ÁCIDO OLEÍCO

The Armington model (Armington, 1969) is based on the premise that each country pro- duces a different good and consumers would like to consume at least some of each coun- try’s goods. This assumption is of course ad hoc, and it completely ignores the “classical” trade forces such as increased specialization due to comparative advantage. However, as we will see, the model (when combined with Constant Elasticity of Substitution (CES) preferences as in (Anderson, 1979)) provides a nice characterization of trade flows be- tween many countries.2

The Armington model (as formulated by (Anderson, 1979)) was important because

2_{Actually, in the main text, Anderson (1979) considers Cobb-Douglass preferences and writes that “there}

is little point in the exercise” of generalizing to CES preferences, doing so only in an appendix. Despite his reluctance to do so, the paper has been cited thousands of times as the example of an Armington model with CES preferences.

it provided the first theoretical foundation for the gravity relationship. It is also a great place to start our course, as one of the great surprises of the international trade literature over the past fifteen years has been how robust the results first present in the Armington model are across different quantitative trade models. By now, as we will discuss in this chapter, models that yield the gravity relationship (3.5) are ubiquitous and much of the rest of what follows will focus on analyzing their common properties.

3.3.1 The model

We now turn to the details of the Armington models and in particular to the supply side of this model, given CES demand.

TheArmington assumptionis that each countryi ∈ Sproduces a distinct variety of a good. Because countries map one-to-one to varieties, we index the varieties by their country names (this will not be true for Bertrand and monopolistic competition when we have to keep track both of varieties and countries).

Suppose that the market for each country/good isperfectly competitive, so that the price of a good is simply the marginal cost. Suppose each worker can produceAi units

of her country’s good and let wi be the wage of a worker. Then the marginal cost of

production is simply wi

Ai. This implies that the price at the factory door (i.e. without

shipping costs) is pi = wAii. What about with trade costs? Recall that with the iceberg

formulation,τ_ij ≥ 1 units have to be shipped in order for one unit to arrive. This means

thatτij ≥1 units have to be produced in countryiin order for one unit to be consumed in

countryj. Hence the price in countryjof consuming one unit from countryiis:

pij =τij wi Ai

Note that this implies that:

pij pi

=τij, (3.7)

i.e. the ratio of the price in any destination relative to the price at the factory door is simply equal to the iceberg trade cost. Equation (3.7) is called ano-arbitrage equation, as it means that there is no way for an individual to profit by buying a good in countryiand sell in countryj(or vice versa). Note, however, that there may still be profitable trading opportunities between triplets of countries even if equation (3.7) holds when the triangle inequality is not satisfied.

3.3.2 Gravity

Assuming that each country produces a different goodω, and substituting equation (3.6)

into equation (3.3) yields a gravity equation for bilateral trade flows:

Xij =aijτ_ij1−σ wi Ai 1−σ XjPjσ−1. (3.8)

To the extent that trade costs are increasing in distance, the value of bilateral trade flows will decline as long asσ>1.

We can actually use equation to get a little close to the true gravity equation. The total income in a country is equal to its total sales:

Yi =

∑

∑

∑

Replacing this expression in the equation (3.8) yields: Xij = aijτij1−σ Y_i Π1−σ i ! Xj P1−σ j ! , (3.9) where Π1−σ

i ≡ ∑jaijτ_ij1−σXjPjσ−1 bears a striking resemblance to the price index [insert

foreshadowing here]. Equation (3.9) which shows that the bilateral trade spending is related to the product of the GDPs of the two countries (gravity!!), the distance/tradecost and a GE component.

Equation (3.9) is actually about as close as we will ever get to the original gravity equation. This is because all of our theories say that bilateral trade flows depend on more than just the bilateral trade costs and the incomes of the exporter and importer; what also matters is so-called “bilateral resistance”: intuitively, the greater the cost of exporting in general, the smaller theΠ1−σ

i ; conversely, the greater the cost of importing in general, the

smaller theP1−σ

i . This means that trade between any two countries depends not only on

the incomes of those two countries but also the “cost” of trading between those countries

relative totrading with all other countries. This point was made in the enormously famous and influential paper “Gravity with Gravitas: A Solution of the Border Puzzle” (Anderson and Van Wincoop, 2003).

3.3.3 Welfare

We will now show that welfare in relationship to trade is given by a simple equation involving the trade to GDP ratio and parameters of the model (but no other equilibrium variables). We will be revisiting this relationship multiple times in these notes. To begin

defineλij as the fraction of expenditure injspent on goods arriving from locationi:

λij ≡ Xij ∑kXkj

.

From equation (3.8) we have:

λij = aijτ_ij1−σ wi Ai 1−σ ∑kakjτ_kj1−σ wk Ak 1−σ ⇐⇒ λij =aijτ_ij1−σAσ_i−1 wi Pj 1−σ (3.10) since P1−σ j ≡ ∑kakjτ_kj1−σ wk Ak 1−σ

. Remember from the CES derivations above that the utility of the representative agent is the real wage, i.e.Uj =

wj

Pj. Assume thatτjj =1. Then

by choosingi=j, equation (3.10) implies that welfare can be written as:

U_j =λ 1 1−σ jj α 1 σ−1 jj Aj, (3.11)

i.e. welfare depends only on changes in the trade to GDP ratio,λjj, with an elasticity of −1/(σ−1)which is the inverse of the trade elasticity.

3.4

Monopolistic Competition with Homogeneous Firms and CES