<p>It is a gradient of <span class="math-container">$Q(P)$</span>. <span class="math-container">$Q(P)$</span> is the demand function. <span class="math-container">$P(Q)$</span> is the <strong>inverse</strong> demand function. Even though confusingly when we plot demand we typically plot <span class="math-container">$P(Q)$</span>, the demand function is actually <span class="math-container">$Q(P)$</span> since the function gives you output (demand) as a function of inputs (price). The inverse demand function inverts the function to get price from demand.</p>
<p>Note both <span class="math-container">$Q$</span> and <span class="math-container">$P$</span> are endogenously determined, so there are no exogenous variables here so one can plot either <span class="math-container">$P$</span> or <span class="math-container">$Q$</span> on y-axis.</p>

CC BY-SA 4.0
2022-04-23T17:38:05.487Z
2022-04-23T17:38:05.487Z
1muflon1
<p>This is a very elementary question from a complete novice,  and aiming first at preventing a possible misunderstanding. Thanks in advance.</p>
<hr />
<p>Suppose we have a linear demand curve with Y intercept <span class="math-container">$(0,20)$</span> and X intercept <span class="math-container">$(10,0)$</span>. Which number counts as &quot; the slope&quot; of this curve in economics : <span class="math-container">$-1/2$</span> or <span class="math-container">$-2$</span>?</p>
<p>In other words: by &quot; slope&quot; do we mean the gradient of the <span class="math-container">$P(q)$</span> function or the gradient of the <span class="math-container">$Q(p)$</span> function?</p>
<hr />
<p>Outside economics, the curve would be said to have a slope of :</p>
<p><span class="math-container">$$\frac{\Delta y} {\Delta x} = \frac {10}{-20} = -\frac {1}{2}$$</span></p>
<p>and would be thought as a representation of the function</p>
<p><span class="math-container">$$P(Q) = -\frac {1}{2} Q + 10$$</span></p>
<p>with Q ( = quantity) as independent variable and P (=price) as dependent variable.</p>
<p><a href="https://i.sstatic.net/xC3rp.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/xC3rp.png" alt="enter image description here" /></a></p>
<p>However, it seems ( from some readings I've made) that the number denoted in economics by the expression &quot; slope of the demand curve&quot; is in fact the slope of the graph representing the following function :</p>
<p><span class="math-container">$$Q(P) = -2P + 20$$</span></p>
<p>with Price as independent variable and Quantity as dependent variable</p>
<p><a href="https://i.sstatic.net/bnxuH.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bnxuH.png" alt="enter image description here" /></a></p>

<microeconomics><demand>
Which number counts officially as the " slope of the demand curve" : $\frac {\mathit d P(Q)}{\mathit dQ}$ or$\frac {\mathit d Q(P)}{\mathit dP}$?
Vince Vickler
# Which number counts officially as the " slope of the demand curve" : $\frac {\mathit d P(Q)}{\mathit dQ}$ or$\frac {\mathit d Q(P)}{\mathit dP}$?

(Asked by: username_0 on 2022-04-23)

This is a very elementary question from a complete novice, and aiming first at preventing a possible misunderstanding. Thanks in advance.

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Suppose we have a linear demand curve with Y intercept $(0,20)$ and X intercept $(10,0)$. Which number counts as " the slope" of this curve in economics : $-1/2$ or $-2$?

In other words: by " slope" do we mean the gradient of the $P(q)$ function or the gradient of the $Q(p)$ function?

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Outside economics, the curve would be said to have a slope of :

$$\frac{\Delta y} {\Delta x} = \frac {10}{-20} = -\frac {1}{2}$$

and would be thought as a representation of the function

$$P(Q) = -\frac {1}{2} Q + 10$$

with Q ( = quantity) as independent variable and P (=price) as dependent variable.

[![enter image description here](https://i.sstatic.net/xC3rp.png)](https://i.sstatic.net/xC3rp.png)

However, it seems ( from some readings I've made) that the number denoted in economics by the expression " slope of the demand curve" is in fact the slope of the graph representing the following function :

$$Q(P) = -2P + 20$$

with Price as independent variable and Quantity as dependent variable

[![enter image description here](https://i.sstatic.net/bnxuH.png)](https://i.sstatic.net/bnxuH.png)

**Tags:** microeconomics, demand


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## 1 answers

### Answer by username_1 on 2022-04-23. Score: 5 | Accepted answer

It is a gradient of $Q(P)$. $Q(P)$ is the demand function. $P(Q)$ is the **inverse** demand function. Even though confusingly when we plot demand we typically plot $P(Q)$, the demand function is actually $Q(P)$ since the function gives you output (demand) as a function of inputs (price). The inverse demand function inverts the function to get price from demand.

Note both $Q$ and $P$ are endogenously determined, so there are no exogenous variables here so one can plot either $P$ or $Q$ on y-axis.


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