starting point was similar to Dunn's, though he gave more attention to market clearing by actors bidding for space. The question of exactly how rents tied to transportation was sharpened by those who took advantage of the duality properties of linear programming. First, there was a spatial price equilibrium perspective, as in Henderson (1957, 1958) Next, Stevens (1961) merged rent and transportation concepts in a simple, interesting paper. In addition, Stevens showed some optimality characteristics and discussed decentralized decision-making. This simple paper is worth studying for its own sake and because the model in the P-J study took the analysis into the urban area, a considerable step. Stevens 1961 paper used the linear programming version of the transportation, assignment, translocation of masses problem of Koopmans, Hitchcock, and Kantorovich. His analysis provided an explicit link between transportation and location rent. It was quite transparent, and it can be extended simply. In response to the initiation of the P-J study, Herbert and Stevens (1960) developed the core model of the P-J Study. Note that this paper was published before the 1961 paper. Even so, the 1961 paper came first in Stevens’ thinking. The Herbert–Stevens model was housing centered, and the overall study had the view that the purpose of transportation investments and related policy choices was to make Philadelphia a good place to live. Similar to the 1961 Stevens paper, the model assumed that individual choices would lead to overall optimization. The P-J region was divided into u small areas recognizing n household groups and m residential bundles. Each residential bundle was defined on the house of apartment, the amenity level in the neighborhood (parks, schools, etc.), and the trip set associated with the site. There is an objective function: wherein xihk is the number of households in group i selecting residential bundle h in area k. The items in brackets are bih (the budget allocated by i to bundle h) and cihk, the purchase cost of h in area k. In short, the sum of the differences between what households are willing to pay and what they have to pay is maximized; a surplus is maximized. The equation says nothing about who gets the surplus: it is divided between households and those who supply housing in some unknown way. There is a constraint equation for each area limiting the land use for housing to the land supply available. where: sih =