-1g-

against the foreign cost advantage n (which ranges from © to
1). There is a family of functions each drawn for a unique
set of pre-trade initial conditions (prices and output
levels), cost characteristics (g2 and se-i ), and utility
Characteristics (r). Above the horizontal axis, D is greater
than zero and trade reduces expenditure. For the
(s2-1,92,r,n) combinations such that D is below the axis,
trade increases expenditure so an autarchy policy dominates
trade.

The DD curve must intersect the horizontal axis twice.
At n=1, Pa=P*i, and Fa=F's so Ea=E. and D=0; free trade and
autarchy expenditures are identical since there is no foreign
price differential. The other intersection is n° defined
implicitly when D equals © and where the consumption benefits
of importing good 1 just balance the cost induced consumption
losses on good 2.2?

Given any DD function, a foreign price lower than ne
(shown as nine?) implies a large consumption gain on good 1,
but nevertheless too much of a demand shift that causes large
price increases for item 2 that outweigh the import
consumption gains thus yielding a higher overall expenditure:
trade should not be allowed. However, so long as the foreign
price is such that n lies between n®© and 1, importing does not
shift the demand curve for good 2 too much; consumption
benefits from imports outweigh losses from the increased

domestic price of good 2 and trade reduces expenditure.


-12-

exceeds autarchy expenditure and the appropriate trade policy
restricts the import of item 1. Free trade causes a great
enough increase in F2 to outweigh the consumption gains
implied by P*,. Therefore, even though the foreign industry
has single product comparative advantage in item 1, the
domestic industry must have product spectrum comparative
advantage.

The post-trade change in the price of item 2 has three
major elements: the cross-price elasticity of demand, which is
composed of the utility elasticity of subsitution between
Products in the consumption basket and the effect on the level
of utiltity of price changes; the output elasticity of average
cost, which is composed of the scale and scope elasticities of
output; and the measure of foreign cost advantage.

Demand shifts are measured by the cross-price elasticity
of demand

B8q2 F. (ir) Pa
(6) @az = o>

QP. qe r r
(Py + Pa +1)

"

@€;2 is positive for substitute goods so long as the price
effects on the level of utility, as measured by i:, are not
too large.*7 When r = -00, e12 = oo representing perfectly
linear utility and infinite cross elasticity of demand. When
r= 1, @i1z2 = 03 the Leontief utility implies zero cross
elasticity of demand. Therefore, e:2 embodies information on
both the magnitude of demand shift and the extent to which

items are substitutable in utility. Increasing e:> implies a


- 22 -

The maximum of the DD curve is at n*. I# the actual foreign
cost advantage equals n*, then the tax rate necessary ta
obtain maximum trade benefits is zero and T=1. At foreign
cost advantage n° and below, autarchy is the expenditure
minimizing policy. The wedge defined at n° prevents trade and
as n falls below n°, the prohibitive rate rises at an
increasing pace keeping the domestic industry protected in
autarchy: the TT curve then shows the shadow value of keeping
the industry protected. If n lies between n* and 1, the tax
rate is actually negative, suggesting a subsidy.

In summary, there are three trade policy regions --
autarchy (A), free trade (F), and restricted trade (R)--
demarked by n° and n*. For n less than n°, autarchy, achieved
via a prohibitive wedge, is the best Policy. Even though
there are substantial benefits generated by the low foreign
Price, it causes too much demand shift and (given cost
characteristics S2-1 and gz, and elasticity r), expenditure to
reach u® in trade exceeds expenditure in autarchy. For 9
greater than n“, trade benefits are as large as possible.
Therefore, free trade minimizes expenditure. It is for a
foreign cost advantage between n* and n®© that there is scope
for a trade restriction that yields lower expenditure and thus
higher utility than either autarchy or free trade. For all n
between n© and n“, there is an appropriate trade barrier that
brings the actual foreign price up to the trade maximizing
price.

These results have important implications for the foreign

producer. If its cost advantage is below ne, it should


-3-

input cost differentials that alter the conditions of
sustainability: marginal costs are lower in the LDCs in part
because of cheaper labor. Therefore, clear foreign
comparative advantage at the labor intensive end of the
product spectrum weakens domestic efficiency arguments against
relinquishing the contested part of the spectrum. But, the
developed country industry may have a comparative advantage in
producing the higher technology items in the spectrum. If the
Product spectrum can be split with relatively few production
inefficiencies, the standard comparative advantage story holds
and the developed country relinquishes the contested items to
the lower cost producer. However, jointness in production
technology and increasing returns to scale may imply that
efficient, lowest cost production obtains only if the product
spectrum is produced in its entirety. Under these conditions,
efficiency gains from trade over only part of the product
spectrum are not clear cut and comparative advantage in the
production of one item within the spectrum is an insufficient
guide for trade policy.

Another wrinkle is that the production of a product
spectrum using ‘joint input technology encourages pricing rules
of thumb. When it is difficult in practice to equate product
specific marginal costs and product specific marginal
revenues, firms often resort to average cost pricing rules.©
Trade conducted in this pricing environment may yield a policy
ranking different from the standard comparative advantage
mociel.

Even though domestic policies are the first defense


- 33 -

Kahn, A. E., "Applications of Economics to an Imperfect

World". American Economic Review Fapers and Proceedings,
1979,

Mann, C. L., “Employment and Capacity Utilization in Import
Sens:tive U.S. Industries", in Trade and Finance Relations
between the Developed and the Newly Industrializing
Countries, (unpublished PhD Dissertation), MIT, 1984.

“Trade Protection and Commercial Policy for the
ining Industry", paper presented to the System Committee
on International Trade, Board of Governors of the Federal
Reserve System, April 1985.

Panzar, John C. and Robert D. Willig. "Free Entry and the
Sustainability of Natural Monopoly". Bell Labs Working Paper
no.S7, 1975.

Salop, Steven, "Monopolistic Competition with Outside
Goods". Bell Journal of Economics, 1979.

Scherer, F. M., Industry Market Structure and Economic
Ferformance. Rand McNally College Publishing Co:Chicago,
1980,

Schmalensee, R., "Comparative Statics Properties of Regulated
Airline Oligopolies". Bell Journal of Economics, 1977.

Spencer, B. and J. Brander, “International R&D Rivalry and
Industrial Strategy". Reveiw of Economic Studies, 19682.

Williamson, O. E., “Economics as an Antitrust Defense: the
Welfare Tradeoffs". American Economic Review, 58:1 (1968).

Willig, Robert D. “Multiproduct Technology and Market
Structure", American Economic Review, 69:2 (1979).


-19-

OFTIMAL TRADE FOLICY

The DD curve reaches a maximum at some foreign cost
advantage n* where the maximum positive benefits from trade
are obtained by the domestic country. At n*, the country
receives consumption benefits of importing at P*, less than
Fi, but the import price is not so low as to cause demand
shifts that yield increased consumer expenditure on the
basket. From the standpoint of the domestic country, the
optimal foreign price for good 1 is n*F,.

Define this optimal post-trade domestic price of good 1
as P*",. F*", is obtained from the actual foreign price of
Pe, (=nPa) via an import surcharge, import consumption tax,
tariff, quota, or subsidy (although we reject the subsidizing
of foreign imports as a realistic policy option). We can
derive this optimal wedge from the optimal foreign cost
differential (n*) and the actual foreign price via the

identity

(11) Pew, = neh, = (1+t "nF
Solve for the optimal wedge by rewriting equation (10)

to include the tax

r r i/r
(12) D = {P, + Fo + 13 ue

r (s2-1)ei2(n-1) r i/r
- {€(TMPs) + (Pelit—— —+g2]) + 13 ue

qe

where T = 1+t and TnP,s is the domestic tax-ridden price of the

imported good.


- 25 -

figure 5

Pp wa

tt
¥
x



-21-

figure 4

Db

n°?



-16-

consumption gains and production losses appear and there may
be scope for trade policy instead of pure free trade.

The most crucial element determining how expenditure
changes with the foreign price level given the cost
characteristics is whether the cross-price elasticity of
demand is small or large. In the most general terms, if this
elasticity is large, (which implies a high degree of
substitutability between the products in the spectrum), then
trade is more likely to reduce expenditure on the consumption
basket if the foreign price is not too low, and the economies
of scale and scope are not too large; if the foreign price is
very low, but the cost economies are important, then the
consumption gain on product 1 is likely to be outweighed by

technology induced consumption losses associated with product

2.

There are many variables here that affect the trade
policy choice —- too many to fully analyze and catalogue their
individual effects on trade policy. Therefore, we will divide
them into three catagories: the utility characteristics, which
will be held fixed for the remainder of the analysis and for
which we examine only the case of elastic demand (r<@ 2°);
cost characteristics, which will be the main variable used to
describe how an industry declines; and the foreign cost
advantage, which is the key exogenous piece of data and which,
given all domestic characteristics, will determine the
appropriate trade policy.

This manner of structuring the problem is depicted in

figure 3. The figure diagrams the difference function D


-8-

profitably price below the domestic price on all items in the
product spectrum, ?>

The foreign item i is a perfect substitute for the
domestic item i, and the foreign producer satisfies all

domestic demand for i at the market entry price. Therefore,

once i is imported, domestic output of i ceases.?4

TRADE POLICY

An item-by-item comparative advantage ranking may not
yield the most efficient trade policy in this environment.
Standard comparative advantage says cheaper foreign goods
should be imported, thus yielding a welfare gain from trade.
However, the interrelationship between the demand curves and
output technology for the individual products creates a new
dimension for comparative advantage. Price changes on all
goods in the spectrum, not just the traded goods must be
weighed when measuring gains from trade, and to determine if
free trade is the welfare enhancing policy. Importing the
foreign item at a lower price shifts demand from all other
products. Given the cost characteristics, losing an item and
demand reduction on other items unambiguously increases costs
of producing all of the remaining items in the spectrum.

With an average cost pricing rule, the equilibrium price of
each remaining good must rise.*® The essential trade policy
decision weighs the consumption gains on product i, now
imported at a lower price, against the consumption losses

associated with increased prices of all remaining domestically


-31-

q -<+

Pa
or

(rl) /r l/r

Pa
=- < dn cit fS27D ere (N71) aga) {S27 )ers
Po Q2 Gz
So

long as S2-1 is not too small, OF a/OF,>1 and the condition

holds. As n--> 1, the sign changes to yield the shape of the
DD curve.

22. The sign of @D/@(-(s2-1)) and @T/@(-(s2-1)) <O for r<o
is unambiguously positive.


- 28 -

*Economist, Federal Reserve Board. This paper is a revision
of part of my doctoral dissertation completed at MIT and
should not be interpreted as reflecting the views of the Board
of Governors of the Federal Reserve System or other members of
its staff.

1. For the most comprehensive review, see Helpman and Krugman
and references to earlier work contained therein.

2. See Spencer and Brander on R&D rivalry, and Brander and
Spencer on export subsidies in particular.

3. See the chapters on differentiated products in Helpman and
Krugman.

4. Grossman‘s (1982) evidence supports the product spectrum
characteristic of the United States declining firm. His
results suggest that the NICs use aggressive export promotion
to encourage output of one item of the spectrum. The NICs
each choose a different item, thus not competing directly with
each other, but forcing the domestic industry to fight import
penetration at many points of the spectrum.

S. If there is no domestic price set sustainable in the face
of foreign competition, the domestic firm loses the contested
markets to the foreign producer just as in the domestic model
the entrant captures part of domestic demand.

6 Scherer, pages 195-190, discusses types of and reasons for
the widespread use of non-marginal cost based pricing rules.

7. Baumol, Panzar, and Willig detail the theoretical
underpinnings of domestic industrial policy. Basically,
economies of scope and scale in production yield cost
advantages to merger. In addition, if excess capacity is of
key importance for the declining industry, then merger or exit
that eliminates redundant fixed capital is the first defense
against foreign competition. Labor productivity improvements
are appropriate if foreign producers have advantages in
marginal costs. Johnson’s seminal work details the welfare
effects of using first and second best policies.

8. Deteriorates means that economies of scale and scope
measures indicate more extreme tradeoffs between cost and
quantity produced.

9. The oligopoly industrial structure yields each firm
operating at above minimum efficient scale. Thus the
production of each firm is characterized by increasing returns
to scale even in the absence of explicit increasing returns to
scale technology.

10. While the Cobb-Douglas functional form cannot specify
item specific or product spectrum general non-marginal casts,
it has constant elasticity properties that make it the best


-5-

industry. Thus, even though there is more scope for
aggressive trade policy in the short run, the long run result
is consistent with standard comparative advantage trade
theory.

The first section formalizes cost and demand

characteristics of the industry and describes foreign

competition. The next section formulates the open economy
problem, determines whether free trade enhances welfare, and
if not, analyzes optimal trade policy. An anatomy of Policy
choices with a deterioration of the cost structure of the

domestic industry concludes the essay.
INDUSTRY AND DEMAND STRUCTURE

The economy is composed of two sectors. The
heterogeneous goods sector (H) Produces a product spectrum of
output with economies of scale and scope. The products within
the spectrum are imperfectly substitutable in consumption. We
can think of the sector as composed of identical
Oligopolistically competitive firms where anti-trust
regulation prevents both merger and excessive profits.” The
all-other-goods sector (A) produces a necessity good under
conditions of perfect competition and constant returns to
scale.

Production Characteristics

There are N firms and I items in the product spectrum
produced using K inputs. Costs of producing each Product i

exhibit increasing returns to scale in the output of i and


-4-

against import penetration,7 only trade policy for the
declining industry is examined in this paper. We focus on the
often second best set of trade policies because many of the
first best industrial policies violate antitrust regulation,
succomb to union pressures, or entail lump sum transfers that
are politically infeasible.

Before presenting the formal model, the fundamental
results will be summarized. First, the framework used here to
analyze the declining industries embodies externalities that
can cause free trade to be too much trade. When the country
opens up to trade, demand substitutes toward the cheaper
imported good. Higher average costs and prices result for the
remaining domestically produced items in the spectrum because
of the downward sloping cost curves and jointness in
production technology. This post-trade price structure may
not maximize country welfare. Even though the cheaper import
generates an undisputable consumption gain, the production
inefficiencies yield price increases on the other items in the
Product spectrum causing a consumption loss. The net gain or
loss over the whole spectrum should determine appropriate
trade policy. Restricting trade may be optimal for the
domestic country.

The second important analytical result of the model is
that as the declining industry’s cost structure
deteriorates,® protection levels fall if the industry had
enjoyed protection. As the domestic industry becomes less
competitive over successive items in the product spectrum,

comparative advantage forces eventually eliminate the


awrarchy

-l7-

figure 3

dd F (srl, ar)



returns oligopelies and regulated industries. Therefore,

average cost pricing is assumed.?7

K sit
(2) P. = AC. =TT Ree we Gi
ket

Demand Characteristics

Representative consumer utility is CES across consumption
of the products produced in the two sectors of the economy.
The CES expenditure dual depends on each of the prices of the
items in the spectrum, (Ps) (which will change as equilibrium
quantity changes), the unchanging price of the composite good
(Pad, and the utility level u(H,A) = us.

Ir rool/r
(Br Eka, eee Xzy Xa) = CQ Pe + Fa) ue
r ranges from negative infinity (completely elastic, linear
utility) where different consumption levels of the various
goods are meaningless to consumer utility, to 1 (completely
inelastic, Leontief utility) where utility is defined uniquely

by minimum consumption levels of each of the goods.

Foreign Competition

The domestic industry faces foreign competition at some
points in its product spectrum of I items. Foreign suppliers
can undercut the domestic price of say item i because foreign
production technology differences and input cost differentials
yield a foreign average cost for i below the domestic average
cost for i. However, because the foreign supplier does not

use the same technology or input ratios, we assume it cannot


- 23-

voluntarily raise prices up to the boundary so as to be
allowed to enter the domestic market. If its cost advantage
lies between n= and n“, then it should increase prices until
Pew, is reached and reap profits instead of allowing the
domestic country to earn tax revenues. Voluntary restraint

agreements perhaps are an example of this kind of behavior

that satisfies both the importer and the domestic country.
Even though the price of good 1 is above its free trade level,

the expenditure over the whole consumption basket is lower.

ANATOMY OF COST CHANGES AND THE OF TIMAL TARIFF

How does the tariff rate change and the size of the
regions change when the cost/output tradeoffs worsen for the
domestic country? The exercise yields a conclusion
supporting standard comparative advantage theory in the long
run, but offers more opportunity for aggressive trade policy
in the short run.

Farst, worsened cost/output tradeoffs reduce the scope
for trade restrictions. There is a smaller range of foreign
prices such that a restrictive or autarchic policy minimizes
expenditure. This implies that the range of foreign cost
advantage where free trade yields the highest utility is
unambiguously wider. There is also however, an expanded set
of foreign prices yielding the autarchy policy. The
restricted trade area is squeezed.

Second, a worsened cost/output tradeoff for the domestic

industry unambiguously reduces the tax protection, if the


International Finance Discussion Papers

Number 259

August 1985

TRADE POLICY FOR THE MULTIPLE
PRODUCT DECLINING INDUSTRY

by

Catherine L. Mann

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an

acknowledgment by a writer that he has had access to unpublished materials)
should be cleared with the author or authors.


-10-

figure 1



-9-

Produced items. If the consumption gain outweighs consumption
losses, then allowing imports is the appropriate policy. But,
if the losses outweigh the gain, then restricting imports is
desirable.

Distinguishing product spectrum comparative advantage

from single product comparative advantage is necessary to

determine appropriate trade policy. The domestic firm has
what will be called "product spectrum comparative advantage"
only if consumer utility is greater when restricting foreign
competition leaves the domestic product spectrum intact. If
there is a utility gain over the whole spectrum from importing
just a portion of the spectrum, then the foreign firm must
have "single product comparative advantage" in the production
of the item most demanded using a utility measure. If this is
the case, even if the domestic firm has single product
comparative advantage in all the remaining items, it does not

have product spectrum comparative advantage.

Two good product spectrum

So as to obtain simple analytical results, collapse the H
sector product spectrum into two items 1 and 2. The autarchy
Price set is (F:,P2,1) where Fa=1. Assume that the foreign
country produces item 1 more cheaply and its market entry
Price is P*,. Imports satisfy demand at P“; less than P,.
Therefore the free trade price set is (P“.,P’2,1) where P's is
the post-trade price of the remaining domestically produced
item. (See figure 1).

The measure of foreign cost advantage, and therefore


- 30 -
share.

16. We can hold utility constant throughout the exercise
because the property of the CES utility function leads to the
gain in utility comine from a reduction in Fa exactly
offsetting the loss in utility coming from an increase in

Po,

17. This assumption is analagous to assuming that income does
not outweigh subsitution effects.

18. We can guarantee that all products (1,2,a) are produced
in equilibrium by assuming that the scale elasticity of output
(s) is the same for products 1 and 2. We need not assume that
the scope elasticity is the same. In this case, stability
requires that

(2-r)/(r-1) s-1

1] fE}[E]

where Si=S2=s is assumed for closed form solution. In this
case, since r-1 < © always, the condition always holds.

19. If demand is completely elastic, then although the Fo
increase is large, since utility is linear between items 1 and
2, the consumer buys only item 1 at the lower imported price
and eliminates item 2 from her consumption basket.
Expenditure to reach u is unambigously lower with free trade
If demand is completely inelastic, then there is no demand
shift, cost structure is irrelevant and the consumer enioys a
lower price of item 1, without affecting Fa.
Therefore, free trade expenditure is unambiguously lower.

To support these proposition, refer to the definitions of
D and F’2 (equations (9) and (10)). If demand is competely

inelastic, e:s=0, F's=Po2, and Do, If demand is completely
elastic, @:2=00, dqz=-qe, (se-1) <« ©, and therefore, Fe --» ©,
soDs0O.

20, See Mann (1985) for the case of the inelastic utility.

21. Appealing to Grossman’s (1982) Paper, foreign firms
target the lower priced end of the Product spectrum first so

that F2>Pi. Therefore, F’2>P", is assured. The condition
that must hold for dD/dn>O given er2>0 but not too large is


- 29 -

functional form for this analysis.

11. The theoretically correct price set for the heterogeneous
goods case is the set of Ramsey prices (see Baumol and
Bradford) that exploits the cross elasticity of demand. These

Prices represent a marginal cost markup rule with a level of
profits set by a constraint on the Lagrangian. The
fundamental results of the analysis are upheld. In fact, any
pricing rule that allows for either an interrelationship
between the demand curves or the cost curves yields the same
broad conditions as the simple average costs pricing rule
employed here.

12. Scherer, pp. 194-200. Other references on average cost
Pricing rules include: Areeda and Turner, Joskow and
Klevorick, Williamson, Joskow and Noll, Joskow (1976) and
(1973), Kahn, and Schmalensee.

13. The foreign production function could have economies of
scope and scale just as for the domestic Producer, or it could
be Codb-Douglas constant returns to scale. All we require is
that at the pre-trade demand levels, the foreign price lies
below the domestic price. However, we assume that the foreign
producer operates at efficient scale; i.e. on the flat portion
of the cost curve if there exists economies of scale or where
average cost equals marginal cost if there are costant returns
to scale. Therefore, foreign price is exogenous of quantity
Produced. This simplification ignores the contention that
foreign entrepreneurs over-build capacity, assuming that they
can capture enough export demand via strategic pricing and
thereby move down the average cost curve onto the flat
Portisn. See Mann (1984). Since we do nat allow such pricing
strategies for the domestic firms, we must have the foreigners
Play by the same rules.

Of course, if the foreign producer can price below the
domestic average cost for all items in the spectrum then the
importer has product spectrum comparative advantage and the
domestic industry disappears.

14. We could relax the assumption of perfect substitutability
between the domestic and foreign product by employing a Salop
circle, measuring the similarity between the foreign and
domestic product as the distance around the unit circle from
the optimally placed domestic product to the substitute
import. While this addition will not alter the broad
characteristics of the results, it does increase the
likelihood of trade protection being the optimal Policy, and
it does imply that the domestic firm continues to produce the
product even as a substitute is being imported. The
difference between the optimally designed domestic product and
the import effectively raises the price of the import thus
reducing the consumption gains generated by trade.

15. We must assume that, because of stockholders and other
capital market constraints, the firm will not take losses and
keep it prices below cost in an effort to retain market


-6-

economies of scope in the ouput of the other items in the
spectrum as specified in the following generalized
Cobb-Douglas cost dual.

K Sa
QQ) Te, = TT Re we Gi lquy a) as

=1
K
Si =1/G ate ca

The at. is the kth factor share for good i with factor
Price we. and the appropriate factor price and share constant
R*,. . So long as the sum of the factor shares is greater than
1, the production function exhibits increasing returns in the
output of product i. The negative derivative for the
cross-output function Gs assures economies of scope in the
output technology. Since the N firms are identical, and we
assume in this essay no merger possibilities, equation (1)
equally well describes the individual firm’s costs and
industry wide costs.

Under conditions of increasing returns to scale and
scope, proper assignment of costs to individual products is
difficult in practice, so firms often resort to Pricing rules
of thumb that yield mark-up or average cost Pricing for
individual products. *°+**2 While marginal cost pricing in the
presence of global increasing returns yields losses,
anti-trust regulation often will not allow firms to exit the
industry, and profitable oligopoly structures exist where
collusion is not obvious. Furthermore, empirical and
theoretical industrial organization studies suggest that

average cost pricing rules in fact are prevalent in increasing


- 20 -

Optimizing (12) with respect to T, yields the wedge that
maximizes trade benefits for the domestic country.

1/(r-1)

—(se-leiz (Ss2a-1)es2(n-1)
-_--------- 1+--------------- + Q2
Qe G2

Ps —(Se-leis
n -- + |----------
Po q2

If economies of scale are non-existent (s2-1=0) or if the
utility function is Leontief or linear
(r=1,@:2=0:r=-00,e:12=00), then the optimal foreign price for
good 1 is zero; since we are, in effect, choosing the foreign
price, this comes as no surprize. However, an examination of
the wedge in an environment of the economies of scale and
scope and with intermediate values of utility substitution
yields more interesting conclusions.

Figure 4 shows the relationship between the trade policy
diagram and the tax diagram drawn for values of T and n. Like
the DD curve, there are a family of TT curves uniquely drawn
for initial conditions, cost, and utility characteristics.
But the TT curve is unambiguously downward sloping. The
smaller the foreign cost advantage (n--> 1) the lower the tax
that achieves the optimal domestic price of good 1 from the
actual foreign price.

We can construct the TT curve from points on the DD
curve. It is well-defined for any foreign cost advantage n
between n“ and n®. Here, given a foreign cost advantage, say
n’ (in figure 4), there is an optimal tax T‘ given by equation

(13). The boundaries of the well-defined curve are nTM and ne.


- 2-

CONCLUSIONS

A world with heterogeneous products that are
substitutable in demand and produced with economies of scale
and scope modifies conventional trade theory wisdom that free
trade is best. Increasing returns combined with demand
substitutability creates the externality whereby there can be
welfare worsening excessive trade. Individual consumer
maximization over the perceived foreign and domestic price set
leads to changes in the domestic prices that can yield a
higher expenditure for the whole consumption basket. In such
a case, an import tax on the foreign product keeps demand
substitution below its free market level. Trade volume falls
to a level such that expenditure is minimized.

Analyzing the function that is defined as the difference
between the pre- and post-trade expenditure on the consumption
basket reveals distinct ranges of foreign prices where the
expenditure minimizing policy is autarchy, free trade, or
restricted trade. The difference function and the policy
regions are uniquely specified for cost characteristics,
utility parameters, and initial conditions. Introducing the
foreign price data determines in which region is the economy
and the appropriate policy.

As the industry cost/output tradeoffs worsen in its
decline, the appropriate policy response reduces protection.
The range of foreign prices where free trade is the

expenditure minimizing policy widens. Therefore, while


-2-

independent product demand curves.

In recent years, international trade economists have
borrowed industrial organization models to analyze the role of
market structure in generating patterns of international
trade.? Once the yoke of perfect competition was thrown off,
authors began to analyze the interaction of market structure
and various international trade policies, especially with
regards to international competitiveness.? Other literature
has focussed on deviations from the perfectly competitive
model from the demand side using multi-product outputs.* This
paper tries to merge these two strands by analyzing the
domestic welfare impact of free trade and optimal trade
policies for a declining industry that produces a product
spectrum of outputs under conditions of economies of scope and
scale.

Cursory examination of many declining industries suggests
that their industry characteristics fit the stylized facts.*
Due to both excess capacity and underlying production
technology, these industries seem to exhibit declining costs
of production. A second observation is that many of the
industries produce a product spectrum of goods. The items are
interrelated both on the supply side due to jointness in
production technology, and, on the demand side, due to
non-zero cross price elasticity of demand.

Readers familiar with the contestable markets literature
will recognize an international analogue.* However, the
international problem is more complex. On an item-by-item

basis, within the product spectrum, there are international


-B-

bigger demand curve shift (given any price change), but also

that differentiating between items 1 and 2 in utility 15 more

difficult.

The average cost elasticity of output describes
characteristics of the cost function for good 2. Keeping qi
constant, we measure the movement along the average cost curve

for good 2 given qi that corresponds to pure scale elastcity

of autput. The more important are scale elastiticities, the
steeper the average cost curve. (Refer to figure 2.)
@ACz ge
(7) Sa-1 = -------
@q2 ACz
Qi

Keeping q2z constant, and changing Ga, we measure the
shift in the average cost curve for good 2 that corresponds to
pure scope elasticity for output for good 2. The greater the
importance of scope in the production process, the greater the
shift in the average cost curve when qi changes.

@AC2 aq: OGe(qi,qe) qa
(8) g2/(@qi/qa) = ---- --- Senn me

dq. ace | dq. Ge
q=

When we introduce shifts in the demand for good 2 that
result from cheaper imports of good 1, a combination of a
shift in the average curve curve and a movement along the new
average cost curve determine the post-trade average cost of

Procucing good 2 and given the pricing rule, the post-trade

price of good 2.


-15-

Let us open the economy to trade and determine the
post-trade price of good 2. With trade, Fs falls to P*,,.
Equating changes in quantities on both the demand and supply
sides of the market, we derive, after some manipulation, the

post-trade price of good 2.

(S2-1)e@12(n-1)
(9) P’e = Pa | 1 + ------------- + G2

The post-trade price of good 2 is higher the greater the cross
price elasticity of demand (ei:z), the greater the scale
elasticity of output (s2-1), and the more important the
elastiticy of scope (gm).

Substituting P’2 into the expenditure difference identity

(7) yields a behavioral specification.

r r l/r
(10) D = {Pi + P2.+ 1} u=

r (Ss2-1)ei2(n-1) r l/r
- €(nPa) + (P201+-------------- +g2]) + 13 ue

The foreign cost advantage (n), the cost structure (g2, s2-1),
and the cross- price elasticity (e:2), (as well as initial
Prices and quantities), all together determine the sign of D
and whether trade increases welfare as measured by expenditure
on the basket of goods.*© When the cross-price elasticity of
demand is at its extremes -- no demand shift when e:2=0 and
infinite demand shift when e:2=-o00-- the expenditure
difference function is unambiguously positive, suggesting a
free trade policy in either of these cases.*” But, it is at

elasticities between the extremes that trade-offs between


INTRODUCTION

Recent economic events of exchange rate appreciation and
current account deficit have increased popular and political
focus on the declining industries in the developed countries.
The loss of jobs and national prestige has engendered a
politically fueled search for a remedy to natural forces of
economic change and development. Workers and management alike
have demanded import protection, although plant mergers, labor
retraining, and wage give-backs have also been used more
recently to ameliorate the problem at its source.

Historically, the adage "free trade is best" captured the
philosophy of most trade economists on the protection issue;
trade theory models generally concluded that the force of
comparative advantage that leads to the supplanting of
developed country production by LDC imports was to the long
run welfare benefit of both the developed countries and the
DCs. Sectoral welfare effects in the developed countries
night appear to be to the contrary, but appropriate transfers
from sunrise to sunset industries evidenced the net welfare
gain to the nation as a whole of allowing market forces to
act. However, the standard trade theoretical result depends
Significantly on strict assumptions of industry
characteristics and structure. Specifically, it posits a cost
structure with decreasing or constant returns to scale,

marginal revenue equals marginal cost pricing rules, and


~ 2h

imported item was subject to a tax. Given a foreign price,
minimizing expenditure when cost/output tradeoffs worsen
requires more consumption gains from the imported item. Any
tax imposed on the foreign price must fall. Therefore, even
if an industry petitioned and received protection from imports
in the early stages of decline, it cannot expect increased
protection as it continues to decline. A declining industry
receives less and less protection as it loses product spectrum
comparative advantage. Referring to figure 5, a more apparent
cost/output tradeoff shifts n© right, n* shifts left squeezing
the R region: both the DD and TT curves rotate downward.?? But
note that the sum of the A and RK regions shrink with a ret
expansion of the T region: there is a greater range of foreign
cost advantages such that free trade is the optimal policy.
T’, the tariff associated with a foreign cost advantage n’,
falls unambiguously: the price protection afforded the
domestic industry is reduced.

The domestic industry's profits must be squeezed by this
cap since the firm cannot pass on the assumed cost increase
without losing additional demand for good 2. Eventually the
reduced profitability leads to the complete demise of the
domestic industry unless it can restructure its cost
characteristics. Thus we assure the long run shifting of all

the products in the spectrum to the foreign producer.


Abstract: Increasing returns to scale and scope in production
technology combined with product substitutability in demand
yields an environment where free trade may not maximize
domestic country welfare. If not, there is an optimal tax on
imports that depends on the cross-elasticity of demand between
the products in the spectrum and on the degree of economies of
scale and scope in technology. However, even if protection
may be warranted in the short run, the long run solution is

consistent with the theory of comparative advantage.


- 32-

REFERENCES

Areeda F. and D. F. Turner. “Predatory Pricing and Related
Practices Under Section 2 of the Sherman Act". Harvard Law
Review, 1975.

Baumol, William J. and David R. Bradford. "Optimal
Departures From Marginal Cost Pricing". American Economic
Review, 60:2 (1970).

eee » John C. Panzar, and Robert D. Willig.
Contestable Markets and the Theory of Industry Stucture.
Harcourt Brace Jovanovich:New York, 1982.

oe » Elizabeth E. Bailey, and Robert D. Willig.
"Weak Invisible Hand Theorems on the Sustainability of
Multiproduct Natural Monopoly". American Economic Review,
67:3 (1977).

Brander, J. and B. Spencer, “Export Subsidies and
International Market Share Rivalry", Journal of
International Economics, 1985.

Business Week. "Republic and Jones and Laughlin Merger?".
October 16, 1983.

"Industrial Policy", September, 1983.

Faulhaber, Gerald R. "Cross-subsidization: Pricing in
Public Enterprises". American Economic Review, 65:5 (1975).

Grossman, Gene. “Import Competition from Developed and

Developing Countries", Review of Economics and Statistics,
64:2 (1982).

Helpman, A. and P. Krugman, Market Structure and Foreign
Trade: Increasing Returns, Imperfect Competition, and the

International Economy. MIT Press:Cambridge, 1985.
Johnson, Harry. “Optimal Trade Folicies in the Presence of
Domestic Distortions", J. Bhagwati, ed. International Trade.

FPenguin:New York, 1969.

Joskow, F. "Contributions to the Theory of Marginal Cost
Pricing". Bell Journal of Economics, 1973.

oe and A. K. Klevorick, "A Framework for Predatory
Pricing", Yale Law Journal, 1979.

and R. Noll, “Regulation in Theory and Practive:
ew", in G. Fromm, ed. Studies of Public Regulation.
MIT Press:Cambridge, 1984.



-27-

appropriate policy might include protection in the early
stages of industry decline, as costs increase the industry as
a viable entity fades. Protection is lifted with forces of

comparative advantage dictating trade policy.


-n-

Price reduction on item 1 when trade opens up, is defined as n

where

(4) n= PY a/Py Oe ne 1

Increasing n means that the foreign product is less
advantageously priced and n = 1 implies no foreign cost or
price advantage on item 1.

Using the expenditure dual, and holding utility constant
at uS, we can determine whether free trade or autarchy is
welfare improving by comparing autarchy expenditure with free
trade expenditure. ?©

r r i/r

(3) Es (P. + Po + 1) us

"

r r l/r
Ee = (PTM, + P'a + 1) ue

D= Ew - Ee
E. is autarchy expenditure. E* is expediture in free trade
that achieves the same utility level. D is the difference
between the two expenditure levels that achieves the same
target utility level.

If D is greater than zero, then expenditure to reach ue
is greater in autarchy than with free trade. The appropriate
policy allows the import of item 1 since the consumption
benefits outweigh the consumption losses on item 2. While the
domestic firm has comparative advantage in producing item 2,
it loses product spectrum comparative advantage: extracting
item 1 from the product spectrum and producing it more cheaply
overseas yields an expenditure reduction and implied utility
gain.

If D is less than zero, then free trade expenditure


-1h-

figure 2

~e— bc,’ (4/4,
ia | 4/42)
3a,

1 he Pure Sto pe,
pure seale i; \ AC, (4 42)
4,
t —_>
° g.