Here in the US, applying the same minimum wage in both Missoula and San Jose is obviously crazy, but that's what we do, and over the years they've had the side effect of gradually pricing younger teens out of the job market.
Actually, minimum wages do vary state by state, with a federal minimum to rule them all. California's wage is higher than Montana's, so I assume that's because the costs of living are different.
As far as teens being priced out of the job market, I believe there are more adults than teens working for minimum wage. Are these adults also being priced out of their markets by rising wages?