Which Assumptions are for Convenience?

Solving a general equilibrium model is normally a difficult task. Usually, one has to simultaneously solve all the good- markets and factor-markets clearing

conditions together with the free entry conditions. Many of the assumptions in the CP model simplify this task by making the model ‘block recursive’ in the sense that certain endogenous variables can be determined from a subset of the equilibrium conditions. With this in mind, we start by pointing out the truly important

assumptions.

The assumption of increasing returns that are internal to industrial firms is absolutely essential. After all, if there is no loss to splitting up production there is

a setting akin to Matsuyama (1991) and Krugman (1991c), he shows that the equilibrium indeterminacy brought about by the possibility that expectations might prevail above history disappears. Common knowledge and rational expectations together give rise to the possibility that expectations might prevail over history in the first place, so it is not surprising that altering the information structure alters the equilibrium set considerably. We conjecture that the same holds true in the present CP model with forward -looking expectations. As Karp (2000) points out, the restoration of the determinacy implies that ‘the unique competitive equilibrium can be influenced by government policy, just as in the standard models.’

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really no location choice to be made.³³ Once we have scale economies, however, marginal cost pricing is out, so we must deal with imperfect competition. Dixit-Stiglitz monopolistic competition is assumed since this is by far the easiest form of imperfect competition to work with in a general equilibrium model, but other forms are also possible (see, for example, Chapter 5). Likewise the locational choice is only interesting when trade in the increasing-return sector is subject to some sort of cost.

The assumption that workers share the same preferences makes it easy to characterise the point of catastrophic agglomeration. It is worth pointing out, however, that different assumptions concerning migration behaviour and/or the existence of some congestion in the core region can yield a smooth transition. For example, if workers display sufficiently different degrees of attachment to their original region, the economy can move from dispersion to agglomeration in a non-catastrophic way (Tabuchi and Thisse, 2002; Murata, 2003). These issues are explored to some extent in Chapter 9.

Most of the other assumptions are a matter of expediency. For example, the model assume that there is only one non- industrial sector and to make this as trivial as possible, the model assumes that it is Walrasian and its output is traded costlessly.

(see FKV chapter 7 for the CP model with transport costs and imperfect competition in the A sector). The only crucial assumption is that the non- industrial sector is intensive in its use of the immobile factor so that inter-regional factor mobility is associated with a concentration of industry. With more than one industrial sectors, Krugman and Venables (1997) show that different sectors may agglomerate in different countries.

The assumption of two regions is not essential but it greatly simplifies the range of locational outcomes and thus greatly simplifies almost every calculation. The cost of this simplification is that the CP model cannot be used to study the many interesting issues that arise with multiple locations, e.g. locational hierarchy.

Likewise, the assumption of only two factors of production is not crucia l, although we do need at least two, since one must be mobile to allow agglomeration and one must be immobile to keep the model interesting. (If all factors were mobile, then everyone would always have an incentive to avoid trade costs by agglomerating in one region or the other; in such a model, agglomeration would either happen immediately, with positive trade costs, or be irrelevant, with zero trade costs).

The CP model makes extreme assumptions about the factor-intensity of the two sectors. Again this is for convenience, what really matters is that the mobile factor is used intensively in the increasing returns sector. The assumption is

convenient in that it makes the two sectors quite independent of each other, allowing us to solve for many endogenous variables using only a subset of the equilibrium conditions.

The model also assumes a very particular form of trade costs, namely iceberg trade cost. This assumption is very convenient in a general equilibrium model because it allows us to avoid, for examp le, the issue of who gets the rents from trade barriers, how transport services are priced and which region’s factors are used up in

overcoming the trade costs.

33 In other words, as pointed out by Koopmans (1957), the location problem of a firm arises because some of its activities are indivisible.

Having trade cost only in one sector is also a simplifying assumption. The point is that agglo meration and dispersion forces do require trade cost in one sector.

Moreover, if we allow trade costs in the other sector, we cannot maintain the

simplifying assumption that that second sector is Walrasian. Davis (1998) showed that trade costs in the Walrasian sector shuts off all inter- industry trade and this, of course, means that each region cannot run a trade deficit in the M-sector. Agglomeration is, therefore, impossible. Of course, Davis (1998) is not a critique of the basic logic of the CP model, it just shows how carefully simplifying assumptions must be fit together. Indeed one mark of an elegant model is that each assumption is critical; it should not be surprising that relaxing only one assumption produces different results.

In particular, KFV (C hapter 7) show that one gets the same sort of results with trade costs in both sectors as long as one assumes differentiated varieties in both sectors (this permits intra- industry trade in both sectors).

The assumption of upper-tier Cobb-Douglas preferences greatly simplifies the algebra since it allows us to work out prices and demands separately in the A and M sector. For more general preferences, expenditure on M would depend upon relative prices, but relative prices would depend upon the level of M-sector expenditure (the expenditure level affects the number of varieties and this in turn affect the M-sector price index).