Mr Birling is presented as a successful businessman, who has been active in local politics and was Lord Mayor of Brumley (although it may become clear that he does not care about the local community). Mr Birling is also wife of Sybil Birling and the father of Sheila and Eric. From the first set of stage directions we know that the family is comfortable in their wealth and also found out that Arthur Birling's wife is his social superior, implying that he began in a lower class and worked his way up to the upper class he is in now. Arthur Birling likes to inform others of his wealth and of the important people he knows, which may be understandable considering how hard he has worked to be where he is, and would like to bask in the glory.
From the very first stage directions we see, at the start of the play we found out that Priestly described Arthur Birling as a, "heavy-looking, rather portentous man". From these stage directions it reveals that Mr Birling is quite large in size which may help to give him a threatening appearance. However, this appearance does not seem to intimidate the inspector, because during some parts of act one the inspector has the higher status and controls the scene; this shows that his appearance is quite ironic.
We all know that Arthur Birling is the father to Sheila and he in act one he is hosting an engagement party for his daughter and her fiance, Gerald Croft. Gerald makes a few speeches throughout act one, during one of them he says, "Gerald...your engagement with Sheila means a tremendous lot to me...Crofts and Birling are no longer competing but are working together - for lower costs and higher prices." This suggests that maybe Mr Birling cares more about his business than he does about his daughters future. Priestly is therefore presenting his character as rather pompous and very self centered, something you wouldn't normally expect to find in a father