyd/modules/eltr.html).


---

