Thünen - Exercise

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!

LYNX Version of this Table

Type of Land Use Rent Function Rent at Market R=Y(p-c) Transport Costs per mile (=Yf) Distance from Market to No-Rent Margin m=(p-c)/f Range of Highest - Rent Land Use in miles from Market
1 R=10-2.5m 10.0 2.50 4 0.0 - 1.7
2 R=7-.7m 7.00 0.70 10 1.7 - 5.0
3 R=4.5-.18m 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. Y(p-c)
  2. Yf
  3. (p-c)/f
Expand the example by giving specific values to Y, p, c, 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)?

Optional: ("We decided" in class to change the "optional" to "non-optional")
(2) Introduce some moderate changes in the variables (change of one variable at a time, including changes in p and 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 changes. (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, c, Y 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 feeling for the importance of different variables.
In the second question, you are asked to make some changes in the variables and observe the effects of these changes.

Type               Rent      Transport    Distance        Land Use Zones
 of     Rent        at       Costs per   from Market     Range of Land Use
Land  Function    Market       mile     to R=0 margin    with Highest Rent
 Use             R=Y(p-c)       =Yf       fm = p-c	    R1 = R2 etc.
  1   R=10-2.5m   10.00	       2.50        4 miles        0.0 - 1.7 miles
  2   R= 7 -.7m    7.00	        .70       10		  1.7  -  5.0
  3   R=4.5-.18m   4.50         .18	  25              5.0  - 19.0
  4   R= 2-.05m    2.00         .05       40              19.0 - 40.0

Other Thünen Graphs:

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2001 []