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In Singapore, a certificate to own a car now costs $106,000
(www.reuters.com)
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Your math is off somewhere. Wikipedia claims that NYC has 302 square miles of land, while Singapore has 283.
This article estimates that the cost of owning a car in NYC is $3000-$5000 per month. So, you pay for the privilege, perhaps not as much up front.
But NYC is surrounded by places you can drive to. Singapore is not. The mainland city of Johor Bahru is a relatively poor city of only 500K people, and beyond that it's farmland until you get to the Malaysian captial, more than 4 hours away. So I wouldn't expect the two cities to have the same preferences for car ownership in any case.