Roman Transport Network Connectivity and Economic Integration

We show that the creation of the first integrated pan-European transport network during Roman times influences economic integration over two millennia. Drawing on spatially highly disaggregated data on excavated Roman ceramics, we document that interregional trade was strongly influenced by connectivity within the network. Today, these connectivity differentials continue to influence cross-regional firm investment behaviour. Continuity is largely explained by selective infrastructure routing and cultural integration due to bilateral convergence in preferences and values. Both plausibly arise from network-induced history of repeated socio-economic interaction. We show that our results are Roman-connectivity specific and do not reflect pre-existing patterns of exchange.


Introduction
Population aging is an important stage of the demographic transition and this stage is expected to have strong eects on the structure of the world economy. According to the United Nations (United Nations, 2013) the percentage of the world population over 60 years of age was 8% in 1950, has risen to 12% by 2013, and is expected to reach 21% by 2050. The rate of change will not be the same in all countries.
Countries with a younger average population will age faster as they begin to catch up with more senior countries. 1 In fact, this part of the demographic transition is predicted to be felt most strongly in the least-developed countries. Recognizing its implications for capital-labor ratios, and savings behavior, economists have begun to look seriously at this stage of the demographic transition. In this paper we propose a new aspect of population aging that has been previously overlooked in the literature: an aging-induced change in consumption patterns.
Our starting point is that the elderly consume more services than the young. For example, a 2013 (Statistics Canada, 2013) survey of Canadian households found that expenditures on health care (apart from what is provided by national insurance) comprised 7.6% of goods and services spending for households headed by a senior aged at least 65 years old and only 2.9% for a household headed by someone under 30. 2 In addition to health care, seniors would be more likely to purchase personal and household maintenance services than the young. For example, Desvaux et al. (2010) project the demand of French consumers over the 2007-2030 time period and show that dwelling, maintenance, and repairs would have a positive annual growth rate of 1.7% for French consumers aged 65 or older and a negative annual growth rate of 1% for individuals under 40. 3 The additional expenditure on services must come at the expense of manufactured goods. As the advertising industry repeatedly emphasizes, the key demographic age for new manufactured goods is between 18 and 54, and not the elderly.
This change in individual consumption patterns has several external eects. Manufactured goods are not only more easily tradable than services, they generally have more signicant economies of scale. 45 Hence, age induced changes in domestic consumption can have important eects on the pattern of international trade.
Our basic idea is threefold. First, consumption patterns change with age. Second, services are less tradable than manufactured goods. Third, increased production of manufactured goods generates more production externalities than does services.
Hence, an increase in the average age of a country can generate an increased reliance on imported manufactured goods and a consequent reduction in economic growth.
We then consider the role of trade and immigration policy in ameliorating any negative outcomes from these demand driven externalities. Although stylized, our model generates clear and sensible policy prescriptions.
In addition to its policy implications our model also incorporates several technical innovations. We build on the Krugman (1980) model of monopolistic competition with transport costs. This model is useful for showing how trade costs can interact with market size in forming rms' location decisions. We extend Krugman's classic framework in several dimensions. First, we allow for heterogenous agents and nonhomothetic preferences. Agents dier by age and older ones spend a larger share of their income on services. We also allow for asymmetric trade costs as well as taris. 6 Finally, in addition to endogenously chosen taris we also consider labor migration.
In this framework we derive the following results. First, the age composition of the population has an important determinant on the share of manufacturing rms located within its borders. In particular, the share is decreasing in the average age of the population. The number of manufacturing rms is decreasing in average age in autarky as well, however, the dierence is smaller in autarky. Furthermore, the ratio of these dierences depends on trade costs. Crucially, the ratio of these changes becomes very large as trade costs become small. Hence, increased globalization will increase rm delocation eects arising from population aging. In addition, welfare is increasing in the number of domestically produced manufactured goods and is, therefore, decreasing in an aging society. This result does not suggest that trade is worse than autarky, however, it does suggest increased globalization resulting in a reduction in the common trade costs (that, in fact, leaves the total number of manufactured varieties unchanged) will generate diering welfare changes in a young and an old country.
We next consider the role of immigration and tari policy in ameliorating some of the population-aging eects on trade. Immigration can reduce the demand-driven eects of an aging society as long as it is not too tilted towards older immigrants. If the immigrants are primarily young, if the population is initially small, purchased services are a small percentage of total income, or the dierence between young and old consumption patterns is small, then a country's share of manufacturing will increase along with increased immigration. Our results on the age of immigrants suggests why countries like Australia, Canada, and New Zealand have stressed a point system (which rewards youth among other things) over family reunication (which can attract elderly parents). 7 With respect to tari policy we show that a unilateral tari increases can increase a country's share of manufacturing rms and increase welfare, however, unilateral tari increases often generate tari wars. All else equal, a country with an older average population will lose a tari war and see a reduction in its share of manufacturing 7 Canada introduced the points-based system of immigration in 1967 followed by Australia in 1989 and New Zealand in 1991. More recently, Czech Republic, Denmark, Japan, The Republic of Korea, Singapore, Sweden, and the UK have introduced the points-based system but on a reduced scale. Australia, Canada and New Zealand consider age as an important factor in order to target young immigrants via their points-based systems. Consequently, there have been less legally admitted immigrants who are 50 or above years of age to these three countries as compared to those legally admitted to the US which relies on a family reunication system prevails. For example, Citizenship and Immigration Canada (2010) provides empirical evidence that there were only about 8 % of all legally admitted immigrants to Canada who were 50 years old or older at admission to Canada during 2002-2008. Birrell et al. (2006 show that there were only 7% of immigrants over 46 years old at admission to Australia during 2000-2005. Grangier et al. (2012 indicate that the ratio of old immigrants (50 years of old and above) at admission to New Zealand was just 5% during 2004-2005. For the US, on the other hand, Carr and Tienda (2013) demonstrate that the immigrant cohort share aged 50 and over at admission to the US rose from 11% during 1981-1985 to 17% for 2006-2009 and they provide empirical evidence that family sponsored migration is largely responsible for the increase in legally admitted immigrants aged 50 years old and above to the US during 1981-2009. rms. Furthermore, even in the unilateral case, if the tari revenue is returned to the citizens, then the increased tari revenue may generate a larger (or smaller) increase in the purchase of services (a luxury good) and diminish (or increase) any rm delocation benet from a tari increase.
It has been common in economic models to assume that the marginal (and average) propensity to consume a good are not dependent on income. These constant income shares, that result from the assumption of homothetic preferences, are frequently employed in the economics literature. Although they have several nice mathematical properties they are repeatedly contradicted by the empirical evidence. From Stone's (1954) seminal work on expenditures through Hunter and Markusen's (1988) groundbreaking work that demonstrates its importance in explaining the pattern of trade, the data continually conrm that preferences are non-homothetic and consumption bundles do change with income. We represent preferences by a Stone-Geary utility function. This representation of non-homothetic preferences is commonly used, in part, because it yields an ane income expansion path, which permits meaningful aggregation. Recent work that introduces non-homothetic preferences into a model of international trade includes Matsuyama (2000), Fieler (2011), Fajgelbaum et al. (2011), Markusen (2013, Caron et al. (2014), and Simonovska (2015). We add to this literature by considering tari policy and immigration in a trade model with nonhomothetic preferences, as well as population aging and combining non-homotheticity with monopolistic competition.
There is a small literature that links the demographic change with international trade, however, these studies dier from ours in that they consider factor market changes as opposed to demand changes. For example, Sayan (2002), Sayan (2005), and Naito and Zhao (2009) show that an aging economy specializes in the capital-intensive sector and incrementally becomes small, while the labor-abundant country specializes in the labor-intensive sector. Cai and Stoyanov (2014) arrive at an analogous result with Sayan (2005) and Naito and Zhao (2009), implying that aging societies would specialize in industries that are age-appreciating-intensive (for example industries that rely more on speech and language abilities) and import age-depreciating-intensive goods that are produced in industries where the production scheme relies mainly on multitasking, memory and speed of information processing. Lim and Saner (2011) suggest that population aging may also increase the demand for education in developing and emerging countries and cause a shift in the world demand for education, which in 5 turn may alter the pattern of international trade of educational services.
In the next section we describe the economic environment. In the third section we consider autarky and trade is considered in the fourth section. Immigration policy is the focus of the fth section and tari policy is analyzed in the sixth section. Our conclusions are contained in the seventh section.

Economic Environment
In this section we develop the simplest possible model that can capture our main points. Each of the L (L * ) agents in the home (foreign) country has preferences over manufactured goods, services, and a numeraire good. These preferences can be represented by the following utility function: The upper tier utility function is of the Stone-Geary variety. 8 Services are a luxury good and the taste for this luxury, γ a , depends on the individuals age, a ∈ {g, r}. Our idea is that services are more of a luxury for younger (green) individuals and more of a necessity for older (ripe) ones. Hence, γ g > γ r > 0. For example, purchases of domestic services, household maintenance, personal care, and even health care are more of a necessity for older individuals, in part, because younger ones can more readily provide many of these services for themselves. In fact, one could also consider γ a as the amount of services that can be enjoyed without being purchased in the market.
In addition to the above mentioned personal, health, and maintenance services, they may also consist of socializing with friends or family, reading, or taking walks.
Although empirical work (such as Stone (1954) and Hunter and Markusen (1988) among others) has repeatedly shown that preferences are not homothetic, it is still not obvious what is the best functional form for representing non-homothetic preferences.
The Stone-Geary function that we have chosen here is most commonly employed because they permit an ane income expansion path, which permits meaningful aggregation. Still, this functional form is not without restrictions. First, they assume a constant elasticity of substitution between the components of the upper tier utility function. Second, the marginal propensity to consume is independent of income for all individuals above a certain minimum level, therefore, changes in income distribution within a country do not aect aggregate demand when all individuals are above this level. 9 The sub-utility for the manufactured goods is a constant-elasticity-of-substitution utility function. The parameter σ > 1 expresses the constant pairwise elasticity of substitution. As this parameter is greater than one, no particular variety of the manufactured goods is essential for consumption and, as will be shown below, the value of this subtlety is increasing in the total number of available varieties. (The services and numeraire sector consumptions could also be considered as coming from a constant-elasticity-of-substitution aggregator where the elasticity of substitution is innite.) Each rm producing in the monopolistically competitive sector has the same technology: where z is the amount of labor used in producing good z, q z is the quantity of good z, φ is the marginal productivity of labor, and f denotes the xed input requirement. We use the convention that the xed cost of production, f , is paid in terms of labor.
The technology for producing the numeraire good is 0 = q 0 ( * 0 = q * 0 in foreign) and the technology for producing services is given by is the labor productivity in services. The labor supply of each country, L(L * ), is assumed to be large enough so that there is positive numeraire and service production in each country. The measure of young individuals in each country is given by η(η * ) so that (1 − η)L are the total number of older individuals in the home country. Each individual is endowed with one unit of labor. 10 As there is no utility for leisure each 9 See Chisik et al. (2014) for an alternative environment where within country distribution matters. 10 Note that changes in the labor supply L and its age composition η can be traced back to 7 agent supplies their labor inelastically to the rm paying the highest wage. The wage in any sector is, therefore, equal to the price of the numeraire good which is one.

Autarky
As shown by Dixit and Stiglitz (1977), the set of purchased manufactured goods can be considered as a composite good D M with corresponding aggregate price ( Maximization of the upper tier utility function subject to the income constraint conventional drivers of aging, a decrease in fertility or an increase in longevity. To see this, consider an overlapping generations framework where an individual who belongs to generation t − 1 lives in two periods: t − 1 and t. The rst period of her life has a unitary length, while the second one has a length v ≤ 1, where v reects a variable longevity. Abstracting from unemployment and retirement, the labor force at time t is thus given L t = H t + vH t−1 , where H t shows the size of the generation born in t. Suppose that successive generations grow at a rate of h, which also denotes the fertility rate; thus, H t = H t−1 (1 + h). Then, we can write the labor force in period t as the following Next, we map the shifts in size and age composition of the labor force onto changes in fertility and longevity. Using the above equation of the labor force, we can write the share of young generation in total labor force as η = 1+h 1+v+h where both a decrease in fertility h and an increase in longevity v lead to reductions in the share of youth η as shown by − dη However, in order to preserve the L t , the condition dv = −dh should be satised. These two conditions together implies that aging without a change in the size of the population requires a small increase in longevity and an equivalent decrease in fertility. An increase in total labor supply L t can be driven by an increase in longevity v or an increase in fertility h. However, the increase in longevity would also lead to a reduction in demographic share of the youth and the increase in fertility to an increase in it. Thus, in order to preserve the age composition while increasing the population, a specic relationship between the changes in longevity and fertility is required. To see this, totally dierentiate the share of young generation in total labor force η to get dv dh = v 1+h , which denotes the corresponding change in v that is required to keep the η xed when h changes.
These piecewise-connected demand functions all switch from the rst to the second component when For I >Î the purchase of services is positive. If labor productivity of services is relatively high, then their price, P S is relatively low and all individuals would purchases services and each individual would consume on the second term in their demand correspondences given above. As will be seen below, after equilibrium prices P S = w χ and income (I = w = 1 from the numeraire good) are derived, a condition on the primitives of the model that guarantees this outcome for all individual is: and we make this assumption throughout our analysis. 11 Aggregate demand for all goods from the manufacturing sector is then given by so that consumer maximization of the sub-utility function yields demand for each variety as 11 As will be clear below, if γ r (1−α) α < χ < γ g (1−α) α , so that only older people buy services, then an older average age population will purchase even more services and less manufactured goods so that all of our results would still hold and even be strengthened.
Each manufacturing rm chooses output to maximize prots, and because there is a large number of rms, each takes the output of the other rms and the aggregate price index, P M , and consumption, C M , as given. This leads to the following pricing rule: p z = σ φ(σ−1) . Hence, and the gross prots of each rm is given by: where Free entry implies that rms enter until prots are zero. From equation (10)

International Trade
We now consider international trade in the manufactured goods and the numeraire, however, we assume that services are non-tradable. Whereas the numeraire is traded without cost, manufactured goods have an iceberg trade cost of τ = θ(1 + t) > 1.
In particular, if one unit is shipped from foreign, then 1 τ arrive. The remaining τ −1 τ melt away. The term θ is the common transport cost between home and foreign. The tari on products that home imports from foreign is t. The total trade cost for goods imported into foreign is τ * = θ(1 + t * ) > 1. Hence, by restricting taris to also be of the iceberg variety we are assuming away any income expenditure eect of tari revenue. 12 In this section we take the tari as given and in the next section we allow countries to choose their taris.
Given this formulation the foreign importer price of a manufactured good z that is produced at home is p * z = τ * p z . The home importer price of manufactured good z that is produced in foreign is p z = τ p * z . Hence, we can derive the price index in the home country as: The foreign price index is similar. Using these price indices, home and foreign demands for a home manufactured variety are: Income is equal to the wage which is given by the price of the freely traded numeraire in both countries. From the given technology, w = P O = 1, therefore, per capita income is equal to one in home and foreign. The prohibitive transport cost on services allows the prices of these non-tradables to dier across borders, however, their simple technology yields P S = w χ = 1 χ = w * A = P * S , so that the price of services is the same in both countries. Combining these results with the above demands for each home variety, and noting that τ * units of a home good need to be shipped for one to arrive in foreign, yields that the total demand for each home manufactured good is: As in autarky, because there is a large number of rms, each rm considers the price of the other rms and their total number as given, therefore, we again have the pricing rule: p z = σ φ(σ−1) . The free entry condition indicates that revenue for each rm must equal total cost for each rm: p z q z = r z = z = qz φ + f . After substituting in the pricing rule we have that σ−1 σ = qz qz+φf . It is immediate to see that the output of each variety is determined uniquely by σ, φ, f and w and that the price is given by σ, φ, and w. In particular, in this formulation the wage is determined by the numeraire good and is not aected by country size or the composition of demand, therefore, neither price nor output per rm are determined by market size or demand composition. As we will show below, it is through its eect on the number of varieties that the age composition will have a meaningful eect on the two economies.
Before proceeding it will be useful to introduce the following notation.
Note that βΨL (βΨ * L * ) describes the market size for manufactured goods in home (foreign) and we will refer to Ψ (Ψ * ) as a market size parameter. Substituting this notation into equation (13), multiplying each side of that equation by the price of a variety, and using that total revenue equals total cost, we can then write the labor used in producing each home variety as: The expression for each foreign variety is similar * Given that output is determined uniquely by σ, φ, f and w and these are the same in both countries we have that z = * z . Using this fact allows us to write the number of varieties of manufactured goods in each country as These two equations are the focus of our analysis. We begin by looking for conditions on when N M and N * M are both positive. In particular, if ΨL Krugman (1980) assumed that τ = τ * and that preferences are homothetic so that Ψ = Ψ * = 1. In this case, if τ = τ * approaches one from above, then it is straightforward to verify that both N M and N * M could not be strictly positive unless L = L * . Hence, all manufacturing activity would accumulate in the larger economy. This is also true in our framework, however, the denition of market size depends not only the population, but also the age composition. Note that Ψ is decreasing in the age of the population (increasing in η) so that a younger population increases the domestic market size for manufactured goods.
We now consider the relative number of manufactured varieties that are produced in the home country. To this end we deneN M = N M N M +N * M . We then havê Examination of the above equations reveals thatN M is weakly increasing in both Ψ and L. In particular, it is strictly increasing when both countries produce manufac-tured goods (as in the middle term in the above equations) and it is non-changing otherwise. As shown above, the area whereN M = {0, 1} also depends on both Ψ and L. From the expression for Ψ we see that Ψ is decreasing in the age of the population (increasing in η) so that a younger population increases the market for manufactured goods. Hence, we have that the share of manufactured goods produced by a country is also decreasing in the age of their population. We summarize these results in Proposition 1 below.
Proposition 1. A country with a smaller population can have a larger eective home market and be a net exporter of manufactured goods if they have a younger population. If both countries export manufactured goods, then an increase in the average age of the population will decrease that countries share of the total manufactured varieties. Furthermore, an increase in the average age of the population will increase the necessary size of the population so that manufacturing output is positive.
Proposition 1 is our rst main result in that it highlights the relationship between age and the pattern of trade. Our result is novel in that it depends only on demand considerations.
If we look further at equation (19) we see that the share of manufactured goods produced by a country increases more rapidly than its share of total market size, which is dened as ΨL ΨL+Ψ * L * . To see this fact note because σ > 1 it must be the case that (1 − τ 1−σ τ * 1−σ ) > (1 − τ 1−σ )(1 + τ * 1−σ ). Furthermore, the change of market share of manufactured goods with respect to changes in population size is given by: As noted above Ψ is increasing in η, therefore, an increase in population will have a larger aect on the share of manufactured goods if the population is younger. We summarize the results in proposition 2.
Proposition 2. If both countries produce manufactured goods, then the share of manufactured goods produced by a country increases more rapidly than an increase in their relative market size. Furthermore, when population increases, the share of manufactured goods produced by a country increases by a greater amount when the population is younger.
14 We illustrate the rst part of proposition 2 with the following gure 1.
First, note the bounds or breakpoints where each country is producing positive amounts of manufactured goods. We also see that the share of manufactured goods is increasing at a faster rate than the market share. Notice as well that this increase depends on the trade costs. Finally notice that even when their market size is equal the countries may not have equal manufacturing shares. They are equal only if the trade costs are equal.
Propositions 1 and 2 describe how an aging population can reduce the share of exportable manufactured goods that a country produces. The idea is that, because these goods have a higher value added than the numeraire good, this reduction generates a loss in welfare. This loss comes about through the reduction in the home price index. In particular, looking at equations (17) and (18) we see that following an increase in the average age of the home population the increase in the foreign varieties is only τ * 1−σ < 1 times the absolute value of the decrease in home varieties: Hence, if τ and τ * are not too dierent, then the price index given in equation (11) must increase following the reduction in N M . Substituting the equilibrium consumption levels, prices, and income into equation (1) yields that social welfare can be written as Hence, an increase in the price index must decrease welfare of both age groups in the population.
It is interesting to compare the dierent eects of an aging population in trade and in autarky. From equation (10) we know that the total number of domestic manufacturing rms in autarky is given by N A M = LβΨ z and in trade it is given by equation (17). As population ages the dierence between these changes is given by the term reecting the foreign trade cost in the denominator.
15 Figure 1: Relative market size and production in manufacturing sector Hence, the change is larger in the trade case. Furthermore, this dierence become larger as the trade cost becomes smaller (becoming innite as τ approaches one). Increased globalization resulting in lower trade costs will, therefore, magnify the negative rm delocation eect resulting form an aging population. We summarize this result in proposition 3.
Proposition 3. An increase in the average age of a country will decrease its number of manufacturing rms by a larger amount under trade than under autarky. The ratio of these dierences is monotonically decreasing in trade costs and approaches innity (one) as trade costs approach one (innity). Increased globalization, as reected in lower trade costs, will magnify the rm delocation eect of an aging society.
We now consider how a country can inuence its share of manufactured goods by their choice of trade and immigration policy.

Immigration Policy
As noted in the previous section a country can aect their share of manufacturing production by increasing their market size or by changing their trade costs. We begin by considering a change in market size.
Apart from policies that encourage child rearing, an increase in market size may be produced by a more open immigration policy. An important caveat is that the eect of immigration depends on the age composition of the immigrants. In particular, the change in the home market size is given by the change in two terms: Ψ and L. Immigration clearly increases L, however, the eect on Ψ depends on the change in the relative number of young people. The change in the home market size can be decomposed into two terms as follows: where (γ G − γ R ) dη dL shows how Ψ changes with respect to immigration. This rst term is the age composition eect and the second term is the population eect. If the immigration policy accepts at least as many young as old people, then dη dL ≥ 0 and the immigration policy will increase the home market size. A more interesting case is if the inux is tilted towards older people, so that dη dL < 0 . In this case if (γ G − γ R ) is large, then increased immigration may paradoxically reduce the size of the home market for manufactured goods and generate a reduction in the share of home manufacturing rms. Hence, for immigration to increase the home market size Even if the average of the population increases age ( dη dL < 0) the above condition may be satised if the population is small in number (L), the dierence between young and old consumption patterns (γ G − γ R ) is small or the amount of purchased services is low. This third condition refers to the term in the numerator (Ψ) and this term is larger if γ G and γ R are both larger and/or labor productivity in services (χ) is lower. Either of these conditions will reduce the amount of purchased services. We state these results as proposition 4 below. Proposition 4. Immigration will increase the home country's share of manufacturing output if it does not increase the average age of the population. Even if the average age increases, the home country's share of manufacturing will increase along with increased immigration if the population is small, purchased services are a small percentage of total income, or the dierence between young and old consumption patterns is small.
The above result may help explain why many countries have instituted a point system for immigration and have reduced the role of family reunication. That is, a point system tends to reward youth and family reunication can be used to bring elderly parents.
An additional aspect of proposition 3 is that it suggests larger countries, or those with with greater labor productivity in services have the most reason to be selective in their immigration policy. As it is usually countries that have a combination of these aspects (large L and large χ) that are most desirable for immigrants, the restrictions in proposition 3 have economic signicance.
6 Tari Policy An additional way in which a country can aect its home market size is through trade policy. We now consider taris.
In analyzing tari policy remember that the trade cost for the home country is τ = θ(1 + t). Hence, taris magnify the eect of any transport cost. Looking at equation (19) for the home market shares in manufacturing, or at gure 1, we can see that an increase in the home tari will reduce the minimum home market share at which home manufacturing output is positive (N M > 0) and at which foreign output is zero (N M = 1). This change is illustrated in gure 2 below.
From gure 2 we can see that the shift of the breakpoints also shifts the segment of N M where both countries produce manufactured goods back towards the origin. Hence, an increase in the home tari must also increase the share of home manufacturing when both countries produce manufacturing goods. We can also see this result analytically from equation (19). It occurs because the increased home tari makes it more expensive to serve the home market relative to foreign. For any home market size more rms would want to locate in home and export to foreign. The home share of manufacturing output must, therefore, increase. Rather than dierentiating equation (19) it will prove more helpful to analyze the changes in home and foreign manufacturing separately as given in equations (17) and (18). Dierentiating each with respect to the home tari we have: An interesting implication of equation (25) is that the changes are fully osetting.
That is, an increase in the home country tari increases the number of rms locating in home and decreases the number locating in foreign by the same amount. The total number of rms stays the same. Furthermore, the eect is independent of the home market size.
If we then substitute equations (25) into the price index given in equation (11) we see that an increase in the home tari reduces the price index. This result occurs because the number of home and foreign rms each enters with a negative exponent, so that more rms reduces the index, and the number of foreign rms is multiplied by the home trade cost, τ . Hence, shifting rms from foreign to home must reduce the price index. Finally, from equation (21), this change must increase welfare. In fact, it would be unilaterally optimal for home to raise its tari until all manufacturing 19 rms were located in the home country. We summarize the results of this section in proposition 5 below.
Proposition 5. An increase in the home country tari does not change the total number of manufacturing rms. It increases the number of home rms and decreases the number of foreign rms by equal amounts. Home welfare is strictly increasing in the home tari as long as foreign manufacturing is positive (and it is non-negative otherwise). The eect of the home tari on rm location is increasing in the foreign market size but is independent of home market size.
Although proposition 5 suggests that a country could increase the number of domestically produce manufactured goods and domestic welfare by unilaterally increasing its import tari, it also indicates that the policy has strong beggar-thy-neighbor implications. Any manufacturing gain to the home country is oset by the loss to the foreign country. There is an additional loss in world welfare as a result of the iceberg trade cost.
This additional loss is relevant for two reasons. First, if the foreign country retaliates against the tari increase, then it is likely that both countries will be worse o in terms of welfare. To see the change in the number of rms in each country consider the case where the tari is the same in both countries. Taking the derivative of equation (19) with respect to this common tari yields that an increase in the common tari will increase a country's share of manufacturing rms if and only if it has a larger relative market size. Referring back to equations (17) and (18) we also see that a change in this common tari will not change the total number of rms. Foreseeing retaliation against its unilateral tari increase a country should, therefore, only increase its tari if it has the larger domestic market size. In as much as the tari is being considered as an antidote to a reduction in market size (as a result of the demand shift that accompanies an aging population), a country that is rendered smaller as a result of the demand shift would be most likely to lose from a tari war that accompanied any unilateral tari increase. We state this observation as corollary 6 below.
Corollary 6. An increase in the common tari will reduce the share of manufacturing rms in the country with the smaller domestic market size and increase it in the other country. All things equal, a country with a greater average age is more likely to lose from a tari war.

20
In addition to the potential for retaliation there is another limitation to mitigating the loss of manufacturing share through tari policy. The additional limitation is the dispensation of the tari proceeds. In the current framework, they have no eect on the model because they are assumed to melt away in the ocean. In as much as they are returned to the people in the country they could aect the composition of demand.
Although preferences are non-homothetic the marginal propensity to consume out of additional income does not depend on income as long as the assumption in equation (6) is satised. If it is not satised, then young people would not purchase services and the results of the model would be strengthened because an aging population would have even higher average purchases of services. If the tari revenue were sizable, then, in this case, it could generate a market demand for services by young people who would otherwise not purchase services solely out of wage income. Hence, any increase in manufacturing market share would be reduced by this added income eect. Although more of a theoretical curiosity, it is even possible for a unilateral tari increase to decrease a county's manufacturing share if the income eect is large enough. Alternatively, if the tari revenue was small, so that the young still did not consume services (if the assumption in equation 6 is not satised), then the domestic aggregate demand for manufactured goods would increase more rapidly in tari revenue than would services and the rm delocation eect of the tari would be augmented, however, by a smaller amount for an older country.

Conclusions
We consider the role of demand driven changes arising from population aging and how they aect the pattern of international trade as well as trade and immigration policy.
An aging society can see a welfare reducing reduction in its share of manufacturing output and this reduction is magnied by a decrease in trade costs (an increase in globalization). Immigration can ameliorate this outcome if it is directed towards younger immigrants. A unilateral tari increase can also reduce rm delocation from an aging country, however, a reciprocated tari increase will unambiguously harm the country with the older average population.