Lecture 1: Equilibrium over Space: The Canonical Urban Models

Edward Glaeser (Harvard University and NBER)

11 June 2020

2020 Lectures on Urban Economics

Equilibrium over Space:The Canonical Urban Models

Edward GlaeserHarvard University and NBER

What is Urban Economics?

• The study of the location of economic activity over space.• This is properly economic geographic, but it is subsumed in urban. • Urban is more fully focused on why things locate in particular cities. • Since proximity reduces transportation costs (for goods, people and ideas),

transportation economics is a closely related field• How does location impact economic activity?• The economics of agglomeration is one subfield. • Human capital externalities; spillovers and neighborhood effects

• What determines the price that people are willing to pay for particular places?• This is why real estate economics is also a close cousin of urban.

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Per Capita Income, 2000Population Change, 2000-2010

Source: U.S. Census

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Change in FHFA, 1996-2012by Quintile of Population Density, 2010

Predicted Telecommuting by Dingel and Neiman and Actual Telecommuting in the Alignable Survey

The Two Models: Within and Across Cities

• The Alonso-Muth-Mills model (hereafter AMM) was produced in 1962. It characterizes a spatial equilibrium within cities. • It holds wages constant and focuses on commuting costs. • It is explicitly spatial in the sense that all locations are indexed by their

proximity to a downtown where everyone works. • The Rosen-Roback model first emerged in 1979. It characterizes a

spatial equilibrium across cities • It treats wages as endogenous, but does not really explain why productivity

might differ across space. • Models of agglomeration economies start with Krugman (1992) will come in a

later lecture. • It is a far less explicitly spatial model– locations are just different spots.

Components of Housing Rent(Graphs are from Denise DiPasquale)

Housing Rent Gradient in a Growing City

Extensions to Transportation Technologies

• You can allow multiple types of linear transportation technologies, but for a fixed cost, you lower the variable cost. • For example, walking has the highest variable cost and no fixed cost,

buses have a lower variable cost and a higher fixed cost, and cars have the lowest variable cost and the highest fixed cost. • Or you can allow an intensive investment– total cost is k+t(k)d. This

will generate a first order condition of 1+t’(k)d=0 so that the investment rises with distance to the central business district.• Either of these changes the shape of the equilibrium bid rent curve

and the shape of the density gradient.

Pascal’s Wager

Brookline: A Streetcar Suburb (S. B. Warner)

Elevated Railroads (NYC)

Multiple Income Groups

• Allowing multiple income groups. With one technology, this means that greater demand for space by the rich battles against a higher willingness to pay to save time. • Becker originally claimed that the tendency of the rich to sort into the

suburbs (in the US but not in Europe) reflects higher demand for land, but this requires an income elasticity of land demand (not housing demand which is slightly different) higher than the elasticity of travel costs with respect to income which seems unlikely to hold. • The alternative explanation is the with multiple technologies, the rich

sort into driving zones, the poor walk and take public transportation. • See LeRoy and Sonstelie or my paper with Kahn and Rappaport.

An Empirical Puzzle: Manhattan House

Manhattan House Today

Rosen/Roback Spatial Equilibrium

• People choose metropolitan areas and each one delivers a bundle of wages, amenities and prices. • A simple linear model would be that for identical people Wages plus

Amenities minus Prices is constant across the U.S. • This means that amenities can be measured as Prices – Wages. • If amenities attract people, then this measure should predict future

urban growth. • If happiness tells us something about amenities, then happiness

measures should work as well.

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