5.3 Destination Principle
5.3.1 Segmented markets
Maximizing (9) (using the demand functions from the previous section, namely (7), (8), and their foreign counterparts) with respect to producer prices separately for each market,
6Since antidumping rules/integrated markets affect pricing behavior directly, I consider Bertrand com-
petition as a natural choice. My guess on Cournot competition would be that it would not make a qualitative difference: It does tend to lead to higher profits in those models, but the basic strategic effects governments’ subsidies have are qualitatively similar. Furthermore, Anderson et al. (1995) show that their result goes through under Cournot competition as well, and the results in Haufler and Pfl¨uger (2007) are pretty similar for price and quantity competition, whereas segmented vs. integrated markets makes a big difference.
and solving these equations, I get the Nash equilibrium in prices: px = 2−γ2+τ γ−γ+t(γ2+γ−2) 4−γ2 , p∗ x = (1−t∗)(1−γ)(γ+ 2)−τ(2−γ2) 4−γ2 , p∗ y = 2−γ2+τ γ−γ +t∗(γ2 +γ−2) 4−γ2 , py = (1−t)(1−γ)(γ+ 2)−τ(2−γ2) 4−γ2 . (10)
Accordingly, consumer prices will amount to:
qx = 2(1 +t)−(1−τ−t)γ−γ2 4−γ2 , q∗ x = 2(1 +τ +t∗)−γ+t∗γ−γ2 4−γ2 , q∗ y = 2(1 +t∗)−(1−τ−t∗)γ−γ2 4−γ2 , qy = 2(1 +τ+t)−γ+tγ+γ2 4−γ2 . (11)
Note that these prices depend, of course, on taxes. Substituting them back into the demand functions, I get quantities depending on only taxes and exogenous parameters. These can then be used in welfare expressions. Welfare consists of consumer surplus, labor income, tax revenues and profit income:
W =CS+ 1 +t(x+y) +π; W∗ =CS∗+ 1 +t∗(x∗+y∗) +π∗. (12) Hence, welfare in country 1 is
Wd,s = (x+y)−1
2 ¡
x2+ 2γyx+y2¢−q
xx−qyy+ 1 +t(x+y) +πd,s, (13)
with ‘d, s’ standing for the ‘destination, segmented’ regime and welfare in country 2 is
W∗d,s = (x∗+y∗)−1 2
¡
x∗2+ 2γy∗x∗+y∗2¢−q
x∗x∗−qy∗y∗+ 1 +t∗(x∗+y∗) +π∗d,s. (14)
Maximizing (13) and (14) with respect to t and t∗ yields7
td, s =t∗d, s =−τ(γ+ 1)
2(γ+ 2). (15)
These taxes are zero when trade is free. There are two basic motives, pulling the tax in different directions. On the one hand, they will be used as a corrective subsidy due to the under-consumption caused by market power. On the other hand, to the extent that they hit imports, they can be used to shift rents away from the foreign firm. It turns out that in the present specification with linear demand, these two effects exactly cancel each other under free trade. This makes intuitive sense as without trade frictions, the foreign industry is just as important to a country (and a subsidy to it just as effective) as the home industry. The taxes turn into subsidies when trade is costly, so there are never positive taxes in this basic version of the model without an exogenous revenue need or foreign ownership. This stems from the effect that the best thing to do in a closed economy would be granting the monopolist the optimal subsidy, which is counteracted by a tax-the-foreigner effect under trade. Observe that an increase in τ makes markets more and more separated, driving up the firms’ market power in their home markets and calling more strongly for corrective subsidies. These results are well-known (see, e.g., Hashimzade et al. (2005)). With those taxes substituted back into (13) and (14), I get the equilibrium welfare levels under destination taxes and segmented markets. Taking country 1, this is
Wd,s = 1
4 (4−γ2)2(γ2−1) ©
τ2¡−2γ4+γ3+ 11γ2−γ−19¢+
4¡γ4−4γ3+γ2+ 9γ−7¢(γ+ 2)2+ 4τ¡γ4+ 2γ3−6γ2 −7γ+ 10¢ª. (16)
For future reference, welfare without profit income (i.e. Wnoprof it =CS+ 1 +t(x+y)) is
Wnoprof itd,s = 1
4 (4−γ2)2(γ2−1) ©
τ2¡−3γ3+ 7γ2+ 3γ−9¢+
4τ¡γ4−6γ2−γ+ 6¢+ 4¡γ6−9γ4+γ3+ 27γ2−20¢ª. (17) These terms are somewhat messy. I restate them for γ = 1/2 as a natural benchmark case of intermediate substitutability across goods, and will make use of this simplification several times in what follows for purely expositional purposes (the role of different values of γ will be become clearer below):
Wd,s| γ=12 = 1 675(4τ(67τ −85) + 1075), W d,s noprof it|γ=12 = 1 675 ¡ 98τ2−260τ + 875¢. (18) The above expressions characterize the non-cooperative solution. As a benchmark for
ensuing welfare analyses, I now turn to the taxes that would prevail under a cooperative solution, i.e. the (common) consumption tax that would maximize the sum of the two countries’ welfare levels:
ts
coop.=−
1
2(2−τ)(1−γ). (19)
This will be discussed further below. One thing to note right away is that td, s is generally
larger (less of a subsidy) thants
coop.. This reflects that when setting taxes non-cooperatively,
governments do not take into account the negative effects on the other country’s industry’s profits (which are negatively affected by a tax increase) and thus end up setting taxes too high (from a global point of view).
Before proceeding to the next section, it is worthwhile to spend a moment considering the outcome of the game. Since with symmetric countries, taxes will be the same in 1 and 2, and since firms absorb some of the freight cost (at least with the linear demand assumed here, and which is suggested to be the case in the bulk of the corresponding empirical literature), there is no way arbitrage alone can prevent firms from earning different producer prices across markets. The next section will now examine how a rule precluding them from doing exactly the latter will influence taxes, and, above all, whether such a rule is desirable.