<p>Graph of Aggregate Demand Curve is as follows :</p>

<p><a href="https://i.sstatic.net/rNmIN.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/rNmIN.png" alt="enter image description here"></a></p>

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2019-10-17T07:50:46.577Z
Can you explain why? That would be helpful.
user708015
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2019-10-17T08:01:43.493Z
When $p >4$, only people in the third category demands 50 units. When $p =4$, there is perfectly elastic demand for the product by those in the second category i.e. they can demand any non-negative quantity $[0, \infty)$. When we add 50 to it, we get demand as $[50, \infty)$. For $p <4$, quantity demanded is infinite (by the second category).
Amit
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2019-10-17T08:03:51.913Z
What about price less than 2? Also, can you help me understand how to think about it when faced with similar problems?
user708015
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2019-10-17T08:09:19.110Z
Category 1 consumers don't matter in the aggregate demand as there is already infinite demand for the commodity by category 2 consumers for any $p < 4$.
Amit
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2019-10-17T07:44:35.913Z
2019-10-17T07:44:35.913Z
Amit
<h2>Mathematically</h2>

<p>To calculate the total demand curve (aggregate demand has a <a href="https://en.wikipedia.org/wiki/Aggregate_demand" rel="nofollow noreferrer">different meaning</a>), you just need to ask yourself that for each price, how many units will be demanded.</p>

<p>You have three groups:</p>

<ul>
<li>A. 20 people, perfectly elastic at <span class="math-container">$p = 2$</span>. This group will buy 20 units as long as <span class="math-container">$p \leq 2$</span>.</li>
<li>B. 40 people, perfectly elastic at <span class="math-container">$p = 4$</span>. This group will buy 40 units as long as <span class="math-container">$p \leq 4$</span>.</li>
<li>C. 50 people, perfectly inelastic. This group will buy 50 units no matter what.</li>
</ul>

<p>Mathematically,</p>

<p><span class="math-container">$$A(p) = \begin{cases} 20 &amp; \text{if $p \leq 2$} \\ 0 &amp; \text{otherwise}\end{cases},\quad
B(p) = \begin{cases} 40 &amp; \text{if $p \leq 4$} \\ 0 &amp; \text{otherwise}\end{cases},\quad
C(p) = 50$$</span></p>

<p>Total demand is just a function of <span class="math-container">$p$</span>: <span class="math-container">$Q(p) = A(p) + B(p) + C(p)$</span>.
If we start at <span class="math-container">$p = 1$</span>, what's <span class="math-container">$A(1) + B(1) + C(1)$</span>? Do this for all prices, and you'll get the total demand curve.</p>

<h2>Graphically</h2>

<p>You could also do this graphically... draw up the demand curve (would look like a rectangle) for each group. The total demand curve will just be the <em>horizontal</em> stack of these rectangles.</p>

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2019-10-17T07:20:02.563Z
Won't the market demand end up in sections? I will have a vertical line at 2500 units and two horizontal lines at prices 20 and 40.
user708015
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2019-10-17T07:21:15.717Z
I've just edited my answer. Let me know if that clears things up for you.
Art
CC BY-SA 4.0
2019-10-17T07:24:57.363Z
I think you misunderstood my question - the first two groups have a perfectly elastic demand at prices 2 and 4 respectively. There are no units mentioned. It is infinite.
user708015
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2019-10-17T07:42:20.880Z
Hm... by saying the first group has 20 people who has perfectly elastic demand, I think this is how the number of people would come into play. Otherwise I'm not sure what the point of specifying number of people in each group is... So having 20 or 2 or 200 people in the first group wouldn't make a difference if each person could demand infinitely many units.
Art
CC BY-SA 4.0
2019-10-17T07:43:31.427Z
I thought the same. It has just been put in a tricky way. Is my first comment correct in that case?
user708015
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2019-10-17T07:46:22.507Z
Where are 2500, 20, and 40 from? Maybe you could show your work a bit.
Art
CC BY-SA 4.0
2019-10-17T07:50:07.197Z
2500 is 50 people multiplied by quantity 50. 20 and 40 is just the price for the elastic demand curve.
user708015
CC BY-SA 4.0
2019-10-17T08:14:00.723Z
You didn't mention there's 50 people in the C group though. Either way, you could either go this way (assume that one person demands one unit), or could go with @Amit's suggestion. The way you do it is the same, but just change $A(p)$ and $B(p)$ to be equal to $\infty$ if price is less than 2 and 4.
Art
CC BY-SA 4.0
2019-10-17T07:14:44.433Z
2019-10-17T08:14:16.520Z
2019-10-17T08:14:16.520Z
Art
<p>I'm aggregating individual demand curves but the demand curves are inelastic or elastic. Say, 20 people have an elastic demand for a product at price of $2. </p>

<p>Another 40 people have an elastic demand for a product at price of $4. There is a third category who have an inelastic demand of 50 units. </p>

<p>How do I aggregate these demand curves (graphically and in equation form)? </p>

<supply-and-demand>
Aggregating individual demand curves
user708015
# Aggregating individual demand curves

(Asked by: username_0 on 2019-10-17)

I'm aggregating individual demand curves but the demand curves are inelastic or elastic. Say, 20 people have an elastic demand for a product at price of $2.

Another 40 people have an elastic demand for a product at price of $4. There is a third category who have an inelastic demand of 50 units.

How do I aggregate these demand curves (graphically and in equation form)?

**Tags:** supply-and-demand


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## 2 answers

### Answer by username_1 on 2019-10-17. Score: 0 | Accepted answer

Graph of Aggregate Demand Curve is as follows :

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

> **Comments:**
> **username_0**: Can you explain why? That would be helpful.  
> **username_1**: When $p >4$, only people in the third category demands 50 units. When $p =4$, there is perfectly elastic demand for the product by those in the second category i.e. they can demand any non-negative quantity $[0, \infty)$. When we add 50 to it, we get demand as $[50, \infty)$. For $p <4$, quantity demanded is infinite (by the second category).  
> **username_0**: What about price less than 2? Also, can you help me understand how to think about it when faced with similar problems?  
> **username_1**: Category 1 consumers don't matter in the aggregate demand as there is already infinite demand for the commodity by category 2 consumers for any $p < 4$.  

---

### Answer by username_2 on 2019-10-17. Score: 0

## Mathematically

To calculate the total demand curve (aggregate demand has a [different meaning](https://en.wikipedia.org/wiki/Aggregate_demand)), you just need to ask yourself that for each price, how many units will be demanded.

You have three groups:

* A. 20 people, perfectly elastic at $p = 2$. This group will buy 20 units as long as $p \leq 2$.
* B. 40 people, perfectly elastic at $p = 4$. This group will buy 40 units as long as $p \leq 4$.
* C. 50 people, perfectly inelastic. This group will buy 50 units no matter what.

Mathematically,

$$A(p) = \begin{cases} 20 & \text{if $p \leq 2$} \\ 0 & \text{otherwise}\end{cases},\quad
B(p) = \begin{cases} 40 & \text{if $p \leq 4$} \\ 0 & \text{otherwise}\end{cases},\quad
C(p) = 50$$

Total demand is just a function of $p$: $Q(p) = A(p) + B(p) + C(p)$.
If we start at $p = 1$, what's $A(1) + B(1) + C(1)$? Do this for all prices, and you'll get the total demand curve.

## Graphically

You could also do this graphically... draw up the demand curve (would look like a rectangle) for each group. The total demand curve will just be the *horizontal* stack of these rectangles.

> **Comments:**
> **username_0**: Won't the market demand end up in sections? I will have a vertical line at 2500 units and two horizontal lines at prices 20 and 40.  
> **username_2**: I've just edited my answer. Let me know if that clears things up for you.  
> **username_0**: I think you misunderstood my question - the first two groups have a perfectly elastic demand at prices 2 and 4 respectively. There are no units mentioned. It is infinite.  
> **username_2**: Hm... by saying the first group has 20 people who has perfectly elastic demand, I think this is how the number of people would come into play. Otherwise I'm not sure what the point of specifying number of people in each group is... So having 20 or 2 or 200 people in the first group wouldn't make a difference if each person could demand infinitely many units.  
> **username_0**: I thought the same. It has just been put in a tricky way. Is my first comment correct in that case?  
> **username_2**: Where are 2500, 20, and 40 from? Maybe you could show your work a bit.  
> **username_0**: 2500 is 50 people multiplied by quantity 50. 20 and 40 is just the price for the elastic demand curve.  
> **username_2**: You didn't mention there's 50 people in the C group though. Either way, you could either go this way (assume that one person demands one unit), or could go with @username_1's suggestion. The way you do it is the same, but just change $A(p)$ and $B(p)$ to be equal to $\infty$ if price is less than 2 and 4.  

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