Urban Economics PSet 1 - Von-Thünen Model I

Urban Economics
Problem Set #1
Due, Fri, Sep 30, 10pm , ONLY ONLINE!
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(1) Von-Thünen Model I
Barely can only be sold at a central market place M. All producers that do not
produce it at M need to haul it there in order to sell it and will incur
transportation cost. People are willing to pay $201.50 per ton of barely; its
marginal production cost equals $20 per ton. Freight cost per ton and mile is
given by T=1.5x2, where x denotes the distance from M in miles.
(a) Calculate the maximum distance to the east of M at which the good will be
produced.
(b) Do the transportation cost exhibit increasing, decreasing or constant
economies to distance?

(2) Von-Thünen Model II
Suppose a certain good (e.g., wheat) can only be sold at a central market place M.
All producers that do not produce it at M need to haul it there in order to sell it
and will incur transportation cost. Consider only
People are willing to pay $20 for the product; freight cost is $3.50 per piece and
mile. The total production cost is given by the function C=10+0.1q
(a) Calculate the maximum production distance from M
(b) Referring to the one-directional (just to the east) Von-Thünen Model,
calculate the overall production cost, the overall transportation cost and the
overall land rent paid.
(3) Locations of Transfer-Oriented Firms
Assume the distance between the resource (R ) and the market (M) is 10 miles. A
firm’s procurement cost is given by PC=4x, where x is the distance from the
resource measured in miles. The firm’s distribution cost is given by DC=2(10-x)2.
Again, x is the distance from the resource.
(a) What is the Total Freight Cost at x=10, x=5, x=0. Where should the firm
locate?
(b) How does your answer to all parts under (a) change if the marginal
procurement cost decrease from 4 to 1?

(4) Suppose customers are distributed on a one-directional path (e.g., to the east) as
follows.
Location
Distance from A
Number of customers

A
0
3

B
1
2

C
8
1

D
2
2

E
6
1

F
18
2

A company has to deliver a unit of its good to each customer and incurs a cost of
$1 per unit and mile. Each unit needs to delivered separately.
(a) Where is the median customer located?
(b) Where is the delivery cost minimizing location and what is its delivery cost?

(5) Suppose a transport cost oriented firm consumes two inputs (one from
source A, the other from source B) in order to produce one output, which is
consumed at the output market.
a) Based on the numbers provided in the graph below, where will the
company locate?

b) Now assume the monetary weight of input source B increases to $44 (all
else stays the same), where will the company locate now?
c) If the all monetary weights (output as well as inputs) were equal to $10,
where will the firm locate? Explain.
d) Is it possible that the firm’s transfer-cost-minimizing location can be
anywhere? If yes, under what circumstances? If no, why not?