GEOG 452: Economic Geography

Dr. Rodrigue

Lab 1: Von Thünen's Land Use Model

==========

Student name: _____________________________________

==========

LAND RENT EQUATION

L = Y(P-C) - YDT

Where:

L = LOCATION RENT
(net profits created by a farmer at some place located at distance "D" from the central market town)

Y = YIELD
(per unit of land)
P = PRICE
(per unit of output, e.g., $/ton)

C = COSTS OF PRODUCTION
(per unit of output, e.g., $/ton. Note that the farmer's own subsistence is considered part of "C.")

T = TRANSPORT COSTS
(per unit of output per unit of distance from central market town, e.g., $/ton/kilometer)

D = DISTANCE
from the central market town

==========

USEFUL VARIATIONS ON THE BASIC LOCATION RENT EQUATION

L = Y(P-C)
This gives you the Y intercept, or the point on the Y axis (vertical axis on the left of the graph) where the location rent curve crosses it. This shows you what location rent would be if a farmer were located right at the central market town.

D = (P-C)/T
This gives you the X intercept, or the point on the X axis (horizontal axis on the bottom of the graph) where the location rent curve crosses it. This shows the distance at which location rent falls to 0 because of the increasing cost of transportation with distance.

By connecting the Y intercept to the X intercept with a straight line, you can easily construct location rent curves in all situations where there is a simple, linear arithmetical increase in transport costs with distance.

==========

EXERCISES

  1. Compute the Y and X intercepts for each of the following crops: 
    
     A)   Watermelons
          Yield per hectare = 100 metric tons/year
          market Price      = $150/ton
          production Costs  = $ 50/ton
          Transport costs   = $4/ton/kilometer

          Y int = ________  

          X int = _________

     B)   Tomatoes                   C)   Corn
          Y = 100 tons/year               Y = 100 tons/year
          P = $200/ton                    P = $100/ton
          C = $125/ton                    C = $ 50/ton
          T = $1.50/ton/km                T = $0.66667/ton/km (2/3 dollar)

          Y int = ________                Y int = ________ 
                                                           
          X int = _________               X int = _________

    ==========

  2. Graph each of the resulting location rent curves below. You might want to use a different color or line pattern for each crop. Use a ruler for the sake of accuracy in interpreting and mapping.

    [ X-Y graph, distance and location rent ]

    ==========

  3. On the basis of your graph, draw a map below showing where each crop is the most profitably grown crop. On the map, let 2.5 cm (~1") stand for 25 km from the market town and place the market town in the center.

    ==========

  4. What would happen if the Transport cost for corn went up to $1/ton/km AND the market Price for watermelons went up to $170/ton BUT all values for tomatoes remained unchanged? Recalculate the Y and X intercepts for watermelons and corn. Then plot all three crops (watermelons, tomatoes, and corn) on the graph below. 

    
Watermelons:    new Y int = ________        Tomatoes:     old Y int = ________

                new X int = ________                      old X int = ________

Corn:           new Y int = ________  

                new X int = ________
    [ X-Y graph, distance and location rent ]

    ==========

  5. Draw a map of the changed agricultural landscape below, using the same scale of 2.5 cm representing 25 km.

    ==========

  6. Very briefly, describe what happened to the agricultural land use map as a result of these fairly minor changes in location terms for the two crops.
    ==========
    © Dr. Christine M. Rodrigue
    First placed on web: 02/12/99
    Last revised: 02/09/01
    ==========