Where do cities develop?
(c) Allen C. Goodman, 2006
Procurement Cost and Distribution Cost
Firms procure inputs, and distribute outputs.
How do they decide where to do it?
• Let’s do some assumptions:
– 1. Single output, shipped from the factory to a
marketplace at location M.
– 2. Single “shipped” input. Must be gathered
from location F.
– 3. Fixed factor proportions. Meaning?
– 4. Fixed input and output prices. Meaning?
(c) Allen C. Goodman, 2006
Monetary weight
• Multiply weight of the input by cost of
shipping it per ton-mile.
• Example
– 5 tons of wood
– costs $1 to ship one mile.
– Weight = 5 tons * ($1 / ton-mile) = $5/mile.
(c) Allen C. Goodman, 2006
Figure 3.1 -- Transport Costs
50
40
$
30
20
10
2
4
6
Distance from Forest
8
10
EXCEL Spreadsheet
Input (wood)
Output (bats)
Weight
5
3
Transport rate
1
1
Monetary Weight
5
3
(c) Allen C. Goodman, 2006
Total Transport Costs - Excel file
Total Transport Costs
60
Dollars
50
40
PC
30
DC
20
TC
10
0
0
5
10
Miles from forest
(c) Allen C. Goodman, 2006
Terminal Costs
• Terminal Costs -- Fixed costs of loading and
unloading the goods and the cost of
shipment paperwork.
• Line-haul Economies -- Shipping cost/mile
may decrease as distance shipped increases.
• What happens?
(c) Allen C. Goodman, 2006
Summary (Excel File)
• No Terminal Costs.
– As we move from the Forest toward the Mkt,
along a straight line,
• Procurement Costs Rise
• Distribution Costs Fall
• Where you locate depends on the relative
magnitudes.
(c) Allen C. Goodman, 2006
Summary
• With Terminal Costs
– You can locate at point 0 (Forest) or point 10
(Market) or anywhere in between.
– Anywhere in between, you incur procurement
costs, distribution costs AND the costs of
procuring through the Forest Terminal, and
distributing through the Market Terminal.
– If you locate AT THE FOREST, you don’t have
to procure through the Forest Terminal, so you
save those costs ($5 in the example).
Summary
– If you locate AT THE Market, you don’t have
to procure through the Market Terminal, so you
save those costs ($10 in the example).
• KEY POINT
– Locating at either the procurement or the
distribution node saves you the terminal costs at
that node.
(c) Allen C. Goodman, 2006
Median Location - Ann’s Pizza
• Ubiquitous inputs.
• Consumers are evenly distributed along
highway.
• Delivery Costs (zero at the restaurant).
Fifty cents/mile away.
(c) Allen C. Goodman, 2006
Median Location
Figure 3-4 Pizza Delivery and Median Location
W
X
Y
S
Distance from W 0
1
2
3
4
5
6
# of Cons.
2
8
1
0
0
0
7
0
Z
9
8
0
0
10
Weight
1.0 4.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 5.0
Cost/mile 0.5
Total Costs
if at point
Minimum
50.0 41.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5
41.0
(c) Allen C. Goodman, 2006
WHY?
Sawmill at the Port
Input Source A
Output
mkt M
If you locate at port …
Port P
Cost = 15*DA + 15* DB + 10 * DM
Monetary wt A = 15/mile
Monetary wt B = 15/mile
Monetary wt M = 10/mile (c) Allen C. Goodman, 2006
Input Source B
What happens
To total costs?
Sawmill at the Port
If you locate here …
Output
mkt M
Input Source A
Port P
DA  and DB 
by same amount
But DM 
Monetary wt A = 15
Input Source B
Monetary wt B = 15
Monetary wt M = 10
(c) Allen C. Goodman, 2006