What has the industrial revolution got to do with Austen's purpose in Pride and Prejudice, and how does the influence of the Industrial Revolution affect the novel?
This is a very good question. While the effects of the Industrial Revolution are more apparent in Persuasion and Sense and Sensibility, and even Emma and Mansfield Park, the subplot premise in Pride and Prejudice is predicated upon the effects of the Industrial Revolution.
While men in the professions--law, medicine, clergy--and men with purchased commissioned positions in the military had always been able to attain high standing in England (some more, some less so), trades people were traditionally more limited and in the fourth tier of the social class divisions (where Mr. Collins was classified). Nonetheless, the Industrial Revolution made it possible for trades people to become "merchants and manufactures on a large scale" and to accumulate great wealth and rise from the fourth tier through the third and to the second tier of the upper classes, where Darcy and Mr. Bennet were both classified.
Mr. Bingley's father was one of these who, through the power of the Industrial Revolution to create new wealth, rose from the fourth class to the same rank as Darcy and Bennet, having wealth rivaling Darcy's and exceeding Bennet's squandered wealth.
They were of a respectable family in the north of England; a circumstance more deeply impressed on their memories than that their brother's fortune and their own had been acquired by trade.
While the Bingley's are the most prominent instance of a family risen to social class and power by industry in Pride and Prejudice, there are other instances as well. Mrs. Bennet, nee Gardiner, and her brother and sister, Mr. Gardiner and Mrs. Phillips, were the children of a Meryton attorney. Mrs. Bennet had the benefit of marrying above her class when she married Mr. Bennet, a country gentleman with an independent fortune in the second tier of the upper class. While this isn't an instance of industry creating a new middle class, it is an instance of one individual rising in social class because of the acquisition of wealth, though the acquisition came through marriage.
Sir William Lucas is another example of the same kind as that for Mr. Bingley. Sir Lucas had been in trade in Meryton where "he had made a tolerable fortune." On the strength of this success, he was elected mayor of Meryton and had the good fortune to make a favorable speech to the king while holding the mayoral office. As a reward, he was elevated to the level of knight, a station of the second class with "baronets, knights, country gentlemen, others of large wealth." This is a significant rise, founded on the Industrial Revolution, from tradesman to fortune to mayor to knight.
Sir William Lucas had been formerly in trade in Meryton, where he had made a tolerable fortune, and risen to the honour of knighthood by an address to the king during his mayoralty.