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A Continuous Model of Transportation

Econometrica 1952 20(4), 643
Abstract : Interlocal commodity flows are considered in terms of vector fields. Efficient transportation then gives rise to a problem in the calculus of variations; the flow functions solving this problem contain price distribution functions as parameters. With net production functions dependent on prices, the model describes the flow and prices in a competitive regional market economy. (Author)

Design Parameters in Housing Construction and the Market for Urban Housing

Econometrica 1980 48(1), 201
[The "new urban economics" is rather explicit with respect to demand for housing but the supply of housing is usually treated in a very cursory fashion. Housing is normally regarded as a one-dimensional good and equilibrium in a city is mostly concerned with the land market rather than the housing market. This paper introduces, on the supply side, the concept of design parameters of a building and, on the demand side, the concept of housing attributes, i.e. multi-dimensional housing. By means of structural analysis an engineering cost function is obtained in terms of design parameters. Due to housing attributes, the demand for housing and the supply of housing, the latter being based on the engineering cost function, should be derived simultaneously. Equilibrium is defined on the housing market rather than on the land market. It is shown how in equilibrium housing rent, land rent design parameters on buildings, and population density all depend on distance from the center of the city and on parameters of the problem: income, city population, diameter of the city, and technical coefficients.]