How does Priestley explore the importance of social class in An Inspector Calls?

Priestly explores the importance of social class in this play by showing how the wealthy Birling family is shielded from the consequences of their actions towards the lower classes. The lower classes are represented by a young woman who is harmed in turned by all of the Birlings, as well as by Sheila Birling's fiancé, Gerald Croft, without any of them being fully aware of what they have done to her. Their wealth and privilege shields them from their wrong-doing and allows them to think they are good and moral people when, in fact, they are moral hypocrites.
They are exposed when an Inspector Goole (Ghoul) arrives at their home to question them about a young woman who has committed suicide. It comes out that in various ways, all the family members contributed to the desperation that caused her to kill herself. Arthur Birling, for example, fired her from her job in his factory because she asked for a raise. He was indifferent to her needs and only concerned to protect himself from paying his employees higher wages. After the young woman, who went sometimes by the name Eva Smith and sometimes by Daisy Renton, got on her feet again and found another job as a shop clerk, Sheila thoughtlessly had her fired for what she thought was rudeness. Sheila gave no consideration to how devastating losing the job might be to the young woman. Both Gerald and Eric took sexual advantage of this lower-class woman's vulnerability and need as a desperate unemployed person, and when she bore Eric's child, Mrs. Birling turned down her request for charity, saying the father should be publicly shamed and named and forced to support the child. Of course, she was willing to do that to someone else, but when she found out it was her own son who would have been shamed, it was another story.
Priestly illustrates how the selfish, cold-hearted, and often petty self-interest of the upper classes can have a cruel and devastating effect on lower class people struggling to survive. The play demands that the privileged to be less oblivious to how their actions hurt people with far fewer resources.

Priestley's main thesis in An Inspector Calls is that the British upper classes have abandoned their responsibility towards society in the headlong pursuit of wealth and pleasure. This selfish attitude is illustrated by the appalling way that the members of the Birling family treat Eva Smith. To them, Eva's little more than an object, someone to be used and abused as and when it suits them. They are so obsessed by wealth and social status that they never stop to think for a moment that Eva, though much lower down in the social pecking order, is still a human being in the fullest sense.
This is the lesson that Inspector Goole hopes to teach them when he turns up on the Birlings' doorstep that fateful evening. He wants this rich, privileged family to understand that they have obligations towards those much less fortunate than themselves. Whether the Birlings are capable of learning that lesson—and by extension, the British upper classes they represent—is a different matter entirely.