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## Thünen - Exercise (Geog 207)

This is a numerical exercise based on the example of the land-use handout and summarized in this table:

• Here is an online version of the handout!
• in color
• Rent Functions and Variables (Table)

General form of the rent function: R = E (p-a) - Efk

where:

• R = Rent (per unit of land)
• p = Price our farmer receives per unit of her products at the market
• a = (average) production costs per unit of product
• f = freight rate (per mile, per unit of product)
• E = Yield (per unit of land)
• Ep = Total revenues at the market (per unit of land)
• Efk = Total transport costs (per unit of land)
• Ea = Total production costs (per unit of land)
• k = Distance in miles from central market

Type of Land Use Rent Function Rent at Market R=E(p-a) Transport Costs per mile (=Ef) Distance from Market to No-Rent Margin k=(p-a)/f Range of Highest - Rent Land Use in miles from Market
1 R=10-2.5k 10.0 2.5O 4 0.0 - 1.7
2 R=7-.7k 7.00 0.70 10 1.7 - 5.0
3 R=4.5-.18k 4.50 0.18 25 5.0 - 19.0
4 R=2-.05m 2.00 0.05 40 19.0 - 40.0

Explanation of Exercise:

(1) The data given to you in the table refer to aggregate values for

1. E(p-a)
2. Ef
3. (p-a)/f
Expand the example by giving specific values to E, p, a, and f for all four land uses, initially without changing the aggregate values. Interpret your new specific values for the different crops. What kind of distance related regularities do you detect? Are these regularities inevitable or could you (at least in part) eliminate them by changing your values (without, however, changing the aggregate values provided in the table)?

(2) Introduce (at least) one moderate change in one of the variables (change of one variable at a time), such as a change in p or f sufficiently large to change the aggregate values of the original example, and, as a result, of the size of the zones. Interpret the sensitivity of land use patterns (size of zones) to such a change. (You might find it useful to remember the area of a circle...)

Further Explanation:
There are two parts to the question: for the first, you use the given aggregate values of the table and disaggregate them into p, a, E etc. so that you make the individual values consistent with all the aggregate values. Ultimately, it is a matter of trial and error. I prefer it that way, so that you actually try it out and get a feel for the importance of different variables.
In the second question, you are asked to make a change in one of the variables and observe the effects of such a change.

Thünen Resources and other Graphs