Question 1 (similar to Exercise 1.1 from textbook)
A manufacturer produces some output called “Product” using a raw material called
“Input”. To production of 1 ton of Product requires 3/5 ton of Input. The manufacturer
has a contract to deliver 50 tons of Product to Store M (Store M is the “market” for
Product). Input is available in Spot N (Spot N is the source of Input, equivalent to “mine”
in the textbook). Store M is 40 miles away from the Spot N. The shipping cost of both
Product and Input are $2 per ton per mile. We will help the manufacturer to find the total
transport-cost minimizing factory location. To arrive at the answer, go through the
following steps in parts (a), (b) and (c).
(a) First consider two potential locations for the factory: Spot N and Store M.
Calculate shipping costs by filling in the cells of the table below. Show your
calculations.
(b) Draw a graph to illustrate your calculations. On the x-axis represent potential
Factory Locations with Spot N on the left corner and Store M on the right corner.
The y-axis represents shipping costs. Clearly label the axis, all three shipping cost
lines and significant points on the graph.
(c) What is the total transport-cost minimizing location for the manufacturer? Does this
location make intuitive economic sense? Explain in 1-2 sentences.
Location of Factory Spot N Store M
Input Shipping Cost
Product Shipping Cost
Total Shipping Cost
Department of Economics 1 of 5 UC Irvine
Econ 144A: Urban Economics I Nilopa Shah
However, our manufacturer faces an additional issue. Store M and Spot N are in
different countries, making the manufacturer subject to tariffs based on trade
agreements between the two countries. The Border is 15 miles from Spot N. The width
of the Border is negligible, placing Store M at 25 miles from the Border. The trade
agreements are such that Product can be moved between the countries freely but
transporting Input across the border involves a payment of $60 per ton in tariffs. Given
this additional information, let us help the manufacturer re-calculate his shipping costs.
We will go through similar steps as earlier, now following parts (d), (e) and (f).
(d) Now, consider four potential locations for the factory: Spot N, Spot N-side of Border
(let’s label this location as N-side of Border), Store M-side of Border (label this
location as M-side of Border) and Store M. Calculate shipping costs by filling in the
cells of the table below. Show your calculations.
(e) Again, present a graphical illustration of your calculations. In addition to the
previous locations on the x-axis, now mark out N-side of Border and M-side of
Border. The y-axis represents shipping costs. Clearly label the axis, all three
shipping cost lines and significant points on the graph.
(f) In this case, what is the total transport-cost minimizing location for the
manufacturer? How do you make intuitive economic sense of this result? Explain in
1-2 sentences.
Location of Factory Spot N N-side of
Border
M-side of
Border Store M
Input Shipping Cost
Product Shipping Cost
Total Shipping Cost
Department of Economics 2 of 5 UC Irvine
Econ 144A: Urban Economics I Nilopa Shah
Question 2 (similar to Exercise 1.2 from textbook)
The residents of cities A, B, C, D and E consume wi-fi routers, with consumption in each
city is 150 routers (see the map below). The firm that produces routers must decide how
to set-up production. It could set up five factories, dispersed across each city, with each
factory producing 150 routers and supplying to its own local city market. In this case, the
firm incurs no cost for shipping output. Alternatively, the firm could locate its factory at
centrally located city C, and supply routers to the entire region. The single factory in city
C must then produce 750 routers, 600 of which are shipped to the cities A, B, D and E
for a shipping cost of $6 per router.
(a) Suppose the average cost of producing a router is AC (Q) = 1500/Q, where Q is the
number of routers produced in a factory. Calculate AC with Q = 150 and Q = 750,
respectively. Note and explain how this production process exhibit economies of
scale.
(b) Based on the AC function from part (a), find the optimal arrangement of production
for the firm (one central factory or five dispersed factories). The optimal
arrangement minimizes total cost for the firm, where total cost is the sum of
production cost and shipping cost. Clearly write down all your calculations.
(c) Now suppose the average cost of producing a router is AC = 14000/(Q+1250). Now,
repeat the calculation of AC with Q = 150 and Q = 750.
(d) Based on the AC function from part (c), now repeat your calculations to find the
cost-minimizing arrangement of production in the case.
(e) Explain intuitively the difference is results between responses to part (b) and (d).
(f) Suppose now production costs are those given in part (a) but let shipping cost per
router be given by t (in the preceding discussion, we had t = 6, now we assume we
don’t know the cost of shipping). What value of t would make the two arrangements
for production (centralized versus separate factories) equivalent in terms of cost?
i.e. what value of t would make the firm indifferent between a centralized versus a
dispersed set-up?
Sample Solution