One such model was developed by Helpman (1984). Building on the standard model of international trade in differentiated products, he introduced a general purpose input (H) which could both be used to produce the homogenous product, and could be adapted at a cost to produce a given variety of differentiated product. Inputs that fit this description include management, distribution, and product-specific R&D (or ‘product development’ as Vernon would have it). Once adapted, input H becomes a firm-specific asset that is tied to the entrepreneurial unit but, crucially, can be used to serve multiple plants simultaneously and need not be present in a plant to serve its product line9. Firms look to maximise profits, and therefore choose cost-minimising production locations based on differing factor rewards. Relative factor rewards are based solely on differences in relative factor endowments across countries. In order to clarify the theory Helpman makes a number of simplifying assumptions. Transport costs and tariffs are assumed equal to zero, so production facilities are not established in order to reduce shipping or to produce behind tariff walls. Other possible reasons for multinationals, such as tax treatment, are also not considered.
Let us briefly describe Helpman’s model. In a competitive equilibrium the price of the homogenous product (y), which is taken as the numeraire, equals unit costs:
1 = c Y( w L, w H)
p.
3]
9 In particular, it can serve multiple plants located in different countries.
where Cy is the cost function for product ‘y \ Wi is unit labour costs and Wh is the unit
cost of the general purpose input.
The production of differentiated products is more complicated. Following the function /(x, hx), 7 ’ units of labour are required to produce ‘jc ’ units of a differentiated product in a single plant when hx units o f ‘H ’ have been adapted for use. Helpman suggests the following as a possible form for 7', where f p>0 and gi(x,hx) is positively linear homogenous:
1 = f P + g \ { x , h x ) |-2
4]
H erejJ results in a plant-specific fixed cost and the variable component exhibits constant returns to scale. More generally, Helpman assumes that l = f p + gi(x,h x) is the inverse of an increasing-retums-to-scale production function in which hxis essential for production. In addition to 7 ' units of labour, a differentiated product must also incur the cost of adapting H, given by g(wi,Wh,hx) , which is associated with a no decreasing-retums-to- scale production function. Combining these, the firm’s single plant cost function for producing a variety of differentiated product becomes:
C x ( w L, w H , x ) = min [ w Ll { x , h x ) + g ( w L, w H , hx ) + w Hh x )
The function, [2.5], has the standard properties of cost functions associated with increasing-retums-to-scale production functions. What is important to note is that the
firm has fixed costs that are corporation specific but not plant specific (i.e. the cost of adapting H), it has plant-specific fixed costs, and it has plant-specific variable costs. By assuming that / = fp + gi(x,hx) is the inverse of an increasing-retums-to-scale production function, in the absence of transportation costs or differences in product prices across locations, production will invariably be located in a single location.
It is assumed that there is Chamberlain-type monopolistic competition in the differentiated product sector. This implies that firms equate marginal revenue with marginal product and free entry competes away any abnormal profits. Combined with [2.5], these formal conditions are those applied to existing models of trade in differentiated products. The novelty in Helpman’s exposition derives from factor H, with firm-specific asset hx permitting production to take place in countries in which hx is not physically present. Note that “the specificity of hx implied that arm’s-length trade in its services is an inferior organizational form to an integrated firm” (p.455). This is the feature that allows the emergence of multinational corporations.
Let us now consider the model’s predictions regarding the pattern of trade. In the case of factor-price-equalisation across countries, the model predicts that the inter-sectoral pattern of trade will be the same as in the Heckscher-Ohlin model. However, in this model intra-industry trade in differentiated products also occurs. There is no multinational activity as the optimal location decision is to locate all production at home and export where necessary.
Now consider the case where factor prices are not equal across countries, with H being
cheaper in country A and / being cheaper in country B. Firms will clearly have an incentive to locate their (^-producing) headquarters in country A and their (x-producing) plant in country B. This will increase demand for H in country A and reduce it in country B, and increase demand for / in country B and reduce it in country A. Equilibrium will be obtained either when factor prices are equalised, or when country A becomes the home for the headquarters of all corporations. This results in country A importing the homogenous (/-intensive) product, and intra-industry trade in differentiated products, with some of this trade being undertaken by multinationals10. The amount o f trade that will be undertaken by multinationals (and the determinant of whether country A will be a net exporter, or net importer, of the differentiated product) is determined by the initial difference in factor prices and how quickly they become equalised. The model therefore demonstrates that factor endowment differences can result in the existence of multinational enterprises, and that this will have an impact on the pattern of international trade.
In his conclusion, Helpman notes that “despite the relative richness of the theory it needs further extensions and elaborations in order to deal with the wide range of problems that are at the head of international economics” (p.470). Indeed, Helpman (1985) and Helpman and Krugman (1985) elaborate and extend the theory. Helpman’s model, and those that have since been developed in its likeness, are commonly known as ‘vertical’ models, because they describe multinational activity in terms of fragmentation of the production process between different geographical locations (i.e. headquarter activities
10 Intra-firm trade will also exist as headquarters export intangible “//-services” to their overseas