Derivation of aggregate demand function for Monopolistic Competition (based on Combes et. al, 2008)
As we have discussed in the comments, the utility function used in the book is Cobb-Douglas: $U = CM^{\mu}A^{1 - \mu}$. The well known fact mentioned in equation (3.3) on page 57 - the one that you highlighted - is that the Cobb-Douglas utility function is homothetic - the share of total income spent on any of the goods is constant over all possible incomes. More specifically here a share of $\mu$ of the expenditure is always spent on manufacturing goods and a share of $1-\mu$ is spent on the agriculture good. $\sigma$ and $p_i$ only determine how the $\mu y$ units of income that the representative consumer spends on manufacturing output is allocated among the distinct manufacturing goods. 
Although the output goods are different most such models assume that both the jobs and the employees are identical and there is a perfectly competitive domestic labor market. Hence the identical wage rate.


Note: $y$ is personal income and $L$ is the number of employees, thus the total income of the economy is $yL$. (E.g. the last sentence on page 56). 

Thus the total expenditure $E = yL$ - the total income, as the model is static. The expenditure on manufactured goods is $\mu E = \mu yL = PM \Leftrightarrow M = \frac{\mu yL}{P}$.