GEOG 452: Economic Geography
Dr. Rodrigue
Lab 3: Brigham's Employment Accessibility Potential
Student name: _____________________________________
Student name: _____________________________________
![[ empl. accessibility potential formula ]](https://home.csulb.edu/~rodrigue/geog452/labs/brigham.jpg)
The Potential at a equals the Jobs at a,
divided by
half the Distance between a and b
(its nearest
neighbor),
plus the sum for all tracts (x) from b
through i
of the Jobs at each tract (x) divided
by
the Distance from that tract (x) to tract a.
Did you get all that?
In other words, Brigham's Employment Accessibility Potential creates an index, which can then be multiplied or divided by an appropriate factor to generate realistic estimates of property values or rents for residential property of a given type all over a given city. Brigham argues that residential value reflects the way most of us pay for our housing, i.e., through jobs. He reasons that access to jobs is a major determinant of residential property value or rent. The effect of jobs reflects the number of jobs in the immediate area and the jobs throughout the city to which one can commute, taking into account the distance of the commute.
Brigham, then, approaches the question of accessibility and location rent from an entirely different angle than did von Thünen and all his intellectual descendents. Brigham's approach could not even be attempted until the arrival of computer technology. It does provide a rigorous analysis of location rent even in the multi-nucleated and sprawling contemporary urban area, where the von Thünen-derived approaches break down. Brigham successfully performed this analysis on Los Angeles, which has been most intractable to conventional analyses of location rent.
This exercise involves an imaginary town, conveniently square in shape, containing nine Census tracts, each also conveniently square in shape. Each tract is precisely 1 km on a side. Let us give each tract a letter, from a through i. Below is a map of the town, showing the actual number of jobs in that tract. Also shown is a place to enter the employment accessibility potential, which you'll be calculating in this exercise.
_________ _________ _________
|a |b |c |
| J=10000 | J= 8000 | J= 1000 |
| P= | P= | P= |
|_________|_________|_________|
|d |e |f |
| J= 6000 | J= 50 | J= 6000 |
| P= | P= | P= |
|_________|_________|_________|
|g |h |i |
| J= 1000 | J= 3000 | J=12000 |
| P= | P= | P= |
|_________|_________|_________|
Note that the center of each tract is one kilometer from neighbors sharing a common border with it; about 1.4 km from neighbors sharing one corner from it; and 2 km from the second tract to the north, south, east, or west. For the four corner tracts, there is 2.9 km separating their centers from those of the tracts at the very opposite corners from them. For all other tracts (i.e., those one tract off in one direction and two tracts off in the other), there are 2.3 km between their centers.
To do this exercise, it is best to use a spreadsheet (e.g., Excel or Lotus 1-2-3). Create a spreadsheet, which will have two rows and nine columns. The first row will represent the actual jobs as shown on the map above, while the columns stand for the names of the tracts above. Go on ahead and enter these numbers in the appropriate cells of Row 1. In cell k1, label the row as "Number of Jobs (Jx)."
Tract letter: __________
In the second row, you'll be factoring in, not just the jobs at each tract, but the jobs in all other tracts in the town and the distance from each of those tracts. This will entail the application of the formula above, Brigham's Employment Accessibility Potential.
To calculate P, enter the following formulae into the appropriate cells of Row 2. They represent Brigham's accessibility potential for each tract. First, the hard way: You move the spreadsheet cursor to each cell and then manually type each formula into the entry box. You need to be VERY careful about typos and punctuation! Alternatively, a much easier way: You open your browser in one window and your spreadsheet in another. You can highlight each formula and then click on the "Copy" function in the browser's Edit menu (or just hit CNTL-C). Then, going to the right cell in your spreadsheet, you can activate the spreadsheet's edit menu and select "paste" (or, in Excel, CNTL-V).
Note that the formulae I'm giving below assume you're in the Excel spreadsheet, which is widely available on campus: You have to include an "=" at the beginning of any formula. If you're using Works, you'd use a "+" instead. Some other spreadsheets don't require this first character at all, as formulae are their default. When you're done entering each formula into the appropriate cell in row 2, you might want to label the row in cell k2 as "Employment Accessibility Potential (Px)."
Cell Formula A2 =(A1/.5)+B1+D1+(E1/1.4)+(C1/2)+(G1/2)+(F1/2.3)+(H1/2.3)+(I1/2.9) B2 =(B1/.5)+A1+C1+E1+(D1/1.4)+(F1/1.4)+(G1/2.3)+(I1/2.3)+(H1/2) C2 =(C1/.5)+B1+F1+(A1/2)+(I1/2)+(E1/1.4)+(D1/2.3)+(H1/2.3)+(G1/2.9) D2 =(D1/.5)+A1+E1+G1+(B1/1.4)+(H1/1.4)+(C1/2.3)+(I1/2.3)+(F1/2) E2 =(E1/.5)+B1+F1+H1+D1+(A1/1.4)+(C1/1.4)+(G1/1.4)+(I1/1.4) F2 =(F1/.5)+C1+E1+I1+(B1/1.4)+(H1/1.4)+(A1/2.3)+(G1/2.3)+(D1/2) G2 =(G1/.5)+D1+H1+(A1/2)+(I1/2)+(E1/1.4)+(B1/2.3)+(F1/2.3)+(C1/2.9) H2 =(H1/.5)+G1+E1+I1+(D1/1.4)+(F1/1.4)+(A1/2.3)+(C1/2.3)+(B1/2) I2 =(I1/.5)+H1+F1+(G1/2)+(C1/2)+(E1/1.4)+(D1/2.3)+(B1/2.3)+(A1/2.9)
Tract letter: __________
__________ yes ________ no
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I poked around on the Internet and found estimates of home values in Chico-Paradise or the North State in general. I rounded them off to create numbers you can use to run your scenarios.
To run the scenarios, you need to pick a cell on your spreadsheet, let's say a6 and use it to calculate the mean Px by entering =average(a2:i2).
To do the home value scenario, let's use an estimated median home value of $150,000 for a three bedroom, two bath house in Chico. Put that number in cell a8. Now, in cell a9, divide the average Px by the median home price (=a8/a6): This is your multiplier. Now, in cell a10, enter this formula: =a2*$a$9 (the $ means the cell is an absolute reference not a relative reference for other formulas copied from this cell). Copy this formula from a10 to b10 to i10 by left-clicking your mouse button when you see the cursor change from a fat white cross to a skinny black one. Voilà: a range of pretty realistic home values in this rustic market.
To do the rental scenario, let's do one bedroom apartment monthly rental. The estimated median fair market value for a 1 bdrm apt is about $425. Enter that in cell a13. Now divide Px by this number by entering the formula =a13/a6 in cell a14. Just as in the last scenario, put =a2*$a$14 in cell a15 and copy it from b15 through i15. Instant rent variations.
Please attach your spreadsheet to your lab when you turn it in.
For the totally bored or totally "techie": You could try to make this model somewhat more realistic by adding more cells to the imaginary town (say, a 5 x 5 grid?), modifying the equations in row 2 of your spreadsheet and adding formulae. The more tracts in the city, the less overwhelming will the edge effects be (the corner tracts, with their paucity of neighbors, are fully 44 percent of the available tracts).
Alternatively, you could experiment with different values in Row 1 of your spreadsheet (whether the original 3 x 3 or a 5 x 5 grid) to see what happens to your model.
Now, imagine doing this for a city as large as Los Angeles, with thousands of tracts, and all of odd shapes. Trying to figure out the centroids for each of these and measuring the distances from each centroid to ALL of the others and then contemplating the math is enough to make you ... nervous. This was done in the 1960s with the mainframe computers of the day. It could be done more easily today with GIS technology, given GIS capacities to compute centroids and determine distances. Even so, it turned out that P correlated closely with actual real estate "comps" and rents.