Living in cities lets us reap the benefits of agglomeration: being near others in similar or complementary industries makes each of us more productive. Wages are higher in cities not because of the cost of living but rather because people are more productive there - otherwise, firms would just move out to the sticks. Higher productivity in cities is what allows the cost of living there to be higher.
In the latest AEJ: Microeconomics (ungated), Ortalo-Magne and Prat build a nice little model explaining how urban homeowners manage to appropriate the agglomeration gains. They invest in housing, then vote against any policy that would allow the supply of housing to increase, whether from suburban growth or increased density. When cities can't grow up or out, prices go up.* The better the city, the stronger the incentive for homeowners to start siphoning out the agglomeration gains via restrictive housing policy. Here's their political economy mechanism:
...we assume that (i) adding a house to a city requires a building permit, and that (ii) local residents have a say (vote) on the number of permits to be issued every period. The issue of building permits affects voters through three channels. First, new housing construction reduces their housing rents for the remainder of their lives. Second, lower future rents imply an immediate drop in the price of their housing investment. Third, voters may capture some benefits from any windfall gains deriving from the new construction permits if permits are sold to developers and the revenues are used for local services (for example).
...We find there are stationary equilibria, where a city is below its optimal size, yet the median cohort and all older agents oppose urban growth because they have made sizeable housing investments. Agents also continue to invest heavily in housing, because they expect the majority to oppose urban growth in the future. Before they made purchase decisions, all agents would have preferred a larger city, so that housing would have been cheaper and more people could have located there but the equilibrium is sustained because the median voter is someone who already owns housing.They find that subsidising housing encourages greater investment in housing and greater homeowner opposition to urban growth, making housing even more expensive. Other implications:
- Moving land use authority away from local governments and up to central government shifts the identity of the median voter and reduces the rentiers' power;
- Splitting up cities into multiple smaller competing jurisdictions can facilitate greater housing supply: basically, the permit fees paid by a developer are split across the smaller number of people in the smaller jurisdiction, but the capital losses from lower house prices are spread over the broader jurisdiction.
* I'm sure I stole this line from Ed Glaeser.