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K. Production has constant returns to scale and is perfectly competitive. The unit cost functions
for good i is bi(w, r), the same in all countries, where w and r are factor prices.
We have chosen to develop the model with three produced goods. The reason is that
three goods gives a much richer pattern of trades than does a two-good model, since both the
pattern of trade and the number of goods produced, traded, or non-traded, will vary across
countries.4 The three-good framework also sets the stage for our analysis of fragmentation,
which we model as increasing the number of traded activities from two to three. With three
goods and two factors production is indeterminate in countries that have zero trade costs, but
such countries lie only on a line in our two-dimensional space of countries.5
The three goods are denoted X1, X2 and X3, with world prices pi, i = 1, 2, 3. Trade is
subject to iceberg trade costs which vary across countries, but which are the same for all goods
to/from a particular country. Thus, if a country with trade costs t $ 1 (where t = 1 is free trade),
imports good Xi , the internal price will be tpi. Conversely, if it exports the good the price will be
pi /t as domestic producers only receive a fraction of the world price. Notice that we assume that
these trade costs are incurred on both exports and imports, and that a particular country has the
same values t on its trade with all destinations. It is this that allows us to talk of a clearly defined
‘world price’; it is as if there is a central market place to which countries export and from which
they import. Of course, this is a fiction, but it is also a great simplification, meaning that we do
not have to work with a full matrix of trade costs between all pairs of countries. It corresponds
with reality to the extent that trade costs are just border costs. For example, if trade costs are
6
simply port handling costs, then they apply to all imports regardless of source and exports
regardless of destination. Similarly, if the barriers are non-preferential import tariffs or export
taxes then they are consistent with our model, although we ignore revenue that any such tariff
barriers might earn.
The equilibrium location of production satisfies a set of inequality relationships. Each
good Xi will be produced in a country only if its unit cost is less than or equal to the import price;
and export opportunities mean that the lower bound on unit cost is the export price, so
(1)
If the unit cost is strictly within this inequality then the country is self-sufficient in the good,
while it may export the good if the unit cost is at the lower end, and import it at the upper end.
Our strategy for describing the equilibrium has two parts. The first is numerical. We use
GAMS to solve for the multi-country equilibrium and details of the code used and dimensionality
of the problem are given in appendix 1. We present results from these simulations in a series of
figures which describe what countries – differentiated by factor endowments and by trade costs –
produce; what they trade; and values of their factor prices and real incomes. These figures
indicate the existence of different regimes, in which countries are specialized in different
activities. The second part of our strategy is to analytically characterize these regimes, showing
how they depend on key parameters of the model.
We start with a symmetric three-good case, and make the following assumptions:
I) Preferences are Cobb-Douglas with expenditure equally divided among the three
goods.
II) X1, X2, and X3 production are Cobb-Douglas with symmetric factor shares, with X1 the
for good i is bi(w, r), the same in all countries, where w and r are factor prices.
We have chosen to develop the model with three produced goods. The reason is that
three goods gives a much richer pattern of trades than does a two-good model, since both the
pattern of trade and the number of goods produced, traded, or non-traded, will vary across
countries.4 The three-good framework also sets the stage for our analysis of fragmentation,
which we model as increasing the number of traded activities from two to three. With three
goods and two factors production is indeterminate in countries that have zero trade costs, but
such countries lie only on a line in our two-dimensional space of countries.5
The three goods are denoted X1, X2 and X3, with world prices pi, i = 1, 2, 3. Trade is
subject to iceberg trade costs which vary across countries, but which are the same for all goods
to/from a particular country. Thus, if a country with trade costs t $ 1 (where t = 1 is free trade),
imports good Xi , the internal price will be tpi. Conversely, if it exports the good the price will be
pi /t as domestic producers only receive a fraction of the world price. Notice that we assume that
these trade costs are incurred on both exports and imports, and that a particular country has the
same values t on its trade with all destinations. It is this that allows us to talk of a clearly defined
‘world price’; it is as if there is a central market place to which countries export and from which
they import. Of course, this is a fiction, but it is also a great simplification, meaning that we do
not have to work with a full matrix of trade costs between all pairs of countries. It corresponds
with reality to the extent that trade costs are just border costs. For example, if trade costs are
6
simply port handling costs, then they apply to all imports regardless of source and exports
regardless of destination. Similarly, if the barriers are non-preferential import tariffs or export
taxes then they are consistent with our model, although we ignore revenue that any such tariff
barriers might earn.
The equilibrium location of production satisfies a set of inequality relationships. Each
good Xi will be produced in a country only if its unit cost is less than or equal to the import price;
and export opportunities mean that the lower bound on unit cost is the export price, so
(1)
If the unit cost is strictly within this inequality then the country is self-sufficient in the good,
while it may export the good if the unit cost is at the lower end, and import it at the upper end.
Our strategy for describing the equilibrium has two parts. The first is numerical. We use
GAMS to solve for the multi-country equilibrium and details of the code used and dimensionality
of the problem are given in appendix 1. We present results from these simulations in a series of
figures which describe what countries – differentiated by factor endowments and by trade costs –
produce; what they trade; and values of their factor prices and real incomes. These figures
indicate the existence of different regimes, in which countries are specialized in different
activities. The second part of our strategy is to analytically characterize these regimes, showing
how they depend on key parameters of the model.
We start with a symmetric three-good case, and make the following assumptions:
I) Preferences are Cobb-Douglas with expenditure equally divided among the three
goods.
II) X1, X2, and X3 production are Cobb-Douglas with symmetric factor shares, with X1 the
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