Varying Income

• Source Code for Location Model (542 KB)
• Shapefile (18 KB)

The previous pages have assumed that agents’ income ranges between 279-628 for type resident and between 1116 and 2512 for type employer (see effects of Space & Income and comparing the Effect of Small Areas). However, income varies between industrial groups. This section will therefore explore how different income ranges affect the spatial distribution of agents within the model (see LocationModel model and the Java Doc for more details). Income is considered an important factor for the location of both residents and employers as it affects their ability to afford a specific amount of space in a given area. Table 1 shows the space and income ranges of different groups of agents used within the simulations presented in this section. As with the previous simulations, the income ranges for the employers are four times greater than that of residents while the space requirements between different groups are varied but kept the same as in the effects of Space & Income. Moreover the same area and number and types of agents were kept the same to allow for comparison between simulations. Within all simulations, small areas and neighbourhood sizes were set to 75m.

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

Table 2 presents the average configurations of agents after 100 iterations where the agents of different type have different income ranges compared to when there is the same income range (see effects of Space & Income especially Table 3). In both models, agents occupy 4 out of the 8 zones by 100 iterations. While the total areas the agents occupy in both models are similar, there are noticeable differences, specifically for industrial residents which require the least amount of space and have the lowest income range. On average, these are excluded from the most accessible area (zone 1) while there are more commerce residents in zone 3 when different income ranges are introduced as this group requires the largest space. However, they have the largest income and therefore can afford the average price for space in that area. For employers, a similar pattern can be seen with commerce employers focusing on the most central zone and excluding the service employers to zone 2. Figure 1 highlights this difference in spatial patterns by presenting typical spatial distributions when income ranges are introduced compared to when agents have the same income ranges between type (e.g. of type employer or of type resident, the outer unoccupied zones are not shown as in both cases, they were unoccupied during the simulations). Animations of these simulations can be seen below. In both instances, the employers can out bid residents for space. However, for the residential groups, the ring-like structure which is apparent when agents have the same income ranges but different space requirements become less discernible as different income ranges are introduced. For example, it is noticeable that the commerce residents do not just occupy the outer ring (zone 4) but can afford more accessible areas (zone 3). Additionally there is more mixing between commerce and service type residents.

Table 2: Average distribution of agents with different income ranges against agents with the same income ranges at 100 iterations.

Figure 1: Typical spatial distribution of agents with different and the same income ranges.

The simulation presented above has highlighted that variable income ranges affect the location of agents. However, the simulations presented above presume that the higher income groups want more space than lower income groups. The remainder of this section will present how the system changes if agents of the same type (e.g. employers or residents) have different income ranges (as the previous simulation) but have the same space requirements. For employers, this range was set between 500m and 1000m and for residents between 200m and 300m.

Table 3 presents the average results of agents occupying different zones at 100 iterations when they have the same and different space requirements and the differences between them. As with the previous simulation, by 100 iterations 4 spaces were empty. When agents have the same space ranges, specifically for residents, the pattern of residential location is reversed. This is seen in Table 3 in the difference between the spatial distribution of agents when they have the same and different space ranges. Unsurprisingly the commerce residents occupy the most central areas and the residents whose income is lower, occupy the less accessible zones when they have the same space ranges. Employers of type commerce force service employers to less central zones. Figure 2 highlights this difference between agents who have different and the same space requirements and different income ranges (animations of these can be seen below). In effect, the more wealthy agents, those of type employer and commerce residents exclude, the less wealthy agents from the centre forcing them to less accessible areas. This has important consequences when considering residential growth. If the population increases and there are no affordable areas (housing) for the residents with lesser income, these residents will be pushed further and further away from the city centre.

Table 3: Average distribution of agents with different income ranges however same the space requirements at 100 iterations.

Figure 2: Typical patterns from simulations where agents have different space requirements.

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A selection of animations of the spatial distribution of agents with different ranges :

Download zip file of images from model runs.

A selection of animations of the spatial distribution where agents have different incomes but same space requirements:

Download zip file of images from model runs.

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