As for how much you pay for a click on any specific keyword, it isn't fixed and depends on two main things. I am simplifying here.
1. How related (google thinks) your page and ad copy is to the intent behind the keyword. More related = (generally) lower cpc
2. The reserve price that google sets for that keyword.
It used to be a second price auction in that you'd only ever pay 1p above the second highest bidder. It has now changed in that there is a reserve price for each keyword based on your page, ad copy and google's valuation of that keyword. This reserve price can be lowered or raised depending on how good and related Google thinks your page and ads are. It can fluctuate lots depending on your input but if google's valuation is high you'll never get it to pennies per click.
Insurance for injury claims for example will always be more than £10 per click no matter how good your page or ad copy is. Google just knows that those conversions are worth tons so people WILL pay high cpcs for them.
So in the Ford Chevy example, Ford's page is much more related to someone searching for Ford, Google knows the intent is likely to find a ford page so ford would pay FAR less than Chevy.
Chevy's page likely isn't matching the intent that google assumes the user has so their reserve price and hence final cost per click would be much higher.
Competitor bidding on google search is expensive.
Brand protection - bidding on your own brand terms - is (in my 7 years experience doing this) always incredibly cheap, 1 or 2 pence per click.
