International Trade and Commercial Policy for Durable Goods

Review of International Economics, 8(2), 275–294, 2000

International Trade and Commercial Policy for Durable Goods Gregory E. Goering and Michael K. Pippenger* Abstract Many commodities traded internationally are durable in nature. A dynamic durable goods oligopoly trade model is analyzed. The analysis indicates that the pattern of intraindustry trade depends fundamentally on the quality or durability of the firms’ output. Indeed, product durability influences the effectiveness of commercial policy. For example, as domestic product durability rises, an increase in domestic tariffs has a smaller impact on domestic production. In addition, the model uncovers a previously unrecognized avenue by which product quality standards act as a barrier to trade.The results may help explain some of the empirical anomalies found in the literature.

1. Introduction While the standard Heckscher–Ohlin model provides many insights into the determinants of the pattern of international trade, one failing of this model is its inability to explain why a country will simultaneously import and export identical or very similar products. Over recent years, starting with Balassa (1966), significant efforts have been made to both define and explain this intraindustry trade. Theoretical models attempting to explain intraindustry trade fall into three broad classes. The neo-Heckscher–Ohlin models modify the standard Heckscher–Ohlin model. One modification to the standard model is to include vertical product differentiation (Falvey, 1981). This modification indicates that a country will specialize in particular differentiated products depending upon that country’s factor endowments. In another extension of the Heckscher–Ohlin model, Davis (1995) develops a Heckscher– Ohlin–Ricardo model and finds that intraindustry trade may result owing to comparative advantage.1 On the other hand, the monopolistic competition trade models, such as those of Krugman (1979) and Helpman (1981), are constructed by assuming one industry produces horizontally differentiated products which employ economies-ofscale technologies. In these models, specialization occurs within the horizontally differentiated industry resulting from economies of scale leading to intraindustry trade.2 Lastly, oligopoly trade models (Brander, 1981; Brander and Krugman, 1983; Brander and Spencer, 1981; Hwang, 1984) construct partial equilibrium models where both domestically and internationally the export commodity market is described by a Cournot model. Intraindustry trade occurs in these models as a natural result of each firm obtaining a share of both the foreign and domestic market. One aspect that the three types of intraindustry trade models have in common is that they examine nondurable commodities.3 However, apart from agricultural commodities, international trade is overwhelmingly composed of durable goods. Clearly, product durability may not only affect the pattern of trade but may also potentially

* Goering: University of Alaska, PO Box 756080, Fairbanks, AK 99775-6080, USA. Tel: 907-474-5572; Fax 474-5219; E-mail: [email protected]. Pippenger: University of Alaska, PO Box 756080, Fairbanks, AK 997756080, USA. Tel: 907-474-6530; Fax 474-5219; E-mail: [email protected]. We wish to thank an anonymous referee for many helpful comments and suggestions. The responsibility for any remaining errors or omissions is, of course, ours. © Blackwell Publishers Ltd 2000, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA

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alter the effects of commercial policy. For example, consider a perfectly durable good; that is, a good which once purchased provides a service stream into the infinite future. Suppose the good is exported and is subjected to a tariff when shipped to the foreign country in the first period. Now consider a nondurable which provides exactly the same service. Since the good is nondurable, in order to generate the same service flow as the perfectly durable good, the good must be shipped to the foreign country each period, resulting in tariff revenue not only in the first period but in all subsequent periods. In a sense, product durability circumvents future tariffs. As the above simple example illustrates, the inclusion of product durability in a model of international trade should provide further insight into the pattern of trade and the effect of commercial policy when goods are durable. Indeed, our model suggests that the expected pattern of trade depends fundamentally on the durability or quality of the country’s output. For example, the analysis shows that if the foreign country manufactures a product of higher durability or quality, current home exports to this country fall but future exports rise. In addition, the model shows that the cumulative effect of higher foreign product durability upon domestic exports is negative. In terms of tariffs, the model indicates that if the home country’s product is durable (e.g., automobiles), an increase in the current tariff will increase current production destined for the home market but decrease future production. The model also shows that the ability of tariff protection to spur cumulative production is diminished the more durable the domestic product. Furthermore the model shows that domestic product quality standards may help insulate domestic exporters from changes in foreign import tariffs and domestic producers from the effects of foreign export subsidies.

2. A Basic Trade Model when Goods are Durable To analyze the impact of durable goods on the pattern of trade, we utilize a simple two-country trade model where the countries are indexed A and B. In country A there are nA ≥ 1 firms while in country B there are nB ≥ 1 firms. These firms manufacture durable output over a two-period horizon. The durable output can be sold in the domestic market or it can be exported. The durability of the output manufactured in country A is given by d A Œ [0, 1], where A d is the fraction of a unit of period-one output that survives and is available for use in the second period. Thus if the good is nondurable d A = 0, and no first-period units remain in service in period two. On the other hand, when d A = 1 the good is perfectly durable and all period-one units remain for use in the second period. Similarly d B Œ [0, 1] is the durability of country B’s output.4 With this specification in mind we can characterize the stock and flow of durable production in each period. Since a firm’s output will be destined for either the home market or foreign market we must distinguish between output allocated in these different markets. Let q1iA and qA2i represent the output produced for country A’s home market by firm i in country A in periods one and two, respectively. Further, let yA1i and yA2i represent the output in each period manufactured by firm i in country A that is to be exported to country B. Thus in the model the superscripts always denote the country of origin, while the subscripts show the date- and firm-specific information.5 Note that the outputs qA1i, qA2i, yA1i, and yA2i represent the periodic production flows of firm i in country A; i.e., the physical amounts manufactured in each period for each market. If we assume that the stock of durables is initially zero, then there is a one-toone correspondence between the output stock and flows in the first period. In other words, the total amount available for use in country A’s home market is simply the © Blackwell Publishers Ltd 2000

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total amount produced for home country use by the firm’s located in country A plus the total exports from country B in the period. This implies that nA

nB

Q = Â q + Â y1Bi A 1

A 1i

i =1

(1)

i =1

is the total market quantity available in country A in the first period. In the second period the total stock for use depends upon the durability of the home country’s output as well as the exporting country’s product durability. The total stock available for use in country A’s home market has two components: (1) the aggregate production in period two for the domestic market produced either in country A or imported from country B, and (2) any of the durable units used in period one which still remain in service in period two. Thus, the total stock of output available for use in country A in period two is given by nA

nA

nB

nB

Q2A = d A Â q1Ai + Â q2Ai + d B Â y1Bi + Â y2Bi . i =1

i =1

i =1

(2)

i =1

Note that (2) shows that if all the output is nondurable (d A = d B = 0) the second-period stock QA2 is simply the amount of period-two home country production plus imports.6 We suppose that the inverse service demands are linear for periods one and two in country A and are given by p1A = a1 - bQ1A ,

(3)

p2A = a2 - bQ2A ,

(4)

respectively. This specification implies the level of demand (choke price) in each period need not be the same (e.g., a1 π a2). Note also that (3) and (4) represent the inverse demands for service of the durable goods in each period, implying that pA1 and pA2 are the rental prices of a unit of production in each period. The asset or selling price of a durable unit in period one is, of course, the discounted stream of rental services the unit provides. Suppose firms in country A possess the same linear cost function. Let the constant marginal manufacturing cost in country A be cA > 0 for each firm. In addition, suppose that when production is exported a tariff may be incurred or a subsidy may be paid. This implies that firm i in country A will have the following profit function: p iA = ( p1A - c A )q1Ai + ( p1B - c A - t1B + s1A ) y1Ai + g ((d A q1Ai + q2Ai ) p2A - c A q2Ai + (d A y1Ai + y2Ai ) p2B - (c A + t 2B - s 2A ) y2Ai ),

(5)

where g Œ [0, 1] is the discount factor, tB1 ≥ 0 and tB2 ≥ 0 represent the specific tariffs incurred by a firm in A when a unit of production is exported to country B in periods one and two, respectively, and sA1 ≥ 0 and sA2 ≥ 0 represent the specific subsidy paid to firms in country A for each unit exported.7 Note that the firm’s profit (5) depends upon prices in both countries as well as the production costs, tariffs, and export subsidies. In particular, (5) captures the durable nature of firm i’s output. We can break (5) into two components based on domestic and exported production. In terms of domestic production destined for the home country’s market, the total discounted profit of a durable unit is simply the first-period service price net of costs plus the second-period service price adjusted by the discount © Blackwell Publishers Ltd 2000

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factor and the fraction of the unit that remains for use. In other words, a durable unit of production provides service or value in both periods (e.g., can be rented in both periods). Thus discounted profit of firm i resulting from production destined for the domestic market is

( p1A - c A )q1Ai + g ((d A q1Ai + q2Ai ) p2A - c A q2Ai ). If the firm produces and rents qA1i units in period one domestically, it can rent the fraction dAqA1i again in period two along with any second-period domestic production qA2i. A similar logic applies for any exports, which indicates that the discounted export profits are

( p1B - c A - t1B + s1A ) y1Ai + g ((d A y1Ai + y2Ai ) p2B - (c A + t 2B - s2A ) y2Ai ). If we combine these two expressions we get the full discounted profit function found in (5). It is worth noting that although the preceding discussion of the profit function in (5) suggests a rental interpretation, (5) can also be viewed as a seller’s profit function. There is a close relationship between rental and sales since a unit of durable production can be viewed as a durable asset. Thus the asset or sales price of a durable unit is simply the discounted stream of rental prices. For example, since the rental price of a durable unit in country A in periods one and two are pA1 and pA2 , the asset or selling price in the first period in country A is q 1A = p1A + gd A p2A . Similarly, for exports of country A to country B the sales price in period one is q 1B = p1B + gd A p2B . This indicates that we can rewrite the profit function (5) as p iA = (q 1A - c A )q1Ai + (q 1B - c A - t1B + s1A ) y1Ai + g (q2Ai q 2A - c A q2Ai + y2Ai q 2B - (c A + t 2B - s 2A ) y2Ai ),

(5¢)

where the sales prices in period two are simply the rental prices (i.e., q A2 = pA2 and q B2 = pB2 . Observe that (5) and (5¢) are equivalent and it is only a matter of preference which form is used (in a standard nontrade durable goods framework, see Bulow (1982) versus Bulow (1986)). Hence, (5) can be viewed as either a renter’s or seller’s discounted profit function. However, as Coase (1972) and Bulow (1982, 1986) note, even though renting and selling firms may have the same discounted profit function, that does not necessarily imply they face the same sort of constraints or that the resulting optimal solutions are the same. If a firm sells only its durable output it is constrained by buyers’ expectations about the future price of the unit (asset value). If, on the other hand, the firm rents only its durable output, consumers’ expectations do not play a role and, consequently, the renter’s optimal solution may differ from the seller’s. Indeed, Coase (1972) noted that rational buyers would realize that the firm in a future period would have an incentive to drop the price (increase production) since the loss in value of the existing stock is borne by buyers and not the firm. If the good is always rented the firm owns the entire stock at each point in time, and hence internalizes this capital loss. In other words, when a unit is sold consumers’ rational expectations may constrain the firm while in rental solutions they do not. Thus, even though the discounted profit func© Blackwell Publishers Ltd 2000

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tions are the same for a renter and seller, the seller may face an added constraint which tends to lessen their optimal profits. A large literature has developed which has examined Coase’s conjecture and the conditions under which the seller’s solution may differ from the renter’s (Bulow, 1982; 1986; Butz, 1990; Purohit 1995). Basically, the analyses suggest that if a firm cannot credibly commit to buyers that it will take into account their future capital losses in its production decisions, a seller tends to earn less profit than a renter. Thus uncommitted sellers typically are assumed to earn less profit than renters owing to the buyers’ exceptional constraint. However, Butz (1990) among others has shown that if the firm can commit to buyers through best-price clauses or other contractual provisions, the seller and renter once again earn the same profit and the resulting solutions are timeconsistent. In essence, the committed sales solution and renter’s solution are identical but typically distinct from the uncommitted sales solution. As in other game-theoretic models, the role of commitment ability can be captured by the notion of subgame perfection. The uncommitted sales solution is typically subgame-perfect while the committed sales solution typically is not. In terms of the current model this implies that, even though (5) can be viewed as a discounted profit function for either a renting or selling firm, the optimal Nash solution to (5) is not subgame-perfect, at least in terms of sales. Unfortunately, in this trade model the subgame-perfect solutions are intractably complex, and so only Nash solutions are calculated. Thus, strictly speaking, the subsequent solutions and analysis in the following sections are valid only for durable-goods sellers with commitment power or for firms that rent their output.8 The assumption of commitment ability on the part of the selling firms is not as onerous as one may think, since as noted above previous durability studies have shown standard contracting tools (e.g., best-price provisions) would give this commitment ability. Furthermore, as is well known, tariffs and quotas typically themselves lead to dynamic inconsistency (i.e., the solutions are not subgameperfect) unless the controlling government bodies can somehow commit themselves to a stream of future tariffs and quotas.

3. Trade in Durable Goods The maximization of (5) with respect to first- and second-period domestic and exported outputs qA1i, qA2i, yA1i, and yA2i gives the following first-order conditions for firm i in country A: ∂p iA = a1 - bQ1A - bq1Ai - c A + gd A (a2 - bQ2A - b(d A q1Ai + q2Ai )) = 0, ∂ q1Ai

(6)

∂p iA = g (a2 - bQ2A - b(d A q1Ai + q2Ai ) - c A ) = 0, ∂ q2Ai

(7)

∂p iA = a1 - bQ1B - by1Ai - c A - t1B + s1A + gd A (a2 - bQ2B - b(d A y1Ai + y2Ai )) = 0, ∂ y1Ai

(8)

∂p iA = g (a2 - bQ2B - b(d A y1Ai + y2Ai ) - c A - t 2B + s 2A ) = 0, ∂ y2Ai

(9)

for all i = 1 to nA, where the stocks of output (e.g., QA1 and QA2 ) are defined in (1) and (2), respectively.9 A similar set of conditions, of course, hold for the i = 1 to nB firms in country B.10 © Blackwell Publishers Ltd 2000

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These first-order conditions show that at the margin firms equate the manufacturing cost inclusive of any tariffs or subsidies to the discounted revenues provided by a durable unit. For example, (6) indicates that a unit of durable (d A > 0) domestic production provides revenues in periods one and two, so the firm rationally equates the discounted present value of this marginal revenue to the first-period marginal production cost, cA. If the firm’s output is nondurable (d A = d B = 0) we see that (6)–(9) collapse to simple static conditions; i.e., intertemporally unrelated conditions. Given the complexity and number of first-order conditions, we now exploit the symmetry of the model; i.e., the same durability and production costs intracountry. This allows us to collapse the number of relevant first-order conditions to a manageable number so that the optimal production outputs home and abroad may be solved. Since the firms in a given country have the same product durability and production costs, we can rewrite (6)–(9) in terms of a symmetrical solution ignoring the firm subscripts as ∂p A = a1 - bn B y1B - b(n A + 1)q1A - c A ∂ q1A + gd A(a2 - bn B (d B y1B + y2B ) - b(n A + 1)(d A q1A + q2A )) = 0, ∂p A = g (a2 - bn B (d B y1B + y2B ) - b(n A + 1)(d A q1A + q2A ) - c A ) = 0, ∂ q2A

(10) (11)

∂p A = a1 - bn B q1B - b(n A + 1) y1A - c A - t1B + s1A ∂ y1A + gd A(a2 - bn B (d B q1B + q2B ) - b(n A + 1)(d A y1A + y2A )) = 0, ∂p A = g (a2 - bn B (d B q1B + q2B ) - b(n A + 1)(d A y1A + y2A ) - c A - t 2B + s 2A ) = 0. ∂ y2A

(12) (13)

These intracountry symmetric first-order conditions hold for all nA firms in country A. Note that (10)–(13) exploit the symmetry within a given country but not across countries. Thus, for example, we do not assume that qA1 necessarily equals qB1 , owing to the different production costs and durability in each country. Remembering that the four intracountry symmetric first-order conditions for firms in country B can be found by simply interchanging the superscripts, we can solve for the intracountry symmetrical outputs and analyze durability’s impact on the pattern of trade. Using (10)–(13) and the analogous equations for country B, we find that the optimal output values for an individual firm in country A are q1A =

a1 - c A (1 - gd A )(1 + n B ) + n B (c B (1 - gd B ) + t1A - s1B - gd B (t 2A - s 2B )) , b(1 + n A + n B )

(14)

q2A =

a2 - (1 + n B )c A + n B (c B + t 2A - s 2B ) - d A q1A , b(1 + n A + n B )

(15)

y1A =

a1 + n B c B (1 - gd B ) + (1 + n B )(( s1A - t1B - c A ) - gd A ( s 2A - t 2B - c A )) , b(1 + n A + n B )

(16)

y2A =

(a2 + n B c B + (1 + n B )( s2A - t 2B - c A )) A A - d y1 . b(1 + n A + n B )

(17)

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As expected, the firm’s optimal outputs fundamentally depend not only on the standard parameters, such as the number of firms, tariffs, export subsidies, and manufacturing costs in each country, but also on the product durabilities, d A and d B. By differentiating these optimal production levels we can ascertain the impact of the various parameters on the trade flows over time. To show the impact of a change in country A’s product durability on the production levels in country A, (14)–(17) are differentiated with respect to d A, which yields ∂ q1A g c A (1 + n B ) = > 0, ∂d A b(1 + n A + n B )

∂ q2A Ê A ∂ q1A ˆ = + q1A ˜ < 0, Ád A A Ë ¯ ∂d ∂d

∂ (q1A + q2A ) ∂ q1A = (1 - d A ) A - q1A . A ∂d ∂d

(18)

∂ y1A g (1 + n B )(c A + t 2B - s 2A ) ∂ y2A ∂ y1A Ê ˆ = > 0, = -Á d A A + y1A ˜ < 0, A A B A Ë ¯ ∂d b(1 + n + n ) ∂d ∂d A ∂ ( y1A + y2A ) A ∂ y1 ( ) 1 d = - y1A , ∂d A ∂d A

(19)

which is summarized in Proposition 1. Proposition 1. As country A’s product durability increases, its own production levels in period one will increase while those in period two will decrease; i.e., ∂qA1 /∂d A > 0, ∂yA1 /∂d A > 0, ∂q2A/∂d A < 0, and ∂yA2 /∂d A < 0. The impact of product durability on cumulative production levels ∂(qA1 + qA2 )/∂d A and ∂(yA1 + yA2 )/∂d A, however, is ambiguous. Proposition 1 indicates that as the home country’s product durability is increased, firms will increase first-period home country production but decrease second-period production (see (18)).This is a standard durability result.As the product becomes more durable the firm can provide more second-period service from a given unit of firstperiod production. Thus, at the margin, the benefit of an additional unit of first-period production is increased and, consequently, first-period production rises. On the other hand, since more second-period service is being provided by remaining first-period units, the firm will optimally decrease the amount manufactured in the second period. In essence, the firm can decrease its discounted production costs by increasing firstperiod production and decreasing second-period production as product durability rises. The derivatives in (19) show that a similar pattern holds for country A’s exported production. Thus as the durability of a country’s output is increased we may expect an increase in current exports but a decrease in future exports.11 Interestingly, the effect of domestic durability upon cumulative production for the domestic market, ∂(qA1 + qA2 )/∂d A, and cumulative exports, ∂(yA1 + yA2 )/∂d A, is ambiguous.12 This ambiguity is due to the fact that the magnitude of the second-period effect is determined partly by first-period production levels. We can also examine the impact of the foreign country’s product durability by differentiating with respect to d B, yielding ∂ q1A g n B (c B + t 2A - s 2B ) ∂ q2A d Ag n B (c B + t 2A - s 2B ) = < 0 , = > 0, ∂d B b(1 + n A + n B ) ∂d B b(1 + n A + n B ) ∂ (q1A + q2A ) (d A - 1)g n B (c B + t 2A - s 2B ) = < 0. ∂d B b(1 + n A + n B )

(20) © Blackwell Publishers Ltd 2000

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∂ y1A g nB c B ∂ y2A d Ag n B c B = < 0 , = > 0, ∂d B b(1 + n A + n B ) ∂d B b(1 + n A + n B ) ∂ ( y1A + y2A ) (d A - 1)g n B c B = < 0. ∂d B b(1 + n A + n B )

(21)

Proposition 2. As country B’s product durability increases, country A’s production levels in period one will decrease while those in period two will increase; i.e., ∂qA1 /∂d B < 0, ∂yA1 /∂d B < 0, ∂qA2 /∂d B > 0, and ∂yA2 /∂d B > 0. Cumulative production levels will also tend to decrease: ∂(qA1 + qA2 )/∂d B < 0 and ∂(yA1 + yA2 )/∂d B < 0. Proposition 2 indicates that, as the durability of the foreign country’s output rises, home country production and exported production both fall in period one but rise in period two. Intriguingly, (20) and (21) show that, while the corresponding increase in home and exported production in period two depends critically on the home country’s own product durability, d A, the decrease in first-period output does not. For example, if country A’s output is almost perfectly nondurable, there is no change in country A’s second-period home or exported production as d B increases, but country A’s firstperiod output still declines in both the home and export markets. This indicates that the pattern of trade depends critically on each country’s product durability. In general, for durable traded goods we would expect country A’s current exports to fall but future exports to country B to rise as country B manufactures a product of higher durability or quality. The cumulative effect of an increase in foreign durability upon domestic production, ∂(qA1 + qA2 )/∂d B, and upon domestic exports, ∂(yA1 + yA2 )/∂d B, is negative as Proposition 2 notes. This second result sheds additional light on the use of product quality standards as a barrier to trade. Typically when product quality standards are discussed as a barrier to trade, the effect of this barrier is usually thought to result from simply increasing the cost of production for foreign firms. Thus, product quality standards will tend to decrease imports owing to an increase in the price of foreign goods. However, when a government sets a product quality standard, that standard is usually imposed upon both foreign and domestic manufacturers.13 As (21) shows, if quality can be proxied by product durability, when the government in country B increases product quality standards and simply causes country B’s product quality to rise, B will import less in the first period and cumulatively. Hence the model illustrates that, in addition to the usual avenue by which product standards act as a barrier to trade, they also may act as a barrier owing to the intertemporal effects of product durability.14

4. Tariffs when Goods are Durable Since the model also contains parametric information on the effect of tariffs and subsidies, we can explore the impact of changes in the tariff and subsidy structure on the pattern of trade. Differentiating (14)–(17) with respect to country A’s tariff levels in each period yields ∂ q1A nB ∂ q2A d A nB = > 0 , = < 0, ∂ t1A b(1 + n A + n B ) ∂ t1A b(1 + n A + n B )

(1 - d A )n B ∂ (q1A + q2A ) = > 0, A ∂ t1 b(1 + n A + n B ) © Blackwell Publishers Ltd 2000

(22)

COMMERCIAL POLICY FOR DURABLE GOODS

∂ y1A = 0, ∂ t1A

∂ y2A = 0, ∂ t1A

∂ ( y1A + y2A ) = 0, ∂ t1A

283 (23)

∂ q1A gd B n B ∂ q2A (1 + gd Ad B )n B = < 0 , = > 0, ∂ t 2A b(1 + n A + n B ) ∂ t 2A b(1 + n A + n B ) ∂ (q1A + q2A ) (1 - g (1 - d A )d B )n B = > 0, ∂ t 2A b(1 + n A + n B )

(24)

∂ ( y1A + y2A ) = 0. ∂ t 2A

(25)

∂ y1A = 0, ∂ t 2A

∂ y2A = 0, ∂ t 2A

Proposition 3. Although an increase in country A’s first-period tariff does not affect its exports, its own domestic production levels in periods one and two increase and decrease, respectively, while cumulative production increases; i.e., ∂yA1 /∂tA1 = ∂yA2 /∂tA1 = 0, ∂qA1 /∂tA1 > 0, ∂qA2 /∂tA1 < 0, and ∂(qA1 + qA2 )/∂tA1 > 0. In contrast, as A’s period-two tariff is increased, its own domestic production levels in periods one and two decrease and increase: ∂qA1 /∂tA2 < 0 and ∂qA2 /∂tA2 > 0. However, domestic cumulative production still tends to increase and export levels remain unchanged; i.e., ∂(qA1 + qA2 )/∂tA2 > 0 and ∂(yA1 + yA2 )/∂tA2 = 0. Proposition 3 indicates, as expected, that a change in country A’s own tariff level does not impact the country’s own exports contemporaneously or intertemporally regardless of the product’s durability.15 On the other hand, changes in the periodic tariffs will influence the time path of output produced for the domestic market. If the product is durable, we see from (22) that, as the government increases the first-period tariff, first-period domestic output destined for the home market increases but secondperiod output decreases in direct proportion. This proportional decrease is due, once again, directly to the durability of the product. As the tariff is increased, imports in period one tend to drop, so domestically marketed production tends to rise. If the product is durable, this causes a corresponding reduction in domestically marketed production in the second period. Thus with durable traded goods, such as automobiles, a change in a tariff will impact the flow of domestically marketed goods over time. The magnitude of these effects depends on the number of foreign and domestic firms (i.e., the relative degree of competition within each country) and the durability of domestic production. Note that while the cumulative effect of an increase in t A1 upon domestic production, ∂(qA1 + q2A)/∂tA1 , is positive, the magnitude of the cumulative change decreases as domestic product durability, dA, rises. Thus, the ability of tariff protection in the first period to spur cumulative production is diminished the more durable the domestic product. Indeed, as the domestic product approaches perfect durability there is essentially no change in cumulative domestically marketed production as t A1 increases. From (24) it is also clear that an increase in a future domestic tariff impacts not only future production, but also the current production of durable goods. An increase in a future domestic tariff that is well publicized may induce the home country’s durable goods manufacturers to decrease their current production while increasing their future production. The magnitude of the change in domestic production depends upon the number of foreign and domestic firms as well as domestic and foreign product durability. As foreign product durability d B rises, an increase in the second-period tariff will result in a larger drop in first-period domestic production and a larger rise in © Blackwell Publishers Ltd 2000

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second-period domestic production. The higher the durability of domestic production, the larger the increase in second-period production when t A2 increases. While the cumulative effect of an increase in t A2 upon domestic production is positive, the magnitude of the change is positively related to d A and negatively related to d B. Once again, the ability to affect a cumulative change in domestic production is determined in part by product durability. In this case the effectiveness of future tariff policy increases as d A increases or as d B decreases. Interestingly, if quality is proxied by product durability, an increase in government mandated quality standards affecting only domestic producers increases the cumulative effect of a change in future domestic tariffs upon domestic production. On the other hand, if an increase in domestic product quality standards affects only foreign producers, there is a decrease in the effectiveness of a change in the second-period tariff upon domestic production. Another area of interest is the effect of a change in the foreign country’s tariff on the home country’s production and exports. Differentiating (14)–(17) with respect to country B’s tariffs gives ∂ q1A = 0, ∂ t1B

∂ q2A = 0, ∂ t1B

∂ (q1A + q2A ) = 0, ∂ t1B

∂ y1A 1 + nB < 0, = ∂ t1B b(1 + n A + n B )

(26)

∂ y2A d A (1 + n B ) = > 0, ∂ t1B b(1 + n A + n B )

(1 - d A )(1 + n B ) ∂ ( y1A + y2A ) =< 0, B ∂ t1 b(1 + n A + n B ) ∂ q1A = 0, ∂ t 2B

∂ q2A = 0, ∂ t 2B

(27)

∂ (q1A + q2A ) = 0, ∂ t 2B

(

(28) 2

)

1 + g (d A ) (1 + n B ) ∂ y1A gd A (1 + n B ) ∂ y2A = , > 0 = < 0, ∂ t 2B b(1 + n A + n B ) ∂ t 2B b(1 + n A + n B )

(1 - g (1 - d A )(d A ))(1 + n B ) ∂ ( y1A + y2A ) = < 0, ∂ t 2B b(1 + n A + n B )

(29)

which is summarized in Proposition 4. Proposition 4. Although an increase in country B’s first- or second-period tariff does not affect country A’s domestic production (∂qA1 /∂tB1 = ∂qA2 /∂tB1 = ∂qA1 /∂tB2 = ∂qA2 /∂tB2 = 0), these tariffs do impact country A’s exports. In particular, the exported production level in period one decreases and in period two increases and the cumulative production decreases as tB1 increases; i.e., ∂yA1 /∂tB1 < 0, ∂y2A/∂tB1 > 0, and ∂(yA1 + yA2 )/∂tB1 < 0. Similarly, as the second-period tariff tB2 is increased, period-one exports will decrease, periodtwo exports will decrease and cumulative exports will decrease. Proposition 4 shows that as the foreign country’s tariff level rises in either period it has no impact on the home country’s domestically marketed output, irrespective of product durability ((26) and (28)). Once again, if country A’s output is durable there is an intertemporal linkage, so changes in a given period’s tariff causes a change in trade in both periods. For example, (27) indicates that, if the traded good is durable, an increase in the foreign country’s first-period tariff tB1 leads to a decline in country

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A’s first-period exports and an increase in second-period exports. Firms will shift away from exporting in the first period and toward the second period, thus partially circumventing the tariff barrier. Also note, as dA rises, the magnitude of ∂yA2 /∂tB1 increases. The cumulative effect of a rise in tB1 upon exports is negative, but the cumulative effect upon exports will be smaller in magnitude the more durable the domestic product. In the extreme case when the domestic product approaches perfect durability, an increase in tB1 does not effect country A’s cumulative exports. Thus, a higher domestic product durability, in a sense, insulates the domestic economy from changes in tB1 . The effect of a change in tB2 is found in (29). When tB2 increases, first-period exports rise and second-period exports decline while the cumulative effect upon domestic exports is negative. This occurs because domestic firms shift toward period-one exports and away from period-two exports when the anticipated period-two tariff increases. In effect, firms will shift exports toward the first period in order to avoid the future tariff barrier. However, in this case the impact of domestic product durability upon the magnitude of the change in cumulative exports is ambiguous. We can also examine the case where the tariffs are equal over time; i.e., t A1 = t A2 = t A and t B1 = t B2 = t B. Differentiating (14)–(17) with respect to tA gives

(1 - gd B )n B ∂ q1A ∂ q2A (1 - d A (1 - gd B ))n B = > 0, = > 0, A A B ∂t b(1 + n + n ) ∂t A b(1 + n A + n B ) ∂ (q1A + q2A ) (1 + (1 - d A )(1 - gd B ))n B = > 0, ∂t A b(1 + n A + n B ) ∂ y1A = 0, ∂t A

∂ y2A = 0, ∂t A

(30)

∂ ( y1A + y2A ) = 0. ∂t A

(31)

Proposition 5. Although an increase in country A’s common tariff level does not affect its exports, its own domestic production levels in periods one and two are both increased; i.e., ∂yA1 /∂t A = ∂yA2 /∂t A = 0, ∂qA1 /∂t A > 0, ∂qA2 /∂t A > 0, and ∂(qA1 + qA2 )/∂t A > 0. For the case where t A1 = t A2 = t A, (31) indicates that country A’s own common tariff level does not affect its exports, as expected. In contrast, from (30) as the common (equal) tariff in each period is increased, domestic production for the home market increases in both periods. However, the more durable the foreign good, the smaller the impact upon qA1 and the larger the impact upon qA2 . The cumulative effect of an increase in t A declines as either d A or d B increases. Thus, the ability of domestic tariff policy to protect the domestic industry is negatively related to product durability in this case. We can carry out a similar exploration for changes in country B’s own common tariff level, t B. Differentiating (14)–(17) with respect to t B gives ∂ q1A = 0, ∂tB

∂ q2A = 0, ∂tB

∂ (q1A + q2A ) = 0, ∂tB

(32)

(1 - gd A )(1 + n B ) (1 - d A (1 - gd A ))(1 + n B ) ∂ y1A ∂ y2A = < 0 , = < 0, ∂tB b(1 + n A + n B ) ∂tB b(1 + n A + n B ) (1 + (1 - d A )(1 - gd A ))(1 + n B ) ∂ ( y1A + y2A ) =< 0. B ∂t b(1 + n A + n B )

(33)

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Proposition 6. Although an increase in country B’s first- or second-period tariff does not affect country A’s domestic production (∂qA1 /∂tB = ∂qA2 /∂tB = ∂(qA1 + qA2 )/∂tB = 0), these tariffs do impact country A’s exports. In particular, exported production levels in both periods decrease: ∂yA1 /∂tB < 0, ∂yA2 /∂tB < 0, and ∂(yA1 + yA2 )/∂tB < 0. From this proposition we see that, although the foreign country’s common (equal) tariff in each period still does not change country A’s domestic output levels, it does decrease exports in both periods. Note again that (33) demonstrates that the magnitude of the decrease in country A’s exports is affected by the degree of product durability. The magnitude of the first-period change declines the more durable the domestic product, but product durability has an ambiguous impact upon the magnitude of the decline in second-period exports. The cumulative effect of an increase in the foreign tariff upon country A’s exports is always negative, and the magnitude of this decline is smaller the more durable the domestic product. Once again, higher domestic product durability helps insulate exports from the foreign country’s tariff policies. What the above results show is that, while an increase in domestic durability may enhance or diminish the effectiveness of domestic tariff policies, an increase in domestic product durability or quality will tend to diminish the effect of foreign tariffs on domestic exports. Therefore, while domestic product quality standards may act as a barrier to trade, these standards may also help insulate a country’s exports from change in foreign tariffs when these standards increase domestic product durability. In addition, the above results may shed light on recent empirical findings regarding the effect of tariffs upon intraindustry trade. Often, when a regression involving the determinants of intraindustry trade is estimated, the estimated parameter for the effect of domestic tariffs upon imports is frequently found to be statistically insignificant, of the incorrect sign, and sensitive to model specification or data periods (Torstensson, 1996). As the above results show, when domestic tariffs rise, the cumulative effect upon domestic imports is always negative; but as product durability rises, the magnitude of the effect falls (in absolute value). Hence, for highly durable goods an increase in tariffs has a relatively small cumulative effect upon intraindustry trade, leading to these apparently anomalous statistical results. Our results may also explain the instability of parameter estimates over time, since different sample periods will tend to possess goods of different durability or quality.

5. Export Subsidies when Goods are Durable Next, we can examine the effect of changes in the subsidy structure upon the pattern of trade. Differentiating (14)–(17) with respect to domestic subsidy level in each period yields ∂ q1A = 0, ∂ s1A

∂ q2A = 0, ∂ s1A

∂ (q1A + q2A ) = 0, ∂ s1A

∂ y1A 1 + nB = > 0, ∂ s1A b(1 + n A + n B )

∂ y2A d A (1 + n B ) = < 0, ∂ s1A b(1 + n A + n B )

∂ ( y1A + y2A ) (1 - d A )(1 + n B ) = > 0, ∂ s1A b(1 + n A + n B ) ∂ q1A = 0, ∂ s 2A

∂ q2A = 0, ∂ s 2A

© Blackwell Publishers Ltd 2000

(34)

∂ (q1A + q2A ) = 0, ∂ s 2A

(35)

(36)

COMMERCIAL POLICY FOR DURABLE GOODS

∂ y1A gd A (1 + n B ) =< 0, A ∂ s2 b(1 + n A + n B )

(

2

287

)

1 + g (d A ) (1 + n B ) ∂ y2A = > 0, ∂ s 2A b(1 + n A + n B )

∂ ( y1A + y2A ) (1 - g (1 - d A )d A )(1 + n B ) = > 0. ∂ s 2A b(1 + n A + n B )

(37)

Proposition 7. Although an increase in country A’s first- or second-period subsidy does not affect its domestic production, its export levels in periods one and two are changed. An increase in the period-one subsidy increases and decreases first- and second-period exports, respectively, while cumulative production increases (∂yA1 /∂sA1 > 0, ∂yA2 /∂sA1 < 0, and ∂(yA1 + yA2 )/∂sA1 > 0). In contrast, as its period-two subsidy sA2 is increased, its export levels in periods one and two decrease and increase, respectively, but domestic cumulative export production still tends to increase (∂yA1 /∂sA2 < 0, ∂yA2 /∂sA2 > 0, and ∂(yA1 + yA2 )/∂sA2 > 0). Proposition 7 shows again, as expected, changes in domestic export subsidies do not affect production for the domestic market. However, while an increase in the firstperiod domestic subsidy increases country A’s exports in the first period, second-period exports will fall and the magnitude of the decline is determined by d A, the durability of the domestic product. This occurs owing to the increase in first-period exports. The higher the durability of the domestic good, the larger quantity is carried into the subsequent period, and hence the smaller the level of export production in that period. Note that the cumulative change in exports is positive; and as domestic product durability rises, an increase in the first period subsidy will have a smaller effect upon cumulative exports. If the good is nearly perfectly durable, changes in first-period subsidies would have little to no effect upon cumulative exports. With respect to changes in the second-period subsidy, (34) indicates that, as the second-period domestic subsidy increases, first-period exports decrease and secondperiod exports increase and the magnitudes of those changes increase as domestic product durability increases. The cumulative effect of an increase in sA2 on exports is positive, but domestic product durability has an ambiguous effect on the magnitude of this change. In order to explore the effect of changes in foreign subsidies, (14)–(17) are differentiated with respect to country B’s first- and second-period export subsidies, which leads to ∂ q1A nB ∂ q2A d A nB = < 0 , = > 0, ∂ s1B b(1 + n A + n B ) ∂ s1B b(1 + n A + n B )

(1 - d A )n B ∂ (q1A + q2A ) =< 0, B ∂ s1 b(1 + n A + n B ) ∂ y1A = 0, ∂ s1B

∂ y2A = 0, ∂ s1B

∂ ( y1A + y2A ) = 0, ∂ s1B

(38)

(39)

(1 + gd Ad B )n B ∂ q1A gd B n B ∂ q2A = 0 > , = < 0, ∂ s 2B b(1 + n A + n B ) ∂ s 2B b(1 + n A + n B ) (1 - g (1 - d A )d B )n B ∂ (q1A + q2A ) =< 0, B ∂ s2 b(1 + n A + n B )

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∂ y1A = 0, ∂ s 2B

∂ y2A = 0, ∂ s 2B

∂ ( y1A + y2A ) = 0. ∂ s 2B

(41)

Proposition 8. Although an increase in country B’s first- or second-period subsidy does not affect country A’s exports, these subsidies do impact on country A’s domestic production. In particular, when the first-period foreign subsidy increases, country A’s domestic production in periods one and two decrease, while cumulative production also decreases (∂qA1 /∂sB1 < 0, ∂qA2 /∂sB1 > 0, and ∂(qA1 + qA2 )/∂sB1 < 0). Similarly, an increase in the period-two foreign subsidy increases period-one and decreases period-two domestic production, while decreasing domestic production cumulatively (∂qA1 /∂sB2 > 0, ∂qA2 /∂sB2 < 0, and ∂(qA1 + qA2 )/∂sB2 < 0). Proposition 8 shows, among other things, that owing to the assumption of constant marginal cost, foreign export subsidies have no effect upon domestic exports ((39) and (41)). Because of the intertemporal connections resulting from product durability, an increase in the first-period foreign export subsidy causes a decline in period-one domestic production and an increase in second-period domestic production, while the cumulative effect in negative. As domestic durability increases, an increase in sB1 has greater impact upon qA2 . Also, as dA rises the cumulative effect of an increase in sB1 upon domestic production diminishes in magnitude. Thus, in this case foreign subsidies will tend to have a smaller cumulative effect on domestic production the more durable the domestic good. The effect of an increase in sB2 on domestic production is positive in the first period and negative in the second period. The higher the durability of the foreign product, the larger the absolute effect of an increase in sB2 has upon qA1 and qA2 . As sB2 increases, the cumulative effect upon domestic production is negative. As dA rises, an increase in sB2 has a greater absolute cumulative effect upon domestic production, while the magnitude of the cumulative effect declines as dB rises. Thus, cumulatively, the effect of a change in second-period foreign subsidies upon domestic production is smaller in magnitude the more durable the foreign product, and the effect is greater in magnitude the more durable the domestic product. The effects of changes in domestic subsidies when held equal across time are given below: ∂ q1A = 0, ∂s A

∂ q2A = 0, ∂s A

∂ (q1A + q2A ) = 0, ∂s A

(42)

∂ y1A (1 - gd A )(1 + n B ) ∂ y2A (1 - d A (1 - gd A ))(1 + n B ) = > 0 , = > 0, ∂s A b(1 + n A + n B ) ∂s A b(1 + n A + n B ) ∂ ( y1A + y2A ) (1 + (1 - d A )(1 - gd A ))(1 + n B ) = > 0. ∂s A b(1 + n A + n B )

(43)

Proposition 9. Although an increase in country A’s common subsidy level does not affect its own domestic production levels, its export levels in both periods increase as do cumulative exports (∂yA1 /∂sA > 0, ∂yA2 /∂sA > 0, and ∂(yA1 + yA2 )/∂sA > 0). However, a subsidy policy will be less effective in domestic industries which manufacture highly durable products.

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When the domestic subsidy rises, yA1 and yA2 increase. As domestic durability rises, the magnitude of the effect of a change in domestic subsidies upon yA1 falls. However, the effect of d A changes upon the magnitude of yA2 is ambiguous. When the domestic subsidy increases, the cumulative effect upon domestic exports is positive, and as d A increases the magnitude of this effect declines. Thus, in this case subsidy policy will be less effective in industries with relatively high domestic product durability. Finally, we examine the effect of changes in foreign subsidies when held equal across time:

(1 - gd B )n B (1 - d A (1 - gd B ))n B ∂ q1A ∂ q2A < 0, =< 0, =B A B B ∂s b(1 + n + n ) ∂s b(1 + n A + n B ) (1 + (1 - d A )(1 - gd B ))n B ∂ (q1A + q2A ) = < 0, ∂sB b(1 + n A + n B ) ∂ y1A = 0, ∂sB

∂ y2A = 0, ∂sB

∂ ( y1A + y2A ) = 0. ∂sB

(44)

(45)

Proposition 10. Although an increase in country B’s common tariff level does not affect country B’s exports, country A’s own domestic production levels decrease in both periods as well as cumulatively (∂qA1 /∂sB < 0, ∂qA2 /∂sB < 0, and ∂(qA1 + qA2 )/∂sB < 0). In addition for domestic industries with high product durability, changes in the foreign export subsidy will have a smaller effect upon domestic production than in industries producing less durable products. Proposition 10 indicates that when foreign subsidies rise, country A’s domestic production falls in both periods and thus cumulative domestic production falls. Note, as d A increases, the magnitude of the effect upon qA2 declines, as does the magnitude of the cumulative effect. As d B rises the effect of a change in the foreign subsidy upon qA1 decreases in magnitude, and the effect upon qA2 increases in magnitude while the magnitude of the cumulative effect declines. Hence, for industries with relatively high durability, changes in the foreign export subsidy will have a smaller effect upon domestic production than in industries producing less durable goods. The results above shed further light upon the potential effect of domestic product quality standards upon the effectiveness of subsidy policies. If an increase in domestic product quality standards causes foreign or domestic producers to increase product durability, changes in foreign subsidies will tend to have a smaller effect upon cumulative domestic production. Hence, domestic product quality standards may help insulate domestic producers from changes in foreign subsidies.

6. Durability and the Optimal Policy As noted above, product durability affects imports and exports as well as the ability of tariffs and subsidies to affect the pattern of trade. The next issue we examine is the effect product durability has upon the socially optimal tariffs and subsidies.16 For our purposes, optimal tariffs and subsidies are those which maximize social welfare—defined as the sum of discounted domestic industry profit, discounted domestic consumer surplus, and domestic tariff revenue minus discounted domestic subsidy payments. Hence, the social welfare functions for countries A and B have the following forms:

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b b Ê ˆ Ê ˆ SWF A = n Ap A + a1 - Q1A - p1A Q1A + g a2 - Q2A - p2A Q2A Ë ¯ Ë ¯ 2 2 + n B (t1A y1B + g t 2A y2B ) - n A ( s1A y1A + g s 2A y2A ), b b Ê ˆ Ê ˆ SWF B = n Bp B + a1 - Q1B - p1B Q1B + g a2 - Q2B - p2B Q2B Ë ¯ Ë ¯ 2 2 A B A B A B B B B B + n (t1 y1 + g t 2 y2 ) - n ( s1 y1 + g s 2 y2 ).

(46)

(47)

The optimal Nash tariffs and subsidies are found by simultaneously maximizing (46) and (47) with respect to tA1 , tA2 , sA1 , sA2 , tB1 , tB2 , sB1 , and sB2 . Let ¯t A1 , ¯t A2 , s¯A1 , and s¯A2 represent the optimal Nash tariffs and subsidies for country A, and ¯t B1 , ¯t B2 , s¯B1 , and s¯B2 represent the optimal Nash tariffs and subsidies for country B. Next we can examine the effect of durability upon optimal tariffs and subsidies. Differentiating ¯t A1 and ¯t A2 with respect to d A and d B yields ∂ t1A g c A n A (n A (n A - n B ) + 2(n A - n B ) + 1) , = (1 + n A )(1 + n A (2 + n A + n B ) + 2 n B ) ∂d A

∂ t 2A = 0, ∂d A

(48)

∂ t1A g (a2 (1 + n A (2 + n A + n B )) + c A n A (1 + 2(n A - n B ) + (n A - n B ) + n A )) , = (1 + n A )(1 + n A (2 + n A + n B ) + 2 n B ) ∂d B ∂ t 2A = 0. ∂d B

(49)

Proposition 11. Although the optimal second-period tariff, ¯t A2 , is unaffected by domestic product durability, d A, the optimal first-period tariff, ¯t A1 , will decrease (increase) as d A rises if the domestic industry is more (less) competitive than the foreign industry. Likewise an increase in foreign durability, dB, has no effect on ¯t A2 , but if the domestic industry is more competitive than the foreign industry, the optimal first-period tariff, ¯t A1 , rises as d B increases. Proposition 11 indicates, as expected, that durability does not affect the optimal second (last) period tariff. However, as domestic product durability increases, the optimal first-period tariff for country A will change. If the domestic industry is more competitive than the foreign industry (i.e., nA > nB), (48) shows that the optimal firstperiod tariff falls as domestic product durability rises. On the other hand, if the domestic industry is less competitive than the foreign industry (i.e., nA < nB) the optimal first-period tariff rises as domestic product durability rises. Given the complicated interaction contained in this model, it is difficult to develop a singular interpretation of this result. However, one implication is that, for domestic industries that are relatively more competitive than foreign industries, those industries with higher product durability or quality, other things equal, should have lower optimal tariff barriers. Equation (49) indicates that an increase in foreign durability has no effect on the optimal second-period domestic tariff. Note that an increase in foreign durability has an ambiguous effect on the optimal first-period tariff when nA < nB. However, when the domestic industry is relatively more competitive than the foreign industry (nA > nB), as d B rises, the optimal first-period tariff rises. Hence, this result indicates that for domestic industries that are relatively competitive, those industries which compete with foreign products of higher durability or quality, other things equal, should have higher optimal tariff barriers. © Blackwell Publishers Ltd 2000

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Solving for s¯A1 and s¯A2 and differentiating with respect to d A and d B yields ∂ s1A g (n A - (n B + 1))(a2 + c B n B (n B + 2)) = , 2 ∂d A (1 + n B ) (1 + n B ) + n A (n B + 2)

(

)

∂ s 2A = 0, ∂d A

∂ s1A g c B n B (n A - n B - 1)(n B + 2) ∂ s 2A , = 0. = ∂d B (1 + n B ) (1 + n B ) 2 + n A (n B + 2) ∂d B

(

)

(50)

(51)

Proposition 12. Although the optimal second-period subsidy, s¯ A2 , is unaffected by domestic product durability, d A, or foreign durability, d B, the optimal first-period tariff, s¯A1 , is. In particular, if the domestic industry is relatively more competitive than the foreign industry, s¯ A1 falls as d A rises but rises as d B increases. Proposition 12 indicates that, as domestic product durability increases, when the domestic industry is relatively more competitive than the foreign industry (in this case, when nA > nB + 1), an increase in domestic product durability causes the optimal domestic first-period export subsidy to fall. On the other hand, if the domestic industry is less competitive than the foreign industry, the optimal first-period domestic subsidy rises. Thus, other things equal, for relatively competitive industries, domestic industries producing products of higher durability or quality should have lower optimal subsidies. Equation (51) shows that, as foreign product durability rises, the optimal domestic first-period export subsidy rises when the domestic industry is relatively more competitive. When the domestic industry is less competitive than the foreign industry, as foreign product durability rises, the optimal first-period subsidy falls. Again, similar to the results concerning optimal tariffs, for domestic industries that are relatively competitive, those industries which compete with foreign products of higher durability or quality, other things equal, should have higher export subsidies. The results above lead to a general conclusion that, for relatively competitive domestic industries, as domestic product durability rises, optimal trade barriers fall. Also, for relatively competitive domestic industries, when foreign product durability rises, optimal trade barriers rise.

7. Final Remarks Many products traded internationally are durable in nature. Our analysis shows that the introduction of product durability into an oligopoly model of intraindustry trade provides insights into the role of product durability in international trade and commercial policy. First, we find that changes in product durability impact a country’s domestic production, exports and imports. In particular, if domestic product durability rises, the cumulative effect on domestic imports is negative. Hence, if domestic quality standards have an effect upon the quality or durability of domestic production, a country’s imports will tend to decline. This result identifies another potential avenue by which product quality standards act as a barrier to trade. Second, we find that product durability has an effect upon the ability of import tariffs and export subsidies to influence the pattern of trade. In particular, as the durability or quality of domestic products rise, increases in foreign import tariffs tend to have a smaller cumulative impact on domestic exports. Hence, higher product durability tends © Blackwell Publishers Ltd 2000

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to decrease the effects of commercial policy upon the pattern of trade, at least cumulatively. Also, this result may help explain some empirical irregularities, namely, the frequently observed result that the measured effects of tariffs upon intraindustry trade are statistically insignificant. This result also implies that the potential benefit due to domestic quality standards may be partly offset by a decrease in the effectiveness of tariff policy when these standards increase foreign product quality. In terms of export subsidies, our model shows that, as domestic product durability rises, changes in domestic export subsidies tend to have a smaller cumulative effect upon domestic exports. Also, when either foreign or domestic product durability increase, changes in foreign export subsidies tend to have a smaller cumulative effect upon domestic production. Thus, while an increase in product durability or quality may decrease the effectiveness of domestic commercial policy, we also find that an increase in product durability may also help insulate the domestic economy from foreign commercial policy. Finally, we have examined the effect product durability has upon optimal tariffs and subsidies. We find that when the domestic industry is relatively competitive, as domestic product durability rises, optimal domestic tariffs and subsidies decline. On the other hand, as foreign product quality or durability rises, when the domestic industry is relatively competitive, optimal tariffs and subsidies rise. There are certainly many issues related to traded durable goods that warrant future study. We hope our basic model can be used as a framework for the exploration of some of these issues. In particular, our analysis assumes that the firm’s product durability is exogenously determined. The impact of commercial trade policy (e.g., changes in tariffs or subsidies) on the firm’s durability or quality choice would likely yield interesting results in an endogenous durability setting. Also the extension of the analysis to include research and development may provided additional insight into the observed trade patterns of durable goods.

References Balassa, Bela, “Tariff Reductions and Trade in Manufactures among Industrial Countries,” American Economic Review 56 (1966):466–73. Brander, James A., “Intra-Industry Trade in Identical Commodities,” Journal of International Economics 11 (1981):1–14. Brander, James A. and Paul R. Krugman, “A Reciprocal Dumping Model of International Trade,” Journal of International Economics 15 (1983):313–21. Brander, James A. and Barbara J. Spencer, “Tariffs and Extraction of Foreign Monopoly Rents Under Potential Entry,” Canadian Journal of Economics 16 (1981):371–89. Bulow, Jeremy I., “Durable Goods Monopolists,” Journal of Political Economy 90 (1982):314–32. ———, “An Economic Theory of Planned Obsolescence,” Quarterly Journal of Economics 101 (1986):729– 49. Butz, David A., “Durable Good Monopoly and Best-Price Provisions,” American Economic Review 80 (1990):1062–76. Christelow, Dorothy B., “Japan’s Intangible Barriers to Trade in Manufactures,” in Philip King (ed.), International Economics and International Economic Policy, New York: McGraw-Hill (1990):41–56. Coase, Ronald H., “Durability and Monopoly,” Journal of Law and Economics 15 (1972):143–49. Davis, Donald R., “Intra-Industry Trade: A Heckscher–Ohlin–Ricardo Approach,” Journal of International Economics 39 (1995):201–26. Driskill, Robert A. and Andrew W. Horowitz, “Durability and Strategic Trade: Are there Rents to be Captured,” Journal of International Economics 41 (1996):179–94. © Blackwell Publishers Ltd 2000

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Falvey, Rodney E., “Commercial Policy and Intra-Industry Trade,” Journal of International Economics 11 (1981):495–511. Goering, Gregory E., “Oligopolies and Product Durability,” International Journal of Industrial Organization 10 (1992):55–63. Goering, Gregory E. and John R. Boyce, “Taxation and Market Power when Products are Durable,” Journal of Regulatory Economics 9 (1996):83–94. Helpman, Elhanan, “International Trade in the Presence of Product Differentiation, Economies of Scale and Monopolistic Competition: A Chamberlinian–Heckscher–Ohlin Approach,” Journal of International Economics 11 (1981):305–40. Hwang, Hong, “Intra-Industry Trade and Oligopoly: A Conjectural Variations Approach,” Canadian Journal of Economics 57 (1984):126–37. Krugman, Paul R., “Increasing Returns, Monopolistic Competition and International Trade,” Journal of International Economics 9 (1979):469–79. Purohit, Devavrat, “Marketing Channels and the Durable Goods Monopolist: Renting versus Selling Reconsidered,” Journal of Economics & Management Strategy 4 (1995):69–84. Schmalensee, Richard, “Market Structure, Durability, and Quality: A Selective Survey,” Economic Inquiry 17 (1979):177–96. Torstensson, Johan, “Determinants of Intra-Industry Trade: A Sensitivity Analysis,” Oxford Bulletin of Economics and Statistics 58 (1996):507–24.

Notes 1. Davis (1995) includes Ricardian-like technological differences across countries and defines intraindustry trade as trade in goods with similar factor intensities. Hence, the type of intraindustry trade discussed in Davis (1995) is not the more common definition which is concerned with trade in similar products. 2. In Helpman (1981) specialization also occurs as a result of comparative advantage. 3. After initial drafts of this manuscript we became aware of Driskill and Horowitz (1996). The strategic trade model developed there incorporates product durability into a model where two firms in different countries compete in a third. They solve for both the rental and sales equilibria and find that it is optimal to tax a firm selling durable output and it is optimal to subsidize a firm renting durable output. As in the earlier work of Goering and Boyce (1996), Driskill and Horowitz find that taxing a firm selling durable output helps to ameliorate the firm’s commitment problem since the tax provides the firm, in effect, with the ability to commit to a lower level of output in the future, which increases their market power. Thus, in Driskill and Horowitz, taxing the seller of a durable good may be socially optimal. In contrast, our n-firm oligopoly model concerns intraindustry trade between two countries and for the sake of tractability we examine only the committed sales or rental equilibrium. Hence, our model and that of Driskill and Horowitz (1996) both provide unique extensions to the current literature. 4. Note that this simple framework assumes that all of the firms in a given country produce output with the same durability. Additionally, the product durabilities d A and d B are treated as parameters rather than choice variables. These simplifications allow us to focus on the impact of durability on trade patterns without the complicating factors of intracountry endogenous durability choice. See Schmalensee (1979) for a survey of earlier work on endogenous durability choice, and Goering (1992) for a more recent look at oligopoly durability choice in rental markets. 5. The variables for country B are defined in a synonymous fashion and are identified by the change of superscripts from A to B. For brevity only country A’s production flows and stocks are explicitly stated, recognizing that with a simple change of superscripts one can go from one country’s output variables to the other country’s. 6. Since qA1i, qA2i, y1iB, and y2iB represent periodic production quantities, the stock formulation in (2) precludes the international trade of used goods. If, for example, qA1i units are manufactured for country A’s own domestic use in period one, equation (2) supposes that all the remaining units in period two, dAqA1i, are still used in the domestic market in country A. This is obviously a © Blackwell Publishers Ltd 2000

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simplification since it may be possible for owners of these dAqA1i old units to export these units to country B. For tractability this type of trade in used goods is abstracted from the analysis. A similar assumption is often made in static settings and is perhaps more relevant for durable products which are often customized for a given market. For example, automobiles produced for country A may be right-hand drive while those manufactured for country B may be lefthand drive. Although this does not change the manufacturing costs of producing units for the different markets, it would make the international trade in used automobiles difficult. Finally, it would seem that the trade in used-goods complication is, perhaps, really only of interest in settings where second-period prices in the countries are not known with certainty. If these prices are uncertain, buyers or sellers of the durable product may make suboptimal first-period decisions which would cause them to ship the existing stock of output to a different country. 7. Alternatively, the nonnegative tB1 and tB2 can be viewed as transportation costs that are incurred as a unit is shipped from country A to country B. 8. Goering (1992) has shown that the Nash rental solution is really a degenerate subgameperfect solution; thus the assumption of commitment ability is really only of consequence in the sales solution. 9. Since this is a linear-demand, constant-marginal-cost framework, the second-order conditions are satisfied; i.e., the Hessian matrix for each firm i is negative definite. 10. All mathematical derivations are available upon request from the authors. 11. Note that the net marginal production cost in period two (cA + tB2 - sA2 ) is assumed to be positive to ensure bounded interior solutions. Otherwise, ¯yA2 tends to infinity. 12. The measurement of international trade flows, say annual exports, may concern both periods of the rental contract. Hence, cumulative trade flows are of interest. 13. For example, the Japanese Industrial Standards Committee awards the “JIS” mark to products made in factories where production technique and quality controls meet committee standards. Also, the Japanese Ministry of Agriculture, Forestry and Fisheries awards the “JAS” mark to forestry products manufactured in factories meeting ministry standards. Products affected by these standards include forest products, automobiles, appliances, and telecommunications. Since the early 1980s, foreign producers have been allowed to apply for these marks. For more discussion of these standards see Christelow (1990). 14. Of course, the total effect of a change in domestic quality or durability standards upon domestic imports is also influenced by the effect those standards have upon foreign product quality. 15. This result is due to the assumption of constant marginal cost. 16. It should be remembered that product durability rises in this model costlessly. A more general model where product durability is a choice variable for firms is the subject of future research.

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