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)

Journal Article A Note on the Optimal Rates of Resource Exhaustion Get access Martin J. Beckmann Martin J. Beckmann Brown University and Technical University, Munich Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 41, Issue 5, December 1974, Pages 121–122, https://doi.org/10.2307/2296376 Published: 01 December 1974

Journal Article Some Aspects of Returns to Scale in Business Administration Get access Martin J. Beckmann Martin J. Beckmann Brown University Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 74, Issue 3, August 1960, Pages 464–471, https://doi.org/10.2307/1883061 Published: 01 August 1960

[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.]