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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

, which implies a demand function: enter image description here

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

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

Thanks.

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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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