specific to country M and to variety i and affects the variable costs of assembly.
In particular, we assume that the marginal cost of assembling one unit of input
x(i) into one unit of output y is 1/I (i). Accordingly, in choosing I (i), Y -firms
face a trade-off between the fixed cost I (i)2 and the variable cost 1/I (i).
Under the outsourcing mode (henceforth, O), also intermediates are pro-
duced in country M . In this case, all technological conditions are the same as
in mode E . However, local intermediate production requires firms to contract
with local intermediate producers. Due to unforeseen contingencies, complete
contracts cannot be written. Therefore, the surplus from the outsourcing agree-
ment can be shared only after the delivery of the specific input on the basis of
the barganing power of the two parties. The share of ex-post surplus appropri-
ated by the local intermediate supplier is denoted by β, β ∈ [0, 1]. The surplus
from the outsourcing agreement accruing to each party is given by the revenue
generated by the final sales minus the value of each parties’ outside options.
For the intermediate suppliers no outside option is available, since the input
characteristics are specific to the final producer (i.e., once produced for the firm
i, intermediates are useless to any other Y -firm). On the contrary, as an outside
option, the Y -firm can produce the intermediate input by itself abroad and ship
it to M for final transformation as under mode E . The timing of events is as
follows. First, the firm i chooses the level of investment I(i) in local trans-
formation. Then, the local intermediate supplier chooses the amount of input
x(i) to supply. The chosen sequence reflects a higher degree of irreversibility of
assembly investment I (i).6
To sum up, the sequence of actions for the whole game is described in Figure
1. In the first stage, Y -firms choose between modes X , E and O.IfX is
chosen, then the firm sets the level of production that maximizes profits. If E
is chosen, there is a second stage in which the firm makes a decision about the
investment I in the trasformation technology. Finally, if O is chosen, there are
two additional stages. In the third the input supplier chooses the amount of
input to produce. In the fourth there is bargaining over the surplus from the
outsourcing agreement.
To ease notation, exploiting the symmetry across firms in terms of prefer-
ences and production technologies, the variety index i will henceforth be omit-
ted. The only index used will denote the alternative chosen by MNEs to serve
market M (i.e., X, E, or O).
4 Payoffs under alternative supply modes
An equilibrium is defined as a situation in which firms maximize profits, con-
sumers maximize utility, and markets clear. In particular, it has to be true
that, given the choices of all other Y -firms, each Y -firm serves market M in
its preferred way, achieving a profit-maximizing scale of production for final as
6 Were the Y -firm and the intermediate supplier to choose simultaneously rather than
sequentially, the main results of the model would be unaffected (no multiple equilibria, non-
linear relation between outsourcing and transport costs).