<p>These expressions can be easily derived formally by taking the derivatives of Walras' law w.r.t $I$ (Engel aggregation) and $p_j$ (Cournot aggregation). 
The Engel aggregation means that not all goods are luxuries ($\eta_i&gt;1$), or necessities ($\eta_i&lt;1$), or inferior goods ($\eta_i&lt;0$). The Cournot aggregation says that the budget share $s_j$ of the good $j$  is small when the good $j$ has many substitutes ($\epsilon_{ij}&gt;0$), and big when it has many complements ($\epsilon_{ij}&lt;0$), or their respective budget shares are large. </p>

CC BY-SA 3.0
2017-10-24T01:18:46.497Z
2017-10-24T01:18:46.497Z
Egg
<p>Could anyone provide a possibly intuitive and friendly explanation to the Engel Aggregation $(\sum s_i \eta_i = 1)$ and Cournot Aggregation$(\sum s_i \epsilon_{ij} = -s_j)$? Here, $s_i = \frac{p_i,x_i}{I} \ge 0$ is the income share, $\epsilon_{ij}, \eta_i$ are price and income elasticities, respectively. I was not sure how this theory of aggregation of consumer demand tell us about the consumption behavior. Thank you in advance for your help! </p>

<microeconomics><elasticity>
Intuition behind Engel Aggregation and Cournot Aggregation
David Kim
# Intuition behind Engel Aggregation and Cournot Aggregation

(Asked by: username_0 on 2017-10-20)

Could anyone provide a possibly intuitive and friendly explanation to the Engel Aggregation $(\sum s\_i \eta\_i = 1)$ and Cournot Aggregation$(\sum s\_i \epsilon\_{ij} = -s\_j)$? Here, $s\_i = \frac{p\_i,x\_i}{I} \ge 0$ is the income share, $\epsilon\_{ij}, \eta\_i$ are price and income elasticities, respectively. I was not sure how this theory of aggregation of consumer demand tell us about the consumption behavior. Thank you in advance for your help!

**Tags:** microeconomics, elasticity

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## 1 answers

### Answer by username_1 on 2017-10-24. Score: 4 | Accepted answer

These expressions can be easily derived formally by taking the derivatives of Walras' law w.r.t $I$ (Engel aggregation) and $p\_j$ (Cournot aggregation).
The Engel aggregation means that not all goods are luxuries ($\eta\_i>1$), or necessities ($\eta\_i<1$), or inferior goods ($\eta\_i<0$). The Cournot aggregation says that the budget share $s\_j$ of the good $j$ is small when the good $j$ has many substitutes ($\epsilon\_{ij}>0$), and big when it has many complements ($\epsilon\_{ij}<0$), or their respective budget shares are large.


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