Crate&Barrel - Shippensburg University - Website

An economic side of transport geography ¨C using map algebra (revisited)

and spatial thinking to derive real price surfaces (new)

Long-term studies of consumer behavior tell us that ¡°the quantity of goods any individual is prepared to buy

depends on the real price that has to be paid for those goods¡±.1 A real price is composed of 3 parts:

1.

the sticker price for the item at the point of sale;

2. applicable sales taxes in the home state; AND

3. any cost incurred to transport the item from the point of sale back home (or the cost to have the

item handled and shipped to your door).2

For example, the real price of a new pair of winter boots includes the sticker price marked on the boots AND

any applicable sales taxes AND the cost you incur while driving to and from the store (e.g., gasoline and auto

insurance, vehicle registration, annual inspection fee, speeding tickets, maintenance costs, etc.). When items

are purchased online, the transport costs that are incurred by the retailer are passed on to the customer as

shipping and handling fees.

This lab provides you with a case study that¡¯s useful for examining how a real price varies over space,

and an opportunity to see how both state borders and regional cost-of-living differences perturb an economic

landscape. Location and proximity matter.

The case study

Crate&Barrel is a firm that sells home furnishings. Crate&Barrel compliments their brick-n-mortar activities

(usually situated in wealthy suburban shopping centers) with online sales. Over the last decade, C&B has

developed a national network of warehouses and distribution centers. They have also been tinkering with

their handling and shipping fees. For this lab you¡¯re going to: a) choose a sofa from the C&B¡¯s online catalog;

b) calculate and visualize the spatial distribution of real sofa prices; and c) map and describe the range 3 of that

sofa. Yes, this lab was inspired by a C&B catalog, but it is in no way an endorsement of Crate&Barrel, its

subsidiaries, or any of its products.

A note about handling and shipping fees

Retailers use handling and shipping fees to offset the money they spend to handle and transport their

products to customers. For example, let¡¯s say C&B spends $59 to handle each sofa (i.e., their pro-rated cost of

warehouse labor, electricity, water, building insurance, packaging materials, etc.). This $59 fixed terminal cost

at the warehouse can be passed on to each customer as a handling fee.

We have to also recognize that C&B spends $1.10/mile (roundtrip cost = $1.10/mile * 2 miles = $2.20) to

move a sofa from its warehouse to a customer¡¯s home (i.e., the pro-rated costs of truck labor, diesel fuel,

vehicle insurance, truck maintenance, etc.). This variable cost can also be passed on to the customer via a

shipping fee. So, the total cost of delivery = the variable shipping fee + the fixed handling; hence the phrase

¡°shipping and handling¡±.

1

Dicken P and Lloyd PE (1990) Location in space: Theoretical perspectives in Economic Geography. Harper & Row

Publishers, New York City.

2

Everyone has heard the real estate mantra ¡°location, location, location¡±, but few people can articulate why location is

such an important business decision. Economic geographers study how accessibility and ease of transport influence

location decisions and customer purchasing behaviors. Yet, because transportation costs are often externalized, they are

sometimes ignored by economists and consumers alike.

3

The range of a good (the range of a sofa) signifies the maximum distance that will be endured by customers in order to

purchase the good at a given price. The maximum price a customer can pay is limited by his or her budget.

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An economic side of transport geography ¨C using map algebra (revisited)

and spatial thinking to derive real price surfaces (new)

RQ1.

How does the real price of a C&B sofa vary spatially across the lower 48 states?

RQ2.

Which customer locations are (not) within the range of the sofa given a particular budget?

To answer the two research questions, you need to assemble several pieces of information:

1. Which sofa will be purchased from C&B (the good)?

2. What is the sticker price of the sofa? (modeled as a constant field)

3. What is the sofa budget at each customer location? (modeled as a constant field)

4. Where are C&B shipping points located (shipping origins)? (modeled as point features)

5. Where are customers located (shipping destinations)? (assume everywhere)

6. What is the distance between each customer location and the nearest shipping point? (modeled as a

continuous field)

7. What is the total delivery fee (the sum of the fixed handling fee and the variable shipping fee) to be

paid at each customer location? (modeled as a continuous field)

8. What is the sales tax to be paid at each customer location? (modeled as a discrete field)

9. What is the real price of the sofa? (modeled as a continuous field)

Simplifying assumptions

Some of the objectives above are easy to model and others are not, so it makes sense to start with some

simplifying assumptions just to get the ball rolling. Then, once you get a good feel for how your workflow is

progressing, you can start to relax your simplifying assumptions and introduce any needed complexity to your

workflow. Let¡¯s start with this set of simplifying assumptions:

1st.

2nd.

3rd.

The study area will include all locations within the continental US (¡®CONUS¡¯).

A customer exists at every location in the study area and is in the market to buy a sofa. Why is this a

simplifying assumption? Because there are many places in the Empty Interior, the Great Plains, and

the ByPassed East, and Appalachia where few or no people live.

All customers earn the same income and have the same budget for a sofa. Why is this a simplifying

assumption? Because cost-of-living differences and land rents vary with location.

Task 1: Prepare a workspace

Prepare a new folder to work in, then extract the file geodatabase and Excel ? workbook that I provided.

Task 2: Pick a sofa and generate a household budget (online)

Visit the C&B website (see URL below) and browse their selection of sofas (no, you do not need to sign up for

an account or actually buy a sofa). Choose the sofa style you like most (or dislike the least) and download a

picture of it; record its name and the advertised sticker price.

Next, use the automatic budget generator I gave you (the Excel ? workbook). Let the dollar value you

get be the maximum dollar value that any customer is willing to spend to buy your sofa. From this point

forward, your analysis will focus on your chosen sofa, your assumed budget, and finding just how far your

budget will stretch.



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An economic side of transport geography ¨C using map algebra (revisited)

and spatial thinking to derive real price surfaces (new)

Task 3: Gather sales tax rate data

We know the sticker price of your sofa does not change with location ¨C it¡¯s the same everywhere.

Sales tax rates do change, however, for they vary by state. I¡¯ve already assembled a polygon feature class that

contains state-level sales tax rate data (see the data I gave you). You¡¯re welcome.

Task 4. Selecting an appropriate map projection and coordinate system.

Your analysis depends on your ability to calculate distances between shipping origins (O) and

customer destinations (D). Unfortunately, there is no map projection that lets you preserve geodetic

distances between every O-D pair, so we¡¯ll have to use a map projection that compromises a little by

minimizing the total amount of distance distortion created across the country. For this kind of analysis, I

suggest using the USA Contiguous Equidistant Conic planar coordinate system.

Task 5: Creating geospatial data

C&B shipping points are not retail stores; rather, they are warehouses and distribution centers that

hold ready-to-ship furniture items. Figure 1 is a copy of the shipping points map posted on the C&B website.

Feel free to use Google Earth, the Geographic Names Information System (see URL below), or another

authoritative source to gather location data for each populated place mapped in Figure 1.



Organize your shipping point coordinate data in x,y,z format (either Excel¡¯s XLSX or the delimited TXT

formats will work) so you can create point features from your XY table. Pay attention to your input coordinate

system while creating those point features! And don¡¯t forget to project your data.

Figure 0. Crate&Barrel shipping point locations (vintage 2018). Click map to visit the original.

Task 6: Rasterize your concept of space

Now that you¡¯ve assembled the data you need, you can begin to analyze. Start by opening a new map

document and creating layers out of your stateMetro, studyArea, and shippingPoint features.

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An economic side of transport geography ¨C using map algebra (revisited)

and spatial thinking to derive real price surfaces (new)

Although your initial datasets are in vector format, the raster approach is better suited for this type of

analysis because we¡¯re interested in how a real price varies continuously over space. So, make sure the

Spatial Analyst extension is checked on.

1.

Use ArcMap¡¯s Catalog window to make the file geodatabase that I provided you as the default

geodatabase.

Your Environment Settings allows you to control every tool in the toolbox and to create gridded surfaces

consistently with the same spatial extent and same raster analysis cell size. Specifying an analysis mask lets

you concentrate on cells that fall inside the study area. See Figure 1.

Figure 1. Three common environment settings during raster geoprocessing: Spatial Extent, Raster Cell Size and

Analysis Mask.

2. Use ArcMap¡¯s ArcToolbox window to access the parent ArcToolbox, right-click it, and set the following

Environments¡­ settings:

a. Processing extent: Study area

b. Raster analysis > Mask: Study area

c. Raster analysis > Cell size: 2000 meters.

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An economic side of transport geography ¨C using map algebra (revisited)

and spatial thinking to derive real price surfaces (new)

INPUTS

(Bolstad, 2016: p443-446 and p449-459)

Use the spatial model in Figure 2 and the Map algebra > Raster Calculator to establish your budget,

sticker price, and sales tax rate surfaces. Also, I strongly encourage you to consult the Help menu whenever

you are not sure about a tool, a parameter, a command, or syntax.

SOFA

BUDGET

SOFA

PRICE

STATES48

OUTPUT

GEOPROCESSING

RASTER CALCULATOR

outRaster = sofaBUDGET

RASTER CALCULATOR

outRaster = sofaPRICE

POLYGON TO RASTER

by tax rates

sofaBUDGET

stickerPRICE

taxRATE

Figure 2. Rasterizing your constants and sales tax rates.

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