ECON 376 "Spatial Demand Cones" Prof. Kilkenny

The 'spatial demand cone' illustrates the how the quantity a shopping good business can sell decreases with distance from the store. It is particularly relevant to shopping goods (in which the consumer provides for the transport by coming to the firm and taking the item away themselves). Retail businesses supply shopping goods. Note that most shopping goods are shipping goods at earlier stages in the marketing chain of events from production through distribution. The gross shipping goods price is part of the cost of supply (C) of the shipping good at the retail stage.

The spatial demand cone has two bases: neoclassical demand (the higher the price, the less purchased); and that space is costly to traverse: the farther the distance the higher the cost. Since the gross price a customer pays includes travel costs, the farther the travel, the higher the price, the less purchased. (voila: spatial demand cone.)

P	Q=E/P
$6.00	1
$4.00	1½
$3.00	2
$2.00	3
$1.50	4
$1.00	6

EXAMPLE: Consider an item on which the customer is willing to spend no more than $6.00:

Expenditure = quantity times price

E = Q·P

From this we can derive a (neoclasical) demand schedule (table to the left) which shows the amount a customer would be willing to pay for each quantity; equivalently, this is the quantity a customer would buy at each price.

Note that more is demanded at lower prices as long as expenditure doesn’t change. Also note that at a sufficiently high price, ($6.01) none is demanded.

P=DP	Q	(DP-C)/t = m*
$6.00	1	45
$4.00	1½	25
$3.00	2	15
$2.00	3	5
$1.50	4	0
$1.00	6	DNA

Now let P reflect denote the full, delivered, or gross price a shopper would incur “DP”. Recall: DP = C + t·m. This is the mill or f.o.b. price “C” plus the round-trip travel costs at the rate "t" per mile "m" between the customer and the retailer.

EXAMPLE: Consider a business that can offer a product at a cost of $1.50 (so that C = $1.50), and travel that costs $0.10 per roundtrip mile (t = 0.10).

The number of miles a customer can afford to travel to obtain the good (m*) can be found as m* = (DP-C)/t. Thus, we can complete the demand schedule to reflect those distances as well (table to the right).

The amount demanded (Q) can be graphed with respect to price or distance.

Flip the graph with respect to price-- the demand curve-- on it's side, and re-label the vertical axis “distance” (or “miles”), and you have a radial cross-section of the "Spatial Demand Cone." (click on the links if the figures do not display on these pages).

IN SUMMARY: Given the expenditure level "E", the retail market price "C", and travel cost rate "t", the quantity "Q" customers would buy at each mile "m" from the store is limited: E = DP∙Q = (C + tm)∙Q If in addition we assume Q=1, we can solve for m* (the radius of a firm’s retail market area): m* = (E-C)/t (when Q=1 per customer)

This formula makes it clear that if :

(i) transport costs (t PER PERIOD) are higher, the retail market area (m*) is smaller;

and if t are lower, the retail market area is larger;

(ii) the level of expenditure (E) is lower, the retail market area (m*) is smaller;

and if expenditure per period is higher, the market is larger

(iii) the retail price (C) is higher, the retail market area (m*) is smaller;

and if the retail price is lower, the market area is larger.

All these implications of our analysis are intuitively reasonable. For an example of (i), items which one buys relatively frequently should be thought of as items for which transport costs are relatively high; e.g., food. Thus, expect the retail market areas for grocery stores to be relatively small. In contrast, (ii) infrequently purchased items that one spends a lot of money on (e.g., cars) have high expenditure thresholds (E). Thus, expect the car market area to be relatively large. For an example of (iii), K-Mart can offer items at lower retail prices (C) than the Mom & Pop store, so (for that and other reasons) K-Mart's market area will be larger.

	E	C	t	m*	Relative market size
	$ 6.00	$ 1.50	$ 0.10	45	100%
(i) double t	$ 6.00	$ 1.50	$ 0.20	22.5	50%
half t	$ 6.00	$ 1.50	$ 0.05	90	200%
(ii) half E	$ 3.00	$ 1.50	$ 0.10	15	33%
double E	$ 12.00	$ 1.50	$ 0.10	105	233%
(iii) double C	$ 6.00	$ 3.00	$ 0.10	30	67%
half C	$ 6.00	$ 0.75	$ 0.10	52.5	117%