How does Priestley explore social class in 'An Inspector Calls'?

It is important, when answering a question such as this, to always keep in mind that every aspect of the play - language, characters, structure, and stage directions/settings - are all decisions on the playwright (in this case J.B. Priestley)'s behalf to convey wider ideas and/or messages to the audience. In 'An Inspector Calls', these ideas are socialism and class consciousness, so you would do well to become familiar and confident in these ideas to recognise what aspects of the play Priestley uses to explore them, as well as the context of the time at which the play was written and how this relates to when it is set.Priestley utilises dramatic irony throughout the play, primarily as a way of juxtaposing the Birlings' (as a representation of the middle and upper classes) perceived self-righteousness with their actual ignorance that the audience is privy to throughout, and that the characters of Sheila and Eric become aware of in the play's final act. This is a technique of criticising the class system, taking narrative power away from characters afforded social power by their class and using it to give voice to the powerless lower classes, represented by the character of Eva. In this way, Priestley presents social class, not as something inevitable and deserved, but an obsolete system that has very little meaning beyond acting as a tool with which to oppress the proletariat.