<p>As the link you provided mentions:</p>

<blockquote>
  <p>"Differential equations can be used to include the dynamic aspects to
  economics into a mathematical framework which takes into account the
  volatility present in economics."</p>
</blockquote>

<p>So the author does not derive the differential equations as the result of a theoretical model -the author just wants to obtain the movement through time of <em>equilibrium</em> price (the author assumes market-clearing), as a second order differential equation.</p>

<p>So it is a purely descriptive/forecasting exercise, devoid of any economic theory background. The author obtains the solution, which includes a number of coefficients to be determined, for which the author mentions</p>

<blockquote>
  <p>"These values can be estimated using statistics and econometric
  methods"</p>
</blockquote>

<p>Some constraints on the parameters may come from observing the past price process (is it oscillating? around a trend or around an horizontal line? etc), and in the end, the hope is that we may obtain a good predictor for the price movements -again, without basing it on economic theory.</p>

CC BY-SA 3.0
2017-05-08T09:47:44.177Z
2017-05-08T09:47:44.177Z
Alecos Papadopoulos
<p>I came across <a href="https://masterofeconomics.org/2009/11/26/the-second-order-differential-equations-of-dynamic-market-equilibrium/" rel="nofollow noreferrer">this</a> discussion, claiming supply and demand are expressible in terms of its price as $$Q_s=c_1+w_1P+u_1P'+v_1P'',\,Q_d=c_2+w_2P+u_2P'+v_2P''.$$Equating supply to demand for an equilibrium gives an ODE one can solve, but where do these formulae for $Q_s,\,Q_d$ come from?</p>

<p>I apologise if, contrary to the impression the page gives, these equations are not a mainstream model.</p>

<macroeconomics><general-equilibrium><ode>
Dynamic Market Equilibrium: motivation for differential equations
J.G.
# Dynamic Market Equilibrium: motivation for differential equations

(Asked by: username_0 on 2017-05-08)

I came across [this](https://masterofeconomics.org/2009/11/26/the-second-order-differential-equations-of-dynamic-market-equilibrium/) discussion, claiming supply and demand are expressible in terms of its price as $$Q\_s=c\_1+w\_1P+u\_1P'+v\_1P'',\,Q\_d=c\_2+w\_2P+u\_2P'+v\_2P''.$$Equating supply to demand for an equilibrium gives an ODE one can solve, but where do these formulae for $Q\_s,\,Q\_d$ come from?

I apologise if, contrary to the impression the page gives, these equations are not a mainstream model.

**Tags:** macroeconomics, general-equilibrium, ode

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## 1 answers

### Answer by username_1 on 2017-05-08. Score: 2

As the link you provided mentions:

> "Differential equations can be used to include the dynamic aspects to
> economics into a mathematical framework which takes into account the
> volatility present in economics."

So the author does not derive the differential equations as the result of a theoretical model -the author just wants to obtain the movement through time of *equilibrium* price (the author assumes market-clearing), as a second order differential equation.

So it is a purely descriptive/forecasting exercise, devoid of any economic theory background. The author obtains the solution, which includes a number of coefficients to be determined, for which the author mentions

> "These values can be estimated using statistics and econometric
> methods"

Some constraints on the parameters may come from observing the past price process (is it oscillating? around a trend or around an horizontal line? etc), and in the end, the hope is that we may obtain a good predictor for the price movements -again, without basing it on economic theory.


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