The Effects of Space and Income

• Source Code for Location Model Same Income (542 KB)
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This model will explore how agents’ income and space requirements affect the spatial distribution of agents throughout the system. Within this model (see LocationModelSameIncome model for further details), agents only desire space and within each type of agent (be it resident or employer), all agents will have the same income range. For residents, this range is between 279 and 628 (see setRandomIncome Method in Resident Class) and for employers, between 1116 and 2512 (four times greater see setRandomIncome Method in Employer Class). The effect that these different income ranges have on groups will be explored further in Varying Income. Clearly employers can out bid residents for land Additionally each agent was given a space requirement between a minimum and maximum value as highlighted in Table 1 where the values for space between types and within groups were chosen to overlap to encourage competition for space (see setOriginalMinSpaceWanted method in Employer and Resident classes).

Table 1: Space requirements within the model for different types of agents.

As with Alonso’s (1964) model, a monocentric city is used, whereby accessibility decreases from the centre as seen within London for example. 1389 residents (478 of group commerce, 201 (35%) of industry (14%), and 710 (51%) of service) and 105 employers (46 (44%) of group commerce, 13 (12%) of industry, and 46 (44%) of service) distributed over 6 areas. Figure 1 highlights the attributes of the area and the typical initial placement of agents within the areas. This composition and mix of types and groups of agents roughly reflects the broad industrial make up of the London workforce.

As with Alonso’s model, a monocentric city is used where accessibility decreases from the centre as seen within London, for example. 1389 residents (478 (35%) of group commerce, 201 (14%) of industry, and 710 (51%) of service) and 105 employers (46 (44%) of group commerce, 13 (12%) of industry, and 46 (44%) of service) are distributed over 6 areas. Figure 1 highlights the attributes of the area and the typical initial placement of agents within the areas. This composition and mix of types and groups of agents roughly reflects the broad industrial make up of the London workforce.

Figure 1: Attributes of initial starting conditions and an example of the typical distribution of agents.

Several simulations were run to explore the spatial distribution of the agents over time as they competed for space. All the simulations had the same parameters and both the small areas (see getLocalNeighbourhoodAttributes in LocationModel class) and agents neighbourhoods were set to 75m (see for example summaryOfNeibourhingAgentsWealth method in Employer class). Table 2 presents the aggregate results from the simulations pertaining to the number of empty zones and the number of agents searching at the end of different time periods. Agents are searching if they cannot afford the desired piece of land which is defined as: minimum space wanted multiplied by the average cost per metre square for their local neighbourhood (calculated in evaluateAndSetHappiness methods which is called in post-Step). By 100 time steps within all models, the number of zones unoccupied by the agents remains constant at 4 while the spatial distribution of agents also remains fairly constant. For example, Table 3 compares the number of agents in different zones at 100 and 200 iterations of the model. Animations pertaining to these can be seen below. However, the number of agents actually searching varies. In none of the simulations did all the residential agents become totally satisfied with their current location (click here to see animations that where trace the model for 550 iterations). This can be explained as a result of agents moving, and trying to locate in the most accessible places. This movement of new agents to a new area is similar to the segregation model and it causes the price to slightly rise in the area. Thus some agents can no longer afford to live in that area and are therefore classed as still searching. This is supported by the number of employers which is nearly always 0 after 100 iterations. Employers can always out bid residents for land and are therefore more likely to be satisfied with their area.

Table 2: Average results regarding the number of empty zones, and the number of both residents and employers searching during the course of the simulation.

Table 3: The distribution of agents in different zones at time intervals 100 and 200.

It was noted above that by 100 iterations/time steps, the spatial distribution of agents within the zones remains roughly constant. There will be a more detailed analysis of this in the following section where we will highlight a characteristic spatial distribution of agents when the model has been run for 100 iterations. Figure 2 highlights that over time, agents move from their initial random location to a more central location as they search for a location that best suits their preference for space which is restricted by income. By time step 30, the majority of agents have moved to the inner 4 rings. The 5 agents occupying the outer rings are classed as old (i.e. 66+) and due to their low probability of moving have not yet moved. However, over time, these agents move as can be seen at time step 50 and from then on, the spatial distribution remains fairly stable (as demonstrated in the animations below). All the agents have moved to the more accessible areas as they can afford the space they want in these areas 1. After time step 100, the distribution of agents is locked into a similar pattern as highlighted above.

Figure 2: A typical evolution of the model at different time intervals as the agents search for their optimal location.

Using the same model results from Figure 2, a closer inspection of the model at time 100 highlights how the agents have distributed themselves based on space and income constraints. It must be noted that by iteration 100, all the resident agents had aged and entered the ‘older’ category for space requirements as no agents were added or removed from the system (to see how residents are made older and given a new space requirement see the step method of the Resident class). Figure 3 maps distance from the centre in relation to the minimum space wanted by each agent. Employers of type service and commerce have lower space requirements than those of type industry and can therefore afford locating nearer to the centre where accessibility is highest. For residents, industrial and service residents want less space than commerce residents and therefore can afford a more central location. Figure 4 supports this by plotting income against distance for different groups of agents. It is noticeable that due to space requirements, agents who desire less space can afford to live in more central locations. Therefore if the space requirements were set higher for industrial residents, they would be excluded from the central area.

Figure 3: Comparison of minimum space wanted and distance from the centre for agents at 100 iterations.

Figure 4: Comparison of income and distance from centre for agents at 100 iterations.

Figure 5 highlights the distribution of residents and employers at time interval 100 in terms of the average underlying cost per m2 for a piece of land in the area 2. As one would expect, land value decreases with distance from the centre. However, as the areas become smaller, greater variation within the zones can be seen (Figure 6). This variation can be explained by the use of small areas which will be explored in greater detail in Comparing the Effect of Small Areas.

Figure 5: Distribution of agents and the resulting land values (cost per m2) at time interval 100 using the original zoning system.

Figure 6: Distribution of agents and the resulting land values (cost per m2) at time interval 100 using 20m Buffers with original zones overlaid on top.

A selection animations up to 200 iterations: note how the distribution of agents changes little between 100 and 200 iterations.

Download zip file of images from model runs.

A selection animations up to 550 iterations: note how the distribution of agents changes little between 100 and 550 iterations.

Download zip file of images from model runs.

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References

Alonso, W. (1964), Location and Land Use: Toward a General Theory of Land Rent, Harvard University Press, Cambridge, MA.

Footnotes:

1 The same colour scheme for agents will be used throughout this chapter to represent agents of different types. The light coloured dots represent residents and the darker coloured dots represent employers. Blue are of type commerce, green are of type service and red are of type industry.

2 Calculated by taking the sum of the all the agents income in the area and then dividing it by the area in meters.

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