By Morris A. Davis, Jonas D. M. Fisher and Toni M. Whited
http://d.repec.org/n?u=RePEc:fip:fedhwp:wp-2010-02&r=dge
The authors construct a dynamic general equilibrium model of cities and use it to estimate the effect of local agglomeration on per capita consumption growth. Agglomeration affects growth through the density of economic activity: higher production per unit of land raises local productivity. Firms take productivity as given; produce using a technology that has constant returns in developed land, capital, and labor; and accumulate land and capital. If land prices are rising, as they are empirically, firms economize on land. This behavior increases density and contributes to growth. They use a panel of U.S. cities and our model’s predicted relationship among wages, output prices, housing rents, and labor quality to estimate the net effect of agglomeration on local wages. The impact of agglomeration on the level of wages is estimated to be 2 percent. Combined with their model and observed increases in land prices, this estimate implies that agglomeration raises per capita consumption growth by 10 percent.
This paper fits in a new line of research that tries to understand cities and agglomeration effects using dynamic general equilibrium models. The basis here is the good old Lucas-Prescott island model, the model is used to study the impact of agglomeration on prices (land, labor, goods). Would this explain why Tokyo and New York City are so expensive?
NEP-DGE Blog 
It looks like macroeconomists are venturing into urban economics and try to reinvent the wheel. It would be better to have urban economists learn some proper dynamic modeling.
Hi Christian, I appreciate the blog entry!
I’d like to add one thought, but related to a different paper.
Francois Ortalo-Magne and I have a paper forthcoming in RED that does two things: (a) argues that expenditures shares on housing are constant across time and place and then (b) solves for allocations and prices in a a simple static urban model with free mobility of the population.
I mention this for this reason: understanding why house prices are high in high-wage cities is (a) easy and (b) has nothing to directly do with supply constraints.
Suppose people have utility from two goods, a tradeable and non-tradeable good (such as housing). If wages are high in an MSA, then consumption of a tradable good will also be high in that MSA. This must mean that, in an equilibrium where the population is mobile, consumption of a non-tradeable good must be low. This is a requirement of equilibrium such that people are indifferent as to where they live.
If the tradeable and non tradeable goods are complements in utility, then the price of the non-tradeable will be high in the high-wage MSA.
What about supply constraints? When households have Cobb-Douglas utility, supply constraints determine the level of house prices everywhere, but do not determine the relative price of housing anywhere.
If we build more houses in San Francisco, people move from Pittsburgh to San Francisco. Price levels in both places fall. The price of housing in San Francisco relative to Pittsburgh remains high.
Morris