LINEARIZED, OPTIMALLY CONFIGURED URBAN SYSTEM MODELS: A DYNAMIC MILLS HERITAGE MODEL WITH REPLACEABLE CAPITAL (INFRASTRUCTURE, TRANSPORTATION, SIMULATION)

A member of the class of general-equilibrium, linear programming land use models initially formulated by Edwin Mills is extended to account for land use changes over time. Interperiod constraints governing the structure of land use change are defined based on an assumption of replaceable, nondeteriorating capital investments. These constraints are the foundation of a multiperiod linear programming model that identifies both noncontiguous land use configurations (sprawl) and mixed exports as optimal land use and production strategies under reasonably general conditions of economic change. In a dynamic context, sprawl arises when land is reclaimed from unprofitable uses, and when vacant land is held in reserve to accommodate future opportunities.; Three different versions of the model are specified and their outputs examined. These include: (a) a static, spatially disaggregate formulation incorporating hexagonal land use zones; (b) a static, spatially aggregate formulation incorporating land use rings; and (c) a dynamic, spatially aggregate formulation. Perfect market conditions are assumed, and production technologies are of the fixed-coefficient type with constant returns to scale. The mathematical representation of production activities is extended to include an increased number of discretized substitutions between various production inputs, thereby increasing the number of alternative, fixed-coefficient technologies associated with each production activity.; The literature's existing, cost-minimizing formulations are converted to profit-maximizing analogs that are driven by exogenous export prices rather than by minimum export requirements, an approach that precludes no-feasible-solution (NFS) outcomes. It is demonstrated that, in a static context, the absence of minimum export constraints results in profit-maximizing optimums corresponding to the exclusive export of the most profitable good. In addition, the model's outputs are shown to be arbitrarily dependent on zone geometry assumptions if export prices are high. Import flows are treated explicitly for the first time in a model of this class, and their inclusion is shown to have a significant impact on optimal land use configurations.