<p>hint: 
sum equation (2) for all i and use the definition of $Q^c$, we get an expression for $Q^c$. then, substitute this expression into (2) and solve for $q^c$.</p>

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2017-11-25T03:54:33.597Z
2017-11-25T03:54:33.597Z
vita nova
<p>I am reading Melitz and Ottaviano (2008), but I find it hard to understand some math in the model. </p>

<p>The preference is given by :
<a href="https://i.sstatic.net/57Px7.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/57Px7.jpg" alt="enter image description here"></a></p>

<p>, which implies a demand function:
<a href="https://i.sstatic.net/KDtaz.jpg." rel="nofollow noreferrer"><img src="https://i.sstatic.net/KDtaz.jpg." alt="enter image description here"></a></p>

<p>Then the paper says the "inverse demand function can then be inverted to yield the linear market demand system for these varieties":</p>

<p><a href="https://i.sstatic.net/YV7Oi.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/YV7Oi.jpg" alt="enter image description here"></a></p>

<p>But what operations do they take in getting the function $q_i$? </p>

<p>I am very confused on dealing with the $Q_c$ variable, which is defined to be :
<a href="https://i.sstatic.net/cBJI7.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/cBJI7.jpg" alt="enter image description here"></a></p>

<p>Thanks.</p>

<mathematical-economics><international-trade><industrial-organisation>
Math in Melitz and Ottaviano (2008)
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# Math in Melitz and Ottaviano (2008)

(Asked by: username_0 on 2017-11-24)

I am reading Melitz and Ottaviano (2008), but I find it hard to understand some math in the model.

The preference is given by :
[![enter image description here](https://i.sstatic.net/57Px7.jpg)](https://i.sstatic.net/57Px7.jpg)

, which implies a demand function:
[![enter image description here](https://i.sstatic.net/KDtaz.jpg.)](https://i.sstatic.net/KDtaz.jpg.)

Then the paper says the "inverse demand function can then be inverted to yield the linear market demand system for these varieties":

[![enter image description here](https://i.sstatic.net/YV7Oi.jpg)](https://i.sstatic.net/YV7Oi.jpg)

But what operations do they take in getting the function $q\_i$?

I am very confused on dealing with the $Q\_c$ variable, which is defined to be :
[![enter image description here](https://i.sstatic.net/cBJI7.jpg)](https://i.sstatic.net/cBJI7.jpg)

Thanks.

**Tags:** mathematical-economics, international-trade, industrial-organisation


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## 1 answers

### Answer by username_1 on 2017-11-25. Score: 4 | Accepted answer

hint:
sum equation (2) for all i and use the definition of $Q^c$, we get an expression for $Q^c$. then, substitute this expression into (2) and solve for $q^c$.


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