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The model simulates the change in urban land use as it results from the real estate market dynamics. The model combines a land rent model a la von Thunen, with a segregation dynamics (Schelling model). Four agents classes are included in the model: retailers, firms, rich, and poor households. A budget to be utilized for bidding for a place where to stay, is assigned to each class. The model dynamics happens on a flat surface divided in square cells. Distances are calculated as crow flies. Each class of agent has an utility function in which the distance from the center of the surface, and the proximity to similar agents play the crucial role. The importance of each component of the utility depends on a parameter, whose change determines a variation in the urban land use pattern. In essence the dynamics run as follows. The agent with the lowest utility is a candidate to the relocation. This agent calculates its utility in the cells having a land rent affordable for him, then he/she relocates in the cells with the highest utility. The land rent of a cells is roughly calculated on the base of the budget of the occupier agent. In case the chosen cell is already occupied, the previous occupier is compelled to relocate with the same method. This method roughly simulates a free real estate market, in which each land use is assigned, in the long period, to the best utilization under the established income distribution. Of course this does not means that the total utility is maximized, but simply that a Pareto equilibrium is reached in which a marginal change from the equilibrium state is profitable for anyone.


To each agent a budget is assigned to be utilized for paying the housing rent and transportation costs. This budget is assigned as follows: retailers: 1000 units, firms: 100 , rich households 800, and poor households: 200. The number of agents is also established. At the beginning agents are distributed at random. Later each agent calculates its utility. The utility function is of the Cobb-Douglas type and is established as follows:

Utility= {[1/(1+distance-from-city-center)]^(1-alpha)}*[(similar-neighbors)^alpha]

where alpha is a parameters that depend on the agent class and is established by the user trough the interface: alpha-retailer, alpha-firm etc. Similar neighbors is the number of similar agents located in the eight cells neighborhood of each agent. In words, the utility of an agent increases with the decreasing of the distance from the city center and with the increasing of the number of similar agents located nearby. On course the utility depends on alpha parameter: when, alpha=1 the agents become indifferent to the distance factor, in turn, when alpha=0 the agent become tolerant and does not care which kind of agents are nearby.

Once the utility is calculated, one agent for each step is chosen for relocation. It is in fact the agent with the minimum utility (utilities are standardized in order to make possible the comparison) which try to find a better location. To do so the agent lists the suitable cells where to relocate. These are cell with an affordable rent, i.e. with a rent lower than the highest bid of the agent. This highest bid is calculated as follows:

bid=budget – distance-from-city-center

This is the classic function of the bid rent theory (Ricardo, von Thunen, Alonso) in which the transportation cost is established equal 1.

Among all the suitable cells the agent chooses that with the highest utility.

The chosen cell can be occupied by an other agent or vacant. In the first case the agent is evicted and will look for a new location in the next step of the simulation.

The land rent is calculated as follows. At the beginning each land plot has a rent equal to 50. It is the basic land rent for, say, the agricultural utilization. Later to each occupied cell a rent is assigned which is equal to the bid of the agent which lives in it, or equal to the minimum bid of the nearby agent, in case nearby agents exist. If any agent is nearby, the land rent is that established by default (50).


First click on setup. The agents will be locate dat random. Later click on go and observe how the city structure is slowly organized, depending on the chosen values of the eight parameters. Two graphes allows to better understand the macro characteristics. These are: the rent structure, i.e. the relation: rent=f(distance-from-city-center) and the average agents density, always as a function of the distance from the city center. The essence of the play consists in observing the variation of the land use structure in dependence of the variation of the parameters. In some case even changing the parameters, the spatial pattern is not changed. This is due to the characteristics of the Pareto equilibrium state: the marginal change is not able to obtain an increase in the utility function. To overcame this problem one can try to increase the temperature of the system, increasing the value if the random factor in the calculation of the utility. In this case may happen (but not necessarily) that the agents will be differently organized.


Start for instance with a value of alpha=1 only for rich-households. You will observe the rich households which segregate in the suburb. The rent structure reflects this pattern with a moderate increase of the land rent far from the city center. Later you decrease the value of alpha parameter, and you will observe a gentrification process: rich households will reach the city center and poor household are pushed in the suburb. A similar process can be observed giving a similar initial values to the alpha parameter related to the poor households, which will be segregated in the suburb.
If you wish to observe a pure segregative dynamics, put all the values of alpha parameters equal 1. The agents will be segregated: each class will try to form an only patch. Later if you increase slowly the alpha parameters, and you will observe the usual urban cluster, around the city center which will be formed.


The model represent the essential features of the real estate market. Several extension could be envisaged. The most crucial is the possibility that the same patch is shared by two or more agents, so that the land rent will increase (as in the real world) because the two or more agents will add their bid in order to become successful in the real estate market, at the expenses of a decrease of the utilized space per capita. This strategy is usually utilized by poor household for make affardable the living nearby the city center, decreasing the floor space per capita or the quality of the dwelling


Comments are welcome, as well as suggestions to improve the model. Please send you comments and suggestions to: semboloniATunifi.it

Copyright 2011 Ferdinando Semboloni. All rights reserved.