Tests and Extensions of the Mills‐muth Simulation Model of Urban Residential Land Use*

Abstract

Mills [13, pp. 96-1081 and Muth [17] have published simulation models of urban residential land use that are similar enough to warrant classifying them as one model type.' The purpose of this paper is to test that model and provide extensions to improve its ability to simulate real urban areas. In Section 1, we discuss the mathematical structure and solution technique of the model. In Section 2, we construct a composite urban area which serves as our benchmark for judging the model's accuracy. Section 3 contains a discussion of parameter values. A comparison of actual and simulated results is made in Section 4. In Section 5, we provide extensions, and in Section 6 we discuss the necessary additional parameter values. Section 7 contains a comparison of actual and simulated values for the extended model. We offer a sensitivity analysis of the extended model in Section 8. Finally, Section 9 contains a brief summary.

Energy footprint of the city: Effects of urban land use and transportation policies

“…In a closed city model, total employment is always exogenous but assumption of a constant employment density function means that the location of firms does not respond to changes in the spatial distribution of households. 9 Overall, the UEFM closely resembles in the literature, particularly those models, like McDonald (2009) and Altmann and DeSalvo (1981), where the goal is to replicate the spatial pattern of housing density in actual cities. This density replication is important for understanding the energy footprint of cities because household energy use is very sensitive to structure type, i.e, single family detached versus multifamily, etc., as discussed in the next section on calibration.…”

“…7 Altmann and DeSalvo (1981) demonstrated that models with a single income group tend to generate cities that are too small and dense. To the extent that the UEFM is used for policy evaluation, effects on different income groups could be an attractive feature.…”

“…Following Muth (1975) and Altmann and DeSalvo's (1981) approach, the distribution parameters of the housing production function are computed using equations:…”

“…Ever since their introduction by Muth (1975), numerical urban simulation models have been used to project the effects of urban land use and transportation policies on spatial patterns of housing within cities. 3 Altmann and DeSalvo (1981) demonstrated that these models could replicate the spatial form and stylized facts characteristic of housing in moderate-sized US cities. Sullivan (1985) pioneered models in which employment was moved out of the central business district.…”

Discontiguous Urban Growth and the New Urban Economics: A Review

“…In fact, what best characterises and differentiates the New Urban Economics from the 'pioneers' is simply the fact that they managed to develop methods of solving the model--which in the early 1960s was only described in abstract terms, and it is in this respect that the work of Muth (1969) can be seen as a bridge between the pioneers and the new approach: he uses a production function of the exponential type and, with respect to demand, he assumes a per-household consumption of housing inversely proportional to price, and that allows him to partially solve the model and produce profiles of density and land rents, even if the full solution for a particular size of city is not explicitly discussed. This was also the approach of an earlier paper (Mills and DeFerranti, 1971) and, still today, sensitivity analysis of numerical results makes interesting contributions (Altman and DeSalvo, 1981). , used a housing production function and a housing demand function for consumers similar to Muth's, and he also included the production of transportation services as a function of land inputs only.…”