Economics Letters
North-Holland
POLITICALLY
REALISTIC
PROFs and Tariffs
Richard
287
24 (1987) 287-290
BALDWIN
Columbia
Unwersity,
Received
29 April 1987
OBJECTIVE
FUNCTIONS
AND TRADE
POLICY
*
New York, NY 10027, USA
This paper demonstrates
a mathematical
correspondence
between the deus ex machina tariff formation approach and political
economy approach. The correspondence
implies that the tariff chosen by lobbying-influenced
policy makers will be equivalent
to a tariff chosen by a deus ex machina government
that gives ‘too much’ weight to profits. This result allows many political
economy issues to be addressed in the simple framework of a deus ex machina government
which faces a politically realistic
objective function (PROF).
1. Introduction
The literature on the political economy of tariffs encompasses
extensive theoretical and empirical
research on the actual process by which trace policy is chosen. Most international
economists concur
with the general conclusions
of this literature, namely, that trade policy is chosen by policy makers
who are interested in more than social welfare. Yet, despite the broad acceptance
of the lessons of
the political economy approach, trade economists
rarely incorporate
political economy factors into
their models.
The reasons for this omission are twofold: (1) the process by which a trade policy is chosen is
often tangential to the positive and normative aspects of the policy itself, and (2) political economy
models are awkward to work with. This note is intended
to at least partially
remove the second
concern.
When the issue arises of how tariffs are chosen, a frequent solution is to assume that governments
choose the tariff to maximize a social welfare criterion. We refer to this as the deus ex machina
approach. Alternatively
the tariff determination
process is sometimes modelled more explicitly by the
political economy approach. This note demonstrates
a mathematical
correspondence
between the two
approaches.
The importance
of this result lies in the fact that it allows us to deal with many political economy
issues without explicitly modelling the political process. Specifically, the correspondence
implies that
the tariff chosen by lobbying-influenced
policy makers will be equivalent
to the tariff chosen by a
deus ex machina government
that gives ‘too much’ weight to profits. We can therefore address many
political economy concerns in the much simpler framework of a deus ex machina government
which
faces a politically realistic objective function (PROF).
* I gratefully
acknowledge
0165-1765/87/$3.50
the helpful
comments
of Paul Krugman.
0 1987. Elsevier Science Publishers
Rob Feenstra.
B.V. (North-Holland)
Harry
Foster
and Robert
Baldwin
288
R. Baldwin / Political.!y reuhstic objective functwns
and wade poliq
2. The dew ex machina tariff process
For the sake of concreteness,
we shall focus solely on tariffs, although the results go through for
other trade policies with obvious modifications.
For the same reason we shall focus on the case of a
single tariff rate. A standard approach to tariff determination
is to assume that governments
choose
tariffs to maximize some social welfare function. With the recent trend toward partial equilibrium
analysis in international
trade, one partial equilibrium
welfare criterion has been especially popular.
In many recent studies [e.g., Dixit (1985) Venables and Smith (1987) Rodrik (1987) and Baldwin
and Krugman
(1986, 1987)] the weighted sum of consumer surplus, profits and tariff revenue has
been taken as the appropriate
measure of social welfare, so that W = aC + C:= , p’n-’ + TH, where C
is consumer surplus, r’ is domestic profits of firm i, H is the tariff revenue and (Y, p’ and r the
weights (often the weights are taken as equal to unity). The deus ex machina government’s
first-order
condition is
cY(dC/‘dT)
+ i
P’(d+‘dT)
+ T(dH/dT)
We assume that the welfare criterion is strictly
sufficient condition on the optimal T.
= 0.
concave
(1)
in T so that (1) constitutes
the necessary
and
3. The political economy tariff process
We present a fairly general political economy model. This model is not intended to incorporate
any novel elements. As such it draws heavily on the contributions
of Findlay and Wellisz (1982)
Feenstra and Bhagwati (1982) Mayer (1984) and Brock and Magee (1978). Robert Baldwin (1986)
provides a useful summary of the positive theory of tariff determination.
All political economy models start from the assertion that policy makers choose tariffs to get
and/or
stay elected. One interpretation
of this is that policy makers choose policy in order to
maximize the number of votes they receive. As Baldwin (1982) points out, ‘. . Pareto efficient
policies will be implemented
under majority rule provided that such conditions
prevail as perfect
information,
no voting costs and the absence of any costs of redistributing
income’. Since such
conditions
do not actually prevail, votes depend upon lobbying expenditures
as well as the welfare
impact of the policies chosen.
This may be formalized
by assuming
that the political
economy
tariff, T”, is defined as
To = argmax V( C(T), r(T),
H(T),
R(T)), where I’ is the function
that maps the components
of
welfare and lobbying expenditures
into votes. 7~ and R are n-element vectors of profits and lobbying
expenditures
respectively.
C. 7, H and R are in general a function of the tariff.
In political economy models policy makers choose tariffs to stay elected. Industry groups lobby to
influence the tariff rate in order to maximize profits. In choosing the tariff, policy makers weigh the
loss of votes due to the negative welfare impact of the tariffs against the votes gained through
lobbying expenditures.
In order to optimize this trade off, policy must be able to evaluate the amount
of additional lobbying that a marginal increase in the tariff will elicit. Likewise, in order to choose an
optimal lobbying expenditure,
lobbyists must be able to evaluate the marginal effect on the tariff of
additional
lobbying.
A complete model of the tariff process would require consideration
of the timing and strategic
assumptions
governing this lobbyisttpolicy
maker game. For the sake of clarity, we skirt this set of
issues by assuming
that the derivatives
dR’/dT
and dT/dR’
exist, are well defined and that
R. Baldwin / Politically realistic ohJectiue functions
289
and trade pohq
dR’/dT=
l/(dT/d
R’). Here R’ is the ith element of the lobbying
vector. We refer to these
derivatives as the lobbying derivatives. Lastly, we assume that there is a unique equilibrium
in the
’
implicit game among policy makers and the lobbyists, so that To is unique.
Under these assumptions
T ’ will be the solution to the equation
(aV,AC)(dC,‘dT)
+ 5
[(aV/&r’)(d+/dT)]
+ ,tI [(aV/aR’)(dR’/dT)]
(2)
= 0.
Lobbying expenditures
for a typical industry
maximization
of r’( T( R’)) - R’. Namely,
(ds’/dT)(dT/dR’)
Having
this note.
exposed
+ (aV,‘M)(dH/dT)
- 1= 0
stylized
for
versions
are characterized
by the first-order
conditions
of the
all i.
(3)
of the two approaches,
we are ready to prove the main result of
Proposition 1. For any given voting function. V, and set of lobbying derivatives, there exists a set of
weights ((YO, /3’“, r” ) such that T chosen by the political economy process will also be the T chosen by
the deus ex machina process faced with these weights.
Proof:
we get
The proof is by construction.
0 = (aV,‘X)(dC,‘dT)
+ t
From (2) (3) and the assumption
(aV/aa’)(d+‘dT)
that dT/d
R’ = l/(dR’/dT)
+ (aV/aH)(dH/dT)
r=l
+
,Fl (W’aR’>kW’dT).
(4)
By the assumed strict concavity of W, and the uniqueness
of To, both (4) and (1) have unique
solutions. We refer to these as To and T * respectively.
Taking (YO= (aV/X),
flfo = (aV/a’) +
(aV/aR’)
and F” = (aV/aN)
it is clear that (1) and (4) are identical equations
so that T* = T”.
Q.E.D.
This proposition
might be taken as a justification
of the weighted, additive welfare criterion, with
the weights being determined
by the marginal voting power of each group. In this light, we can
interpret Proposition
1 as saying that the tariff chosen by lobbying-influenced
policy makers will be
equivalent
to the tariff chosen by a deus ex machina government
that gives ‘too much’ weight to
profits. It would be straightforward
to incorporate
labor union lobbying into the models. In which
case we would conclude
that the tariff were chosen givng ‘too much’ weight to the welfare of
unionized
labor. Lastly, it is worthwhile to note that the size of the weight given to profits varies
directly with the marginal effectiveness of lobbying.
290
R. Baldwin / PoliticaN?, realrstic objective functions and
tradepobcy
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