<p>Recall, that the directional derivative of a function is defined as the the rate at which the function <span class="math-container">$f(x,y,z)$</span> at a given point <span class="math-container">$(x_0, y_0, z_0)$</span> changes in  direction of the vector <span class="math-container">$v$</span>, where <span class="math-container">$||v||$</span> is the <a href="http://mathworld.wolfram.com/Norm.html" rel="nofollow noreferrer">norm</a> of <span class="math-container">$v$</span><sup>1</sup>.</p>
<h1>What comes to mind</h1>
<p>Applications of the directional derivative can be used in determining the rate of switching inputs in <a href="https://en.wikipedia.org/wiki/Production_function" rel="nofollow noreferrer">production functions</a>, which can be very helpful in determining/forecasting switching costs for a given bundle of inputs. <strong>Though it does not tell you where the optimum points are</strong> it does tell you the rate of change (i.e. the switching costs) of  moving to a different bundle.</p>
<p>Hope this is helpful</p>
<p><sub><sup>1</sup> <a href="http://mathworld.wolfram.com/DirectionalDerivative.html" rel="nofollow noreferrer">http://mathworld.wolfram.com/DirectionalDerivative.html</a></sub></p>

CC BY-SA 3.0
2017-11-19T19:58:43.953Z
By "the rate of switching inputs" do you mean MRTS?
EconJohn
CC BY-SA 3.0
2017-11-19T20:00:28.020Z
To summarize what you said, you use the directional derivative to identify the direction of the optimal bundle?
EconJohn
CC BY-SA 3.0
2017-11-19T20:15:00.140Z
@EconJohn The directional derivative can be used for any bundle be that optimal or not,
Bensstats
CC BY-SA 3.0
2017-11-19T19:54:15.623Z
2017-11-19T20:19:36.130Z
2020-06-17T09:40:54.643Z
Bensstats
<p>In a basic mathematics for economists course one is exposed to the concept of directional derviative. Recall that a directional derivative is defined as:</p>

<p>$$\nabla f \frac{\mathbb{v}}{\|\mathbb{v}\|}$$</p>

<p>I know that it mathematically tells you the direction the function is increasing on a two or three dimensional graph, however I am yet to see an application of such a formula in any economics problems.</p>

<p>What are some applications of the directional derivative in Economics?</p>

<mathematical-economics>
What are directional derivatives used for in economics?
EconJohn
# What are directional derivatives used for in economics?

(Asked by: username_0 on 2017-11-19)

In a basic mathematics for economists course one is exposed to the concept of directional derviative. Recall that a directional derivative is defined as:

$$\nabla f \frac{\mathbb{v}}{\|\mathbb{v}\|}$$

I know that it mathematically tells you the direction the function is increasing on a two or three dimensional graph, however I am yet to see an application of such a formula in any economics problems.

What are some applications of the directional derivative in Economics?

**Tags:** mathematical-economics

---

## 1 answers

### Answer by username_1 on 2017-11-19. Score: 1 | Accepted answer

Recall, that the directional derivative of a function is defined as the the rate at which the function $f(x,y,z)$ at a given point $(x\_0, y\_0, z\_0)$ changes in direction of the vector $v$, where $||v||$ is the [norm](http://mathworld.wolfram.com/Norm.html) of $v$1.

# What comes to mind

Applications of the directional derivative can be used in determining the rate of switching inputs in [production functions](https://en.wikipedia.org/wiki/Production_function), which can be very helpful in determining/forecasting switching costs for a given bundle of inputs. **Though it does not tell you where the optimum points are** it does tell you the rate of change (i.e. the switching costs) of moving to a different bundle.

Hope this is helpful

1 <http://mathworld.wolfram.com/DirectionalDerivative.html>

> **Comments:**
> **username_0**: By "the rate of switching inputs" do you mean MRTS?  
> **username_0**: To summarize what you said, you use the directional derivative to identify the direction of the optimal bundle?  
> **username_1**: @EconJohn The directional derivative can be used for any bundle be that optimal or not,  

---

