At the start Arthur showed his dominance with his speeches during the celebration. During the speeches he brags on about his status within the community as a public figure in Brumley. Arthur wanted the people to understand that he is not a man to be messed with at all. But ever since the inspector comes in Arthur have to endure being challenged not only from the inspector, but also members of his family as well. Arthur is not used to being challenged at all and from this he was both irritated and impatient. So he attempted to win over the inspector by trying to play the interview according to his own rules. At first he attempts to offer the Inspector a glass port. But the Inspector rejected his offer. Arthur then tries to change the subject by saying that he plays golf. The Inspector however replied that he doesn’t play golf. Arthur tries an another attempt to impress the Inspector by showing him his record in public offices like Lord Mayor. The Inspector wasn’t interested at all.
The Inspector is no where near like Arthur, and the Inspector doesn’t share the same views with him. From this Arthur was pretty annoyed that his plans didn’t work. So he tries again. Arthur introduces Gerald Croft of Crofts Limited with pride, The Inspector however doesn’t really care who he is. Arthur later on says to Sheila that the Inspector is going to leave. The Inspector contradicts this claim - “I’m afraid not”. The Inspector then ordered Arthur to let Eric have a drink - “look at him. He needs a drink.” From this Arthur is actually obeying an intruder, he doesn’t know who he really is or what’s his purpose but he still obeys his orders which show a change in Arthur’s power and dominance in the play.
Later after the inspector had left, Arthur really doesn’t quite get the message on what the Inspector had tried to show him. Though he was a bit concern on how his public image will be affected from it, he didn’t want the story to ruin him for good. But when Gerald phoned the infirmary, they said that there is no record of a girl who died there that day. Much to the family’s delight, Arthur considered the Inspector’s visit as a farce and a joke. From this it showed how selfish and self-centred he was. And from it, doesn’t give a second thought from what the Inspector had tried to tell him.
Overall Arthur is a stereotyped businessman who doesn’t care for anyone else except for himself and his family. He only thinks within his ‘limited world’ where his business is far more important than any human, branding them as “cheap labour”. He also tries to make his family see the world he is in. Like for example, sending his wife and Sheila out of the room to be protected from hearing about prostitutes. Mr Birling is self-centred and essentially heartless. For him as long his public reputation is safe, Mr Birling will never change from the person he is.