<p>This seems to address the question :</p>
<p><a href="https://mitsloan.mit.edu/shared/ods/documents?DocumentID=4171" rel="nofollow noreferrer">https://mitsloan.mit.edu/shared/ods/documents?DocumentID=4171</a></p>
<p>An Euler equation is a difference or differential equation that is an intertempo- ral first-order condition for a dynamic choice problem. It describes the evolution of economic variables along an optimal path. It is a necessary but not sufficient condition for a candidate optimal path, and so is useful for partially characterizing the theoretical implications of a range of models for dynamic behavior. In models with uncertainty, expectational Euler equations are conditions on moments, and thus directly provide a basis for testing models and estimating model parameters using observed dynamic behavior.</p>
<p>From : Euler equations∗ Jonathan A. Parker†
Northwestern University and NBER December 2007</p>

CC BY-SA 4.0
2021-12-02T11:26:13.723Z
Links break, please quote the gist of the answer from the source. Also name/credit the source.
Giskard
CC BY-SA 4.0
2021-12-02T11:20:59.420Z
2021-12-02T11:32:52.963Z
2021-12-02T11:32:52.963Z
dm63
<p>In Economics, Euler equation is:</p>
<p><span class="math-container">$u'(c_{t})=\beta Ru'(c_{t+1})$</span></p>
<p>What is the origin of the name of 'Euler' in this equation?</p>
<p>I know that, in fluid dynamics, Euler equation is</p>
<p><span class="math-container">\begin{aligned}{D\mathbf {u}  \over Dt}&amp;=-\nabla w+\mathbf {g} \\\nabla \cdot \mathbf {u} &amp;=0\end{aligned}</span></p>
<p>However, I cannot catch the similarity between economics and fluid dynamics for the Euler equation.</p>

CC BY-SA 4.0
2021-12-01T15:04:34.387Z
There are dozens, if not hundreds, of Euler equations/identities/theorems in math, physics, engineering, economics, etc. It shouldn't be too surprising that there is another Euler equation in fluid dynamics.
user141240
CC BY-SA 4.0
2021-12-01T15:08:49.327Z
My guess is that it came from the Euler-Lagrange equation in calculus of variation. When you are doing utility maximization in continuous time, you are basically doing *constrained* calculus of variation, aka optimal control.
user141240
CC BY-SA 4.0
2022-05-31T13:21:22.230Z
@user141240 is correct.  Physics of the time was just discovering the Lagrangian in connection with optimal paths of particles, a completely separate view from the older Newtonian physics. Lagrange and Euler were contemporaries.  I think Euler was rumored to have said "there is no dynamics, where a choice is made of some trajectory, without optimization".  And economics is all about rational optimization of choices. https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1834&context=jhm
Kiers
<macroeconomics><mathematical-economics><history-economic-thought>
What's the origin of the naming of Euler equation in economics?
martian03
# What's the origin of the naming of Euler equation in economics?

(Asked by: username_0 on 2021-12-01)

In Economics, Euler equation is:

$u'(c\_{t})=\beta Ru'(c\_{t+1})$

What is the origin of the name of 'Euler' in this equation?

I know that, in fluid dynamics, Euler equation is

\begin{aligned}{D\mathbf {u} \over Dt}&=-\nabla w+\mathbf {g} \\\nabla \cdot \mathbf {u} &=0\end{aligned}

However, I cannot catch the similarity between economics and fluid dynamics for the Euler equation.

**Tags:** macroeconomics, mathematical-economics, history-economic-thought
> **Comments:**
> **username_1**: There are dozens, if not hundreds, of Euler equations/identities/theorems in math, physics, engineering, economics, etc. It shouldn't be too surprising that there is another Euler equation in fluid dynamics.  
> **username_1**: My guess is that it came from the Euler-Lagrange equation in calculus of variation. When you are doing utility maximization in continuous time, you are basically doing *constrained* calculus of variation, aka optimal control.  
> **username_2**: @user141240 is correct.  Physics of the time was just discovering the Lagrangian in connection with optimal paths of particles, a completely separate view from the older Newtonian physics. Lagrange and Euler were contemporaries.  I think Euler was rumored to have said "there is no dynamics, where a choice is made of some trajectory, without optimization".  And economics is all about rational optimization of choices. https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1834&context=jhm  

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## 1 answers

### Answer by username_3 on 2021-12-02. Score: 1

This seems to address the question :

<https://mitsloan.mit.edu/shared/ods/documents?DocumentID=4171>

An Euler equation is a difference or differential equation that is an intertempo- ral first-order condition for a dynamic choice problem. It describes the evolution of economic variables along an optimal path. It is a necessary but not sufficient condition for a candidate optimal path, and so is useful for partially characterizing the theoretical implications of a range of models for dynamic behavior. In models with uncertainty, expectational Euler equations are conditions on moments, and thus directly provide a basis for testing models and estimating model parameters using observed dynamic behavior.

From : Euler equations∗ Jonathan A. Parker†
Northwestern University and NBER December 2007

> **Comments:**
> **username_4**: Links break, please quote the gist of the answer from the source. Also name/credit the source.  

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