How does the power dynamic between the characters change over the course of the text?

This is a pretty involved topic for a short answer forum. You might want to check out the gradesaver summary and study guide I've linked below;

At the start of the play the family are sitting in the dining room, celebrating the engagement of Shiela Birling and Gerald Croft. The mood is relaxed and cheerful because everyone is happy two lovers have committed their lives to each other, except Mr Birling. He is happy because this link between the Birlings and the Crofts can only mean his business will be even more prosperous and he will become more wealthy.

you might want to read the article I've cited above in its entirety; the link is provided again below;