Three equations:
1. If Sn < F/tx: when Sm = 0 then West can be a hinterland (and East is a core).
2. If Sn > 1-F/tx when Sm = 1 then East can be a hinterland (and West is a core).
3. If F/tx < Sn < 1-F/tx
when Sm = Sn, the East and West can each manufacture for their own market.
The larger F/tx, the more likely the nation is to have a core hinterland pattern.
If F/tx > .5, then regional manufacturing for regional markets is never a possibility. The nation must always have a core hinterland pattern.
Larger economies of scale and lower transportation costs raise the value of F/tx. But note that an increase in the value of x, the number of units marketed, reduces the value of F/tx.
The point of this highly simplified and unrealistic model is that even if regions were identical and even if resource endowments were irrelevant to the location of firms, a core hinterland pattern would emerge whenever F/tx is large enough. One region doesn’t have to be ‘better’ than another in any sense to become the core; it just has to get an initial edge in the size of its market. Once it has that edge, the smaller region cannot compete for ‘footloose’ manufacturing, that is manufacturing which is not tied to a location by factors such as natural resources (forestry, fishing, mining) or by the impossibility of shipping its output (haircuts).
The model also shows that the preferred pattern of distribution may change suddenly as key values hit ‘switch’ points. So F/tx may be slowly and steadily rising from a value less than Sn. Firms are more profitable if they locate near their market and avoid shipping output, even if the market is smaller than in a neighbouring region. But as soon as F/tx crosses a threshold that makes it larger than Sn, firms in the bigger region will be able to drive firms in the smaller region out of business, since their costs to ship ‘extra’ output into the small region will be less than the costs of maintaining the fixed plant in the smaller region. As firms close down in the smaller region and expand in the bigger region, workers must move between the two. The difference in size between the two increases and makes it ever more advantageous for firms to locate in the ever bigger region. In the real world the change won’t be instantaneous, because different industries will hit the switch point at different times, and because the opportunity cost of sunk capital is near zero, so established firms may continue to produced in the small region until their capital wears out. However, very large changes may occur over a short period of time, such as the dramatic reduction in manufacturing in the Maritimes in the 1920s. The sudden change is confusing to observers, because the process, rising F/tx, has been going on at the same rate for a long time, but all of a sudden firms react dramatically to a tiny change.
In the 19th and 20th centuries, F rose while t fell, encouraging concentration of manufacturing. Since the later 20th century, the growth in average plant size has slowed or stopped entirely. The size of the market, x, has been growing throughout these centuries, offsetting to some extent the tendency of F/t to rise. The general tendency of manufacturing to concentrate one central location in North America was likely a result of rising F and falling t. The ability of some regions to capture some manufacturing, for example automobile assembly in California, may be the result of tendency of F to cease rising while x has kept growing.
The emergence of some industries with zero transportation costs, call centres for example, provides an interesting new wrinkle to all of this. If transportation costs are zero, F/tx is undefined. In practical terms, firms can locate anywhere without worrying about the cost of reaching their market. There may be more and more industries with positive, but very low, t costs. Being near the bigger market only matters if saving on transportation costs is an issue. Once t costs become very low, other factors ignored in this model, such as the cost of labour, may become more important. Therefore Nike locates in third world countries.
While transportation costs become less important in today’s world other locational factors remain important. The film industry was able to concentrate in Hollywood, far from the major markets in the eastern U.S. because the cost of transporting films was trivial. However, the various forms of urban scale economies often remain quite important. In most industries, workers prefer to live within a reasonable commuting distance from work. Many, although not all, of the interactions between firm depend on frequent and easy personal contact between people, not just the low cost of shipping goods between firms. Falling transportation costs may allow auto part firms to locate far from auto assembly plants, but firms in computer technology may want to have informal lunches with the people in other computer technology firms.
The Krugman model becomes less relevant, but it still serves a purpose. It demonstrates that the forces that resulted in the distribution of manufacturing encountered in the past are changing as t costs change. The direction in which they are changing is hard to predict. Remember, when firms are free to locate anywhere because transportation costs are trivial, they may be free to go where urban scale economies are greatest, not where the cost of labour is lower because housing costs are lower.