I Part: Closed Book (5 Minutes, select one):
Define and explain the role and significance
of the following theoretical tools:
 the "spatial isooutlay line" (including: how does it assist in
finding optimal solutions?)
 Glossary
 Hoover,
Ch.2.6 [2.6 LOCATION AND THE THEORY OF PRODUCTION]
Locations I and J have different sets of delivered prices, and therefore
the possible combinations of inputs x1 and x2that any given outlay TO can
buy will vary according to location. Figure 26 presents the
isooutlay lines associated with locations I and J for a given total
outlay and prices.
The isooutlay line associated with location I is represented by
AA', and that associated with location J is represented by BB'. The
shorter distance
involved in transporting input 1 to I rather than to J implies that
the price ratio (p'2/p'1) will be greater at location I. Since this price
ratio
determines the slope of the isooutlay line (see equation (3) and
footnote 13), we find that the slope of AA' is greater than that of BB'.
Also, it is
important to recognize that the slope of any ray from the origin,
such as OR, defines a particular input ratio (x1/x2). Movement out along
such a ray implies that more of each input is being used and that the rate
of output must be increasing.
OR
 the "spatial demand curve" (including: Why is the spatial demand
curve convex to the origin?)
 Glossary

Hoover, Ch.4.2.2
It is now possible to define the firm be established. A lower f.o.b.
price implies a larger quantity demanded, for two reasons. First, because
the nonspatial, individual demand curves
are negatively inclined; when consumers are faced with lower prices
they buy more. Second, the lower the f.o.b. price the larger the market
radius, and hence the market area. Thus the number of buyers within
the market area of the firm also depends on the f.o.b. price established.
The spatial demand curve relates f.o.b. price to the quantity
demanded over the entire market area, accounting for these two effects.
Such a
spatial demand curve is shown in Figure 43 and is labeled Ds.
Note that the spatial demand curve is convex to the origin. Its
shape stems directly from the two effects mentioned above. Because the
nonspatial demand curve is negatively inclined, we expect that
higher (lower) prices will decrease (increase) the quantity demanded in a
spatial
context as well. However, because the market area, and therefore the
number of customers, changes with each change in f.o.b. price, we should
not expect the relationship between price and quantity demanded to
be linear, even when there is a linear nonspatial demand curve and when
the transfer cost gradient is linear.3 Recognizing the usual
tendency of transfer costs and rates to increase less than proportionally
with distance,
we find still further basis for the usual convexity of the spatial
demand curve.
Please hand in your Part I before starting with Part II!
II Part: Open Notebook (15 minutes, select one)
 Assume that you would want to apply the Weber
model to finding solutions to residential location problems. Also assume
that the three corner locations represent the job/employment locations of
the household's two breadwinners plus the location of the only large
shopping center. Assuming that you have specified the parameters
(structure, variables + constants) for the Weber model, how would you now
proceed to introducing "substitution" into your model?
Applying the Weber model with fixed "weights" would mean that the
aggregate weighted distances (distances may be differently onerous for the
two spouses depending e.g. on who has to be home for the schoolage kids
coming home from school) are
minimized with given frequencies of commuting/shopping (which are thus
independent of the eventual location). If we allow for substitution, then
aggregate distances and weights are not given. In this case we could
consider that the spouses might adjust their commuting & shopping
frequencies and
their time of commuting (during rush hour or not) at the same time as they
select their location something which appears to be increasingly
common at a time of twowage earner families and shared and flexible
household responsibilities.
 Your evolving ROOTS
project: Please identify
and discuss the link(s) between your (classrelated) interests and the
theoretical ideas which you plan to trace through the literature from one
major theoretical breakthrough to another.
You were asked to provide evidence that you had thought through such
links, that you had understood the objectives and theoretical
(nonempirical) nature of
this project (by having read the ROOTS guidelines), that you were aware
that different theoretical approaches were appropriate for different
realworld interests and that you will have to "trace" an individual
theoretical idea over time (i.e. NOT assemble a large number of different
theoretical ideas).
As always: If you feel that you have "blown" one or more of your answers,
do NOT hesitate to submit a "redo" by Thursday.
"Redos" can also be submitted later. In fact, all
answers I could not grade because I could not understand your answer,
there was not enough there to grade, or you misunderstood the question,
should be rewritten, because you want to provide as much evidence as
possible that you have understood the basic concepts of this class.