That's a policy choice in a few cities[1], not an unalterable natural law. It's also confounded by how you do the comparison. If you're asking how much it costs to buy a 4,000 square foot single family dwelling, yes, cities are far more expensive but it's not that simple because, for example, suburbanites are far more likely to need cars ($11k/year average according to AAA) and people who live in cities don't need as much space because e.g. rather than having to pay for a lawn their kids play in the local park.
It's also again important to consider how much of this is policy. For example, Tokyo is far more affordable that many American urban areas because they didn't have policies preventing density and the city wasn't gutted to provide highways for suburbanites who only contribute minimally to the economy and culture. In the U.S. the history of racism behind the rise of suburbs makes that really complicated because the neighborhoods most likely to be bulldozed or cut off for highway projects / parking lots were the poor neighborhoods, reducing the supply available for low-income residents.
It's also again important to consider how much of this is policy. For example, Tokyo is far more affordable that many American urban areas because they didn't have policies preventing density and the city wasn't gutted to provide highways for suburbanites who only contribute minimally to the economy and culture. In the U.S. the history of racism behind the rise of suburbs makes that really complicated because the neighborhoods most likely to be bulldozed or cut off for highway projects / parking lots were the poor neighborhoods, reducing the supply available for low-income residents.
1. And, for example, the median income in NYC is $43k so there are definitely reasons to question stereotypes: https://www.census.gov/quickfacts/fact/table/newyorkcitynewy...