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.
   
   

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 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 = ________
   
   

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

   

   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
   Last revised: 02/12/99