<p>If you have <span class="math-container">$J$</span> consumers therefore <span class="math-container">$J$</span> demands for a good <span class="math-container">$X$</span>. Denoting the individual demand of each consumer with <span class="math-container">$x_j^*$</span> as you have it, if <span class="math-container">$X$</span> is the aggregate demand, it is just the sum of every individual demand:</p>
<p><span class="math-container">$X=\sum_{j=1}^{J}x_j^*$</span></p>
<p>Then for your case it's: <span class="math-container">$x_1^*+x_2^*=\frac{(I_1+I_2)}{2P_X}$</span>, and the same with <span class="math-container">$Y$</span>.</p>

CC BY-SA 4.0
2020-07-10T01:04:04.880Z
2020-07-10T01:04:04.880Z
manifold
<p>Assume that we have two people with the same utility function of <span class="math-container">$U_i = x^{1/2} + y^{1/2}$</span> where <span class="math-container">$i=1,2$</span> and <span class="math-container">$I_i$</span> is the income. Let <span class="math-container">$P_x$</span> denote price of good <span class="math-container">$x$</span> and <span class="math-container">$P_y$</span> denote price of good <span class="math-container">$y$</span>.</p>

<p>I'm being asked to derive the aggregate demand function. The only thing I got so far was finding the market demand for each good per person, which is </p>

<p><span class="math-container">$x^*_1 = {I_1}/2P_x$</span> , <span class="math-container">$y^*_1 = {I_1}/2P_y$</span>, for person 1</p>

<p><span class="math-container">$x^*_2 = {I_2}/2P_x$</span>, <span class="math-container">$y^*_2 = {I_2}/2P_y$</span> for person 2</p>

<p>Am I missing something? Please help.</p>

<p>Thanks.</p>

CC BY-SA 4.0
2020-02-10T09:36:19.713Z
Do you know what aggregate means?
Giskard
CC BY-SA 4.0
2020-02-10T09:46:53.400Z
The total demand for a good. So I'm just supposed to just add $x^*_1$ and $x^*_2$ together?
user25621
CC BY-SA 4.0
2020-02-10T09:52:08.730Z
Well, if a total is the sum of its parts then that certainly makes sense.
Giskard
CC BY-SA 4.0
2020-02-10T12:00:32.333Z
**Hint:** Aggregate demand is the sum of individual demands.
VARulle
<utility><consumer-theory><demand>
How do I derive the aggregate demand function given two utilities functions?
user25621
# How do I derive the aggregate demand function given two utilities functions?

(Asked by: username_0 on 2020-02-10)

Assume that we have two people with the same utility function of $U\_i = x^{1/2} + y^{1/2}$ where $i=1,2$ and $I\_i$ is the income. Let $P\_x$ denote price of good $x$ and $P\_y$ denote price of good $y$.

I'm being asked to derive the aggregate demand function. The only thing I got so far was finding the market demand for each good per person, which is

$x^\*\_1 = {I\_1}/2P\_x$ , $y^\*\_1 = {I\_1}/2P\_y$, for person 1

$x^\*\_2 = {I\_2}/2P\_x$, $y^\*\_2 = {I\_2}/2P\_y$ for person 2

Am I missing something? Please help.

Thanks.

**Tags:** utility, consumer-theory, demand

> **Comments:**
> **username_1**: Do you know what aggregate means?  
> **username_0**: The total demand for a good. So I'm just supposed to just add $x^*_1$ and $x^*_2$ together?  
> **username_1**: Well, if a total is the sum of its parts then that certainly makes sense.  
> **username_2**: **Hint:** Aggregate demand is the sum of individual demands.  

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## 1 answers

### Answer by username_3 on 2020-07-10. Score: 1

If you have $J$ consumers therefore $J$ demands for a good $X$. Denoting the individual demand of each consumer with $x\_j^\*$ as you have it, if $X$ is the aggregate demand, it is just the sum of every individual demand:

$X=\sum\_{j=1}^{J}x\_j^\*$

Then for your case it's: $x\_1^\*+x\_2^\*=\frac{(I\_1+I\_2)}{2P\_X}$, and the same with $Y$.


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