<p>Let <span class="math-container">$Q = \sum_{i} q_i$</span> be aggregate demand where <span class="math-container">$q_i$</span> is individual demand.</p>
<p>Then:
<span class="math-container">$$
\frac{\partial Q}{\partial p} = \sum_{i} \frac{\partial q_i}{\partial p},
$$</span>
So:
<span class="math-container">$$
\frac{\partial Q}{\partial p} \frac{p}{Q} = \sum_i \frac{\partial q_i}{\partial p} \frac{p}{q_i} \frac{q_i}{Q}.
$$</span>
Now let <span class="math-container">$w_i = \frac{q_i}{Q}$</span> be the share of <span class="math-container">$i$</span>'s demand in total demand then we can write:
<span class="math-container">$$
\varepsilon^Q_p = \sum_i w_i \varepsilon^{q_i}_p.
$$</span>
where <span class="math-container">$\varepsilon$</span> is the price elasticity. This shows that the price elasticity of the aggregate demand, <span class="math-container">$\varepsilon^Q_p$</span>, is a weighted average of the individual demand elasticities, <span class="math-container">$\varepsilon^{q_i}_p$</span>, where the weights, <span class="math-container">$w_i$</span>, are given by the share of the individual demands in the aggregate demand.</p>

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2024-04-27T08:47:20.847Z
2024-04-27T08:47:20.847Z
tdm
<p>Price elasticity of demand is defined as <span class="math-container">$\frac{\delta q}{q}\frac{p}{\delta p}$</span>. If aggregate demand <span class="math-container">$q = q_1 + \ldots + q_n$</span>, then <span class="math-container">$\delta q = \delta q_1 + \ldots + \delta q_n$</span>, and the price elasticity should essentially become <span class="math-container">$\frac{\sum\delta q_i}{\sum q_i}\frac{p}{\delta p}$</span>, and go no further right? Can this be simplified?</p>

<microeconomics><elasticity>
How do you calculate price elasticity of aggregate demand?
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# How do you calculate price elasticity of aggregate demand?

(Asked by: username_0 on 2024-04-27)

Price elasticity of demand is defined as $\frac{\delta q}{q}\frac{p}{\delta p}$. If aggregate demand $q = q\_1 + \ldots + q\_n$, then $\delta q = \delta q\_1 + \ldots + \delta q\_n$, and the price elasticity should essentially become $\frac{\sum\delta q\_i}{\sum q\_i}\frac{p}{\delta p}$, and go no further right? Can this be simplified?

**Tags:** microeconomics, elasticity


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## 1 answers

### Answer by username_1 on 2024-04-27. Score: 1 | Accepted answer

Let $Q = \sum\_{i} q\_i$ be aggregate demand where $q\_i$ is individual demand.

Then:
$$
\frac{\partial Q}{\partial p} = \sum\_{i} \frac{\partial q\_i}{\partial p},
$$
So:
$$
\frac{\partial Q}{\partial p} \frac{p}{Q} = \sum\_i \frac{\partial q\_i}{\partial p} \frac{p}{q\_i} \frac{q\_i}{Q}.
$$
Now let $w\_i = \frac{q\_i}{Q}$ be the share of $i$'s demand in total demand then we can write:
$$
\varepsilon^Q\_p = \sum\_i w\_i \varepsilon^{q\_i}\_p.
$$
where $\varepsilon$ is the price elasticity. This shows that the price elasticity of the aggregate demand, $\varepsilon^Q\_p$, is a weighted average of the individual demand elasticities, $\varepsilon^{q\_i}\_p$, where the weights, $w\_i$, are given by the share of the individual demands in the aggregate demand.


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