I Part: Closed Book (5 Minutes, select one):

Define and explain the role and significance of the following theoretical tools:

1. the "spatial iso-outlay 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 2-6 presents the iso-outlay lines associated with locations I and J for a given total outlay and prices. The iso-outlay 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 iso-outlay 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

2. 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 4-3 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 non-spatial 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.

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Please hand in your Part I before starting with Part II!

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II Part: Open Notebook (15 minutes, select one)

3. 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 school-age 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 two-wage earner families and shared and flexible household responsibilities.

4. Your evolving ROOTS project: Please identify and discuss the link(s) between your (class-related) 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 (non-empirical) nature of this project (by having read the ROOTS guidelines), that you were aware that different theoretical approaches were appropriate for different real-world 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.