I understand that Islam allows a man to marry multiple wives within the rules of Sharia. However, what is the wisdom in such marriages as it relates to the first wife who often undergoes jealousy and depression?
Bismillah
Thank you for your question. In our scriptural sources women are not encouraged to have these feelings as they are considered a blameworthy type of ghirah (when you want something only for yourself). They are feelings that are not validated. Similar to the feelings of jealousy and depression when someone doesn't want anyone to do better than them, it is not upon people to not do better than that person, but upon the person to control and work on themselves. As to the wisdom of allowing polygyny there is much wisdom, such that the feelings of the first wife in some cases is not enough of a reason to make it impermissible. Rather, the first wife has to control these tendencies and get used to the idea in the knowledge that this is something that God has allowed. At times, if polygyny is done with wisdom it can improve the situation of the first wife and the relationship between her and her husband.
These feelings are also enhanced by expectations and cultures, which are again not factors that influence permissibility as it is upon Muslims and Muslim society to create expectations and cultures in line with what is permissible and impermissible.
May you always be successful