Car prices haven't gone up, the average purchase prices of cars has gone up but that's because people are buying more expensive cars, Large trucks, SUVs, luxury sedans, higher trims etc.

If you look at lower end sedans there price hasn't changed much and has even gone down. For example if you look at the Chevy Malibu the current base price is $25,100 , in 2014 the base price was $22,340 or $29,400 adjusted for inflation, in 2004 it was $18,700 or $31,067

Auto workers wages have gone down but they've steadied in recent years in 2004 hourly wage was $21.71 or $36.07 adjusted for inflation, in 2014 it was $21.38 or $28.17 adjusted for inflation now they are around $30.

So since 2004 the price for a car has gone down 24% and auto wages have also gone down 20%. The recent UAW contract wage increases with little to no increase in price shows there is some room for workers to get more out of that $25,000 cost pie, but there would be no room if that pie is shrunk to $10,000 to compete with Chinese manufacturers.