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.

  • 2
    $\begingroup$ 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. $\endgroup$
    – user141240
    Dec 1 '21 at 15:04
  • 4
    $\begingroup$ 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. $\endgroup$
    – user141240
    Dec 1 '21 at 15:08

This seems to address the question :


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

  • $\begingroup$ Links break, please quote the gist of the answer from the source. Also name/credit the source. $\endgroup$
    – Giskard
    Dec 2 '21 at 11:26

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