Perhaps, this question is wrong in that it separates the automobile as a symbol of American culture and the automobile as a symbol of American industry. American industry is as much a symbol of American culture as the automobile is. The culture of the tinkerer is what comes up with the innovations in much the way Steve Jobs and Steve Wozniack fiddling in the garage eventually established the PC industry. Harry Ford, a garage-type hobbyist eventually brought the automobile to the masses.
The automobile industry and American culture can be looked at as one in the same because the industry provided the jobs. In American culture, people tend to define themselves through their jobs. That’s how we gain our influence not through inherited titles. It’s not nobility or a monarchy. Employees aren’t subjugated to the heirs of a company and are free to work where they please. We aren’t forced into the trade our fathers were in.
The newly emerging auto industry greatly aided in maintaining this almost uniquely American system. However, as with any new technology or industry, you end up with a lot of startup companies which will eventually go bust or be acquired.
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It’s not an easy business to be successful in. The two thousand automobile startups of the early nineteenth century were like the dot com startups of the1990s. The dot coms and the automobile manufactures were the new technologies of the time. People flocked to them in the hopes of making riches.
Most of the automobile companies failed. As Warren Buffet once said, “There were two thousand auto companies… But of the two thousand companies, as of a few years ago, only three car companies survived… Now, sometimes it's much easier to figure out the losers. There was, I think, one obvious decision back then. And of course, the thing you should have been doing was shorting horses. ” 
The auto industry went through that right around the time of the Great Depression. As bad as the Great Depression was for many Americans, most of the world’s population was still worse off.
It’s been said that John Steinbeck’s book, Grapes of Wraths, was considered by many to show the failure of American capitalism. However, when the movie adaptation was brought to the Soviet Union as propaganda to demonstrate this, there was a backlash when Russian citizens saw supposed poor Americans owning the ultimate luxury: the automobile. They viewed it as the Americans complaining their castles were not large enough. This backlash eventually caused Joseph Stalin to ban the film.
It’s so ingrained in the culture even as a poor person, you can still own cars.
Another innovation in the auto industry was to allow customers to pay for their purchases in monthly installments, thus merging the auto industry and the banking industry. Once again the comparison can be made between the Great Depression and the recent economic downturn. The automobile companies and brokerage houses allowed people to borrow indefinitely and people would mistake their borrowing power for their earning power. People’s borrowing power far surpassed their earning power and that was a major contribution to the Great Depression and that’s also what happened with the economic downturn of not too long ago.
In true American fashion, the criminal element was just as quick to embrace the new auto industry, even setting up their own industry of stealing, stripping, exporting, modifying and selling the stolen vehicles.
This in turn required new laws and police tactics. And, even required law enforcement to embrace the idea of more technologically advanced automobiles.
“Unlike other stolen goods, the automobile enabled its own escape.” 
|During WWII, auto makers switched to making military vehicles.|
“For obvious reason, American citizens chafed against rules implemented by their local boards.” 
The automobile has probably had a bigger impact on American culture and industry than any other invention. The automobile took people off of their islands which were their own towns. It has allowed the freedom of travel and erased state lines. It has allowed city folk to enjoy a day in the country while also allowing a farmer to venture into the city.
“Since the colonial era, Americans have been on the move, seeking new opportunities or simply to reinvent themselves.” 
1. History 306: Week 4 Assignment, Karin Enloe
2. Alice Schroeder, The Snowball: Warren Buffett and the Business of Life, (Bantam Books), 18
3. John Heitmann, The Automobile and American Life (Jefferson: McFarland, 2009), 47
4. John Heitmann, The Automobile and American Life (Jefferson: McFarland, 2009), 126
5. John Heitmann, The Automobile and American Life (Jefferson: McFarland, 2009), 34