James Cassing

Steven Husted

English

Research Papers in Economics

Very Preliminary
LOBBYING AS A TRANSPORT INDUSTRY
by
James Cassing and Steven Husted
Department of Economics
University of Pittsburgh
Pittsburgh, PA 15260
September 20061. Introduction
The first lecture on commercial policy to the undergraduate international economics class
often begins with a reference to Bastiat and the revealing insight that tariffs and transport costs
impose economically equivalent barriers to trade.  Of course, at first face in light of some
contributions to the transport cost literature, this is not quite correct since tariffs raise revenue at no
direct resource cost while transportation charges divert revenue to a resource using shipping industry.
Recent contributions to international political economy, however, have similarly introduced a
resource using and revenue squandering element into the tariff model through rent and revenue
seeking.  The purpose of this paper is simply to highlight the analytical equivalence between these two
large but mutually oblivious bodies of literature: lobbying models and resource using shipping models.
As it happens, each literature has independently derived some similar theorems.  Along the way, we
also steal some theorems from each of the literatures and introduce them into the other as a new
theorem, no proof necessary.
Section two discusses the formal similarities between models.  Section three notes parallel
results.  Section four offers some cheap new results.  While we focus on revenue seeking and tariff
seeking as analogs to resource using transport costs, note that any DUP activity would be analogous
as well.  For example, Bhagwati and Hansen (1973) and Sheikh (1974) analyze resource using “illegal
trade” and Bhagwati, Panagrariya, and Srinivasan (1998) allude to the use of the “melting ice”
assumption, reminiscent of Samuelson’s early characterization of transport costs, in describing a
model of smuggling.
2. The Model(s)
We assume a competitive world with linear homogeneous production functions which2
combine capital, Ki, and labor, Li, to produce output Xi at price Pi.  The factors are in the aggregate
perfectly inelastically supplied and command rewards,  r and w.  There are three industries: exports
(E),  imports (M), and, variously, transport or tariff/revenue seeking (T).  For concreteness, we think
of the transport industry as comprised of international shipping firms and the tariff/revenue seeking
industry as comprised of law firms, all of which use some portion of the resource base. 
Formally, using “*” for foreign variables, and denoting consumption and unit input-output
coefficients by Ci and aij respectively, the equilibrium model is given by equations (1) - (10).
(1) aLE  XE  +  aLM  XM  +   aLT  XT =  L
(2) aKE  XE  +  aKM  XM +  aKT XT = K
(3) aLE  w +   aKE  r  =  P
*
E -  J
(4) aLM w + aKM r =  P
*
M  + t
(5) aLT w + aKT  r = PT
(6) J = "E   PT
(7) t = "M PT
(8) "E  (XE - CE) +  "M (CM - XM) = XT
(9) Y = P
*
M  XM + P
*
E XE + t(CM - XM) + J(XE - CE)
(10) Ci = Ci (PE , PM , Y)
While the equilibria are formally the same, the interpretation of the variables differs for each
of the transport, revenue seeking, and the tariff seeking models.
Resource Using Transportation:
Equations (1) - (2) are the usual full employment conditions and equations (3) - (5) are the1Versions of this model appear in Herberg (1970), Falvey (1976), Cassing (1978), and
Casas and Choi (1989).
3
competitive conditions.  In particular, J and t represent the per unit cost of shipping exports and
imports respectively.  PT is the competitive unit price of shipping so that, as in equations (6) - (7), the
unit cost of shipping goods is given by how many units of shipping are required per unit of the
commodity, "E and "M, times the unit price of shipping.  Equation (8) guarantees the provision of
adequate shipping and the model is closed by the consumption functions (10) which utilize the
definition of national income (9).
1
Revenue Seeking:
In the revenue seeking models, the existence of trade taxes J and t, assumed exogenously
determined, creates revenues which are sought by resource using law firms, possibly serving on behalf
of the Congress or public service.  In equation (5), PT is the competitive price of a law firm unit and
so in equations (6) - (7), "i  has the interpretation of the number of lawyer units used to secure the
revenue created by one unit of (taxed) exports or imports.  (Apparently, "E and "M are defined by (6)
- (7) and are not technical parameters as in the shipping model.)  Full revenue seeking is implied by
equation (8) since, substituting from (6) - (7),
J(XE - CE) + t(CM - X) = PTXT
That is, the trade tax revenues just equal the value of law firm services expended.  Partial revenue
seeking is also admissible.
Partial revenue seeking would correspond to a combination of trade taxes and resource using
shipping.  Formally, equations (6) - (7) would be replaced  by2Versions of this model have been explored by Bhagwati (1982), Bhagwati and Srivivasan
(1982), and Husted (1991).
4
6') J  =  "E  PT +  Jr
7') t  =  "M PT + tr
there Jr and  tr are the tax components of the additional cost of international trade.  Equation (9) in
either model would now include some unsought tax revenue which could be used to augment
consumption.
2
Geometrically, the equivalence of the models is illustrated in Figure 1, which appears
independently in Falvey’s (1976) resource using transport cost paper and in Bhagwati and
Srinivasan’s (1980) revenue seeking paper.  In the transport literature, the price line tangent to Pt
represents the transport cost inclusive domestic price.  In the DUP literature, that price line represents
the domestic price ratio following the imposition of a tariff.  The production of transport services
requires the use of capital and labor, and this shifts the production point to Pr. In the DUP literature,
revenue seeking leads to DUP activity and a shift in production also to Pr.  The actual production
point is determined by the factor intensity in the production of transport or lobbying services; here
the two are assumed to be the same.  In both cases, the consumption point lies at Cr.  This is due to
the resource cost effect of the shift of otherwise productive resources into activities that, in most
cases, cannot be exchanged for imports. But, as we noted in our introduction, there is one difference
between the transport literature and the tariff literature.  In the absence of revenue seeking,
consumption in the latter occurs at Ct. 
[Insert Figure 1 about here]3Versions of this model appear in Findlay and Wellisz (1982),  Feenstra and Bhagwati
(1982), and Wellisz and Wilson (1986) .
5
Tariff Seeking:
In the tariff seeking model, trade taxes are determined endogenously.  Equations (6) - (7) now
have the interpretation of a “tariff formation function.”  Since tax levels depend on the amount of
resources expended, however, we must write
6")  J = J (XTE) =  "E (XTE) PT
7")   t  =  t(XTM)  =  "M (XTM) PT
where XTi is the share of XT devoted to lobbying for or against trade taxes on good i and so "i has
the interpretation of the per unit trade tax secured as a proportion of the price of one unit of law firms
devoted  to the legal struggle.  This model is always qualitatively equivalent and exactly equivalent
in equilibrium to the model of transport costs if the height of the barriers are the same, J > 0, t > 0,
and if the value of the resources used in tariff seeking equal the tariff revenue which is raised (which
equals the transport costs in the shipping model).  If the value of the resources expended on tariff
seeking are less than the tariff revenue raised, then the tariff seeking model resembles the transport
cost model with tariffs.
3
Isomorphisms:
In equilibrium, the models look mathematically very similar.  Thus, we will be able to compare
theorems which rely only on the configuration of the equilibrium.
For notational convenience, denote:
TC, transport cost model6
TS, tariff seeking model
RS, revenue seeking model
Assume away income redistribution problems – say, tastes are identical and homothetic.  Suppose that
capital intensities are the same across models no matter what the interpretation of the industry, and
that the heights of the trade barriers are the same.  Then, to summarize the earlier discussion of
equilibria, we offer as a lemma the insight to be used in our proofs below:
Lemma 1
1. The TC, the full RS, and the TS where total lawyers fees equal tariff revenues are
identical.
2. The TC with trade taxes (“partial TC”), the partial RS, and the TS where lawyers fees
are less than tariff revenues (“partial TS”) are identical.
Of course, if we are to compare equilibria before and after the introduction of some new
resource using transport industry then we must recognize that TC and full RS represent analysis in
an already distorted world.  Alternatively, models of the TS variety, or TC moving from no transport
costs to resource using transport costs, represent analysis between initially undistorted (or less
distorted) equilibria to distorted (or more distorted) equilibria.
3.  Old Theorems in New Bottles
In this section we enumerate several interesting results which have been derived in either the
transport or lobbying literature and introduce the theorem to the other literature.  For example, if the7
transport industry uses resources, then one might think it possible that the industry withdraw
resources from the economy in a way that paradoxically reduces exports enough to improve welfare
through a favorable terms of trade improvement.  But this cannot happen, as is “proved” in the
revenue seeking literature.
Theorem 1
Relative to free transport, the existence of a resource using transport industry can lead to a
terms of trade improvement, but welfare cannot increase.
proof:
i.  Full revenue seeking reduces welfare (Bhagwati - Srinivasan (1980)).
ii. TC and RS are equivalent by lemma 1.
Note that either of the TC and RS results follow from the well known result in the trade
literature that, with some qualifications, transfers cannot enrich the donor country.
Theorem 2
Technological  regress in transport (e.g., the Suez canal closes) accompanied by tariff
reductions which keep domestic prices the same can improve welfare.
proof:
i.  Partial revenue seeking increasing can improve welfare (Bhagwati - Srinivasan (1980)).
ii. Partial TC and partial RS are equivalent by lemma 1.
Corollary 2.1
Technological progress in transport accompanied by tariff increases which keep domestic8
prices the same can reduce welfare.
Corollary 2.2
In the presence of quantitative restrictions (QRs), technological progress (regress) in shipping
will lead to an improvement (a deterioration) in welfare.
proof:
Increases in DUP activities in the presence of QRs leads to decreases in welfare (Krueger
(1974)).
Interestingly, some of the results on technical progress in shipping and welfare changes have
been around in the transport cost literature independent of the DUP activity literature (Casas and
Choi (1989); Cassing (1980),(1986)).
Theorem 3
Transport cost induced capital flows leave domestic welfare unchanged: They cannot lower
welfare as they can with tariffs a la Brecher-Diaz Alejandro (1977).
proof:
i.  Tariff induced capital flows leave domestic welfare unchanged with full revenue seeking
(Rieber (1986)).
ii. The TC and full RS are equivalent by lemma 1.
There are also some theorems in the transport cost literature which relate to the internal
distribution of income when tariff are altered.  These theorems carry over to the DUP models.9
Theorem   4
In the presence of tariff/revenue seeking, an increase in the price of the relatively labor-
(capital-) intensive traded good can result in a fall in the factor price of labor (capital).  That
is, tariffs can fail to protect the intensively-used factor in the importable industry even for a
small country.
proof:
i. The Stolper-Samuelson result can be lost with respect to traded goods in the presence of
a resource using transport industry (Cassing (1978)).
ii. TC, TS, and RS are equivalent by lemma 1.
Activities that use resources should have an impact on comparative advantage and the pattern
of trade.  In the resource using transport cost literature there is a theorem showing, in the context of
a fairly general model, that the existence of resource using transport cannot reverse the pattern of
trade (Cassing (1979)).  We would conjecture that this result carries over to the DUP models.
Finally, there is a small literature of foreign lobbying which has implications for the transport
models (Hillman and Ursprung (1988) ; Husted (1991)).  We offer one such carry-over theorem.
Theorem 5
Suppose that the home country produces shipping solely for export.  If foreign demand for
home shipping increases, home welfare will not change from free trade levels if home is small.
However, if the home country is large, then home welfare may rise, fall, or remain unchanged
relative to free trade levels.10
proof:
i.  Foreign expenditures on lobbying in the home country results in unchanged welfare if home
is small and may raise, lower, or leave welfare unchanged if home is large (Husted (1991)).
ii. Lemma 1.
4.     Conclusions
Transport costs and tariffs both drive a wedge between foreign and domestic prices.  The
effects generally are not the same if in addition the transport industry requires some of the domestic
resources.  This has been explored in the transport cost literature.  However, if tariffs are also
associated with demands on the resource base, then an equivalence between tariffs and transport
emerges.  This association between tariffs and directly unproductive uses of resources is just what
the DUP activity literature investigates.  Since the mathematics of the two models are the same,
reinterpretation of the variable has enabled us to establish some “new” results for each of the two
literatures by borrowing theorems already proven in one of the literatures.11
References
Bhagwati, Jagdish (1982), “Directly-Unproductive Profit-Seeking (DUP) Activities,” Journal of
Political Economy, 90, pp. 988-1002.
Bhagwati, Jagdish, Richard Brecher, and Tatsuo Hatta (1984), “The Paradoxes of Immiserizing
Growth and Donor Enriching ‘Recipient-Immiserizing’ Transfers: A Tale of Two
Literatures,”  Weltwirtschaftliches Archiv, pp. 228-42.
Bhagwati, Jagdish and B. Hansen (1973), “A Theoretical Analysis of Smuggling,” Quarterly Journal
of Economics, 87, pp. 172-87.
Bhagwati, Jagdish and T.N. Srinivasan (1980), “Revenue Seeking: A Generalization of the Theory
of Tariffs,” Journal of Political Economy, 88, pp. 1067-87.
_____ and Arvind Panagariya (1998), Lectures on International Trade, (Cambridge: MIT Press).
Brecher, Richard and Carlos Diaz-Alejandro (1977), “Tariffs, Foreign Capital and Immiserizing
Growth,” Journal of International Economics, pp. 277-88.
Casas, F.R. and E. Kwan Choi (1989), “Transport Costs and Immerserizing Growth Under Variable
Returns to Scale” International Journal of Transport Economics, pp. 3-18.
Cassing, James (1978), “Transport Costs in International Trade Theory: A Comparison with the
Analysis of Nontraded Goods,” The Quarterly Journal of Economics, pp. 535-50.
_____ (1979), “Trade Pattern Predictions and Resource Allocation in a Model with Jointly Supplied
International Transport Services,” International Journal of Transport Economics, pp. 293-
317.
_____ (1980), “Shipping Innovation in the Pure Theory of International Trade,” International
Journal of Transport Economics, pp. 301-25.12
_____ (1986), “A Wicksellian Model of International Freights and Prices,” International Journal of
Transport Economics, pp. 7-20.
Falvey, Rodney (1976), “Transport Costs in the Pure Theory of International Trade,” Economic
Journal, pp. 536-50. 
Feenstra, Robert C. and Jagdish Bhagwati (1982), “Tariff Seeking and the Efficient Tariff,” in Jagdish
Bhagwati (ed.), Import Competition and Response, Chicago: University of Chicago Press.
Findlay, Ronald and Stanislaw Wellisz (1982), “Endogenous Tariffs, the Political Economy of Trade
Restrictions and Welfare,” in Jagdish Bhagwati (ed.), Import Competition and Response,
Chicago: University of Chicago Press.
Herberg, Horst (1970), “Economic Growth and International Trade with Transport Costs,”
Zeitschrift fur die Gesante Staatswissenschaft, pp. 577-600.
Husted, Steven (1991), “Foreign Lobbying: A Theoretical Analysis,” The Eastern Economic Journal,
pp. 89-99.
Krueger, Anne (1974), “The Political Economy of a Rent-Seeking Society,” American Economic
Review, pp. 291-303.
Rieber, William (1986), “
Sheikh, M (1974), “Smuggling, Production, and Welfare,” Journal of International Economics, pp.
355-64.
Wellisz, Stanislaw and John D. Wilson (1986), “Lobbying and Tariff Formation: A Deadweight Loss
Consideration,” Journal of International Economics, pp. 367-75.13
Figure 1

Directly-Unproductive Profit-Seeking (DUP)

Foreign Lobbying: A Theoretical Analysis,”

Lobbying and Tariff Formation: A Deadweight Loss Consideration,”

Revenue Seeking: A Generalization of the Theory of Tariffs,”

Shipping Innovation in the Pure Theory of International Trade,”

Tariffs, Foreign Capital and Immiserizing Growth,”

The Paradoxes of Immiserizing Growth and Donor Enriching ‘Recipient-Immiserizing’ Transfers: A Tale of Two Literatures,” Weltwirtschaftliches Archiv,

The Political Economy of a Rent-Seeking

Trade Pattern Predictions and Resource Allocation in a Model with Jointly Supplied

Lobbying as a Transport Industry

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