Journal
of International
Economi:s
9 (1979? 47-55. 0 North-Holland
Publishing
DOMESTIC MONOPOLY AND REDUNDANT
PROTECTION
Gideon FISHELSON
Company
TARIFF
and A,rye L. HILLMAN*
Tel-Aviv University, Ranzat Aviv, l.prael
Received February
1977, revised version received December
1977
This paper examines the redundancy
of tariff protection
when there is a single domestic
monopolist
producer. The cases where the monocolist
exp jrts in free trade and where he
confronts import competition
are distinguished
and a genera: rule characterizing water-in-thetariff in protected equilibrium is derived.
1. Introduction
One of the problems confronting researchers in an evaluation of the
heights of protective tariff barriers is that some component of ths degree oi
protection indicated by officially dictated restraints on international trade
may not be utilized by domestic producers. Such redundant tariff protection
has been noted in the literature under the nomenclature, water-in-the-tariff.
Our purpose in this paper is to inj#estigate and distinguish between
circumstances wherein tariff protection is redundant at the margin, and
wherein the full degree of protection offered is utilized.* The case where the
domestic industry is competitive will not be considered. For then the nature
of tne relation between provided and utilized protection is straightforward:
water-in-the-tariff occurs if and only if the world price plus the tariff exceeds
the competitively determined domestic autarkic price. We shall be concerned
rather with the case where the domestic industry consists of a single profitmaximizing firm : this yields an interesting range of subtle and diverse
outcomes.’
*We are grateful to Jagdish Bhagwati and E. Tower for helpful comments and have also
benefited from the advice of an anonymous referee. F’ull responsibility remains with the authors.
The finan.cial support of the Foerder Institute for E,conomic Research, Tel-Aviv IJniversity, is
acknowledged.
‘We shall not be concerned with the rationale underlying protection. nor with the question of
why tariffs may have been employed as policy instruments
rather than Pareto superior tax
subsidy policies. On deployment of policy instruments, see Bhagwati (1971).
2For a review of partial equilibrium analyses of the implications of monopoly for international
trade, see for example, Corden (1974, ch. 8), Caves and Jones (1977, ch. 9). fi general equilibrium
analysis of domestic monopoly and the gains from trade is provided by A,Ielvin and Warne
(1973).
48
G. Fishelson
and A.L. Hillman, DoFes:ic monopoly
In section 2 we assume that the domestic mtinopolist exports in free-trade,
and in section 3 that he csnfronts import-competition. Then in section 4 ‘we
present a general rule characterizing water-in-thetariff in a protected equilibrium. Conclusions are summarized in the final section.
’ 2. Comparative
advantage
Consider a profit-maximizing fu:n which is the sole domestic producer of a
tradeable good, but does not have monopoly power in the world market3
Given. free-trade, the firm’s position as sole domestic producer is of no
significance for its market behavior. The imposition of a tariff, however,
separates the domestic and foreign markets, and so permits the firm to
exploit its domestic monopoly position.
Suppose the firm iras a comparative advantage in international trade in a
free-trade equilibrium. Such a case is depicted in fig. 1, where p* is the
exogenous world price and D, MR and MC' respectively indicate the
domestic (inverse) demand, marginal revenue and marginal cost functions.
With free-trade, output g1 is produced, of which q2 is sold domestically and
(4,. -q2) is exported.
pY[ I +
p”(I+
Fig. 1.
“We assume that domestically
produced and foreign produced versions of the good are
identical. That is, the good is homogeneous. This then rules out the appearance of water-in-thetariif [noted by Corden (1971, p. 20611 due to quality differences between domestically produced
goods ar,d imports. Obserje that water-in-the-tariff
due to quality differences requires that
domestic goods be of higher quality than imports. In developing economies one might generally
expect the quality differential to be in the opposite direction. We shall further not be concerned
with redundancy of tariffs in the sense of provision of duplicate protection. As Jagdish Bhagwati
(1966, p. 66) has nsoted, an industry may seek a protective tariff even though the protective
effects which the tariff has to offer are alre.ady provided by quantitative
restrictions. The redson
is that direct controls may be subject to frequent revision, while tariffs might Se exnected to be
more lasting.
G. Fishelson and 4.L. Hillman, Domestic monopoly
49
Let an ad valorem tariff now be imposed at rate t, yielding a maximum
feasible domestic price, p*(l + t). When will t be such that some part of the
protection otrered by the tariff is redundant? An answer to this question
follows by considering the nature of successive profit-maximizing equilibria
as the tariff-rate is continuously enlarged away from zero. The imposition of
a marginal tariff, and subsequent tariff increases thereafter, do not alter the
firm’s profit-maximizing output, which remains ql. Independently of the
tariff, the rule for profit-maximization remains that marginal revenue in the
world market p* be equated with domestic MC. The effect of the tariff is to
permit the firm to enhance its profits by price discrimination between
domestic and foreign sales. A marginal tariff increase manifests itself in an
increase in domestic price by the full extent of the increase in protection and
a reallocation of the invariant output q1 from the domestic to foreign
market -until a domestic price p*(l + t2) is attained with domestic sales qs.
The consequences of the tariff may be viewed in terms of movements of the
point G on the dornpstic demand function: a tariff-rate t, shifts G to G”,
where the full tariff is utilized G;nd exports are increased io (ql -q3); the
maximum quantity of exports is (4i -q4), at G’, where the domestic price is
p*( 1 +tz j. Tariff increases beyond the level of t, manifest therselves as
water-in-the-tariff, for at G’ the discriminating monopoly profit-maximizing
condition p* - MR = MC is satisfied. Hence p*(l + tz) is the highest domestic price which the firm would choose to impose. It would accordingly ignore
the opportunity afforded by a higher tariff than ta to raise the domestic price
further.
3. Comparative disadvantage
Suppose now that the industry exhibits a comparative disadvantage in
international
trade, so that in the free-trade equilibrium the domestic
produc.:r confronts import-competition. We shall distinguish two cases: that
where the equality of marginal cost and marginal revenue as derived from
the domestic demand function yields a value less than the world price: and
that where, conversely, the world price is less. In the first case, in the
profit-maximizing equilibrium at the maximum exploitable tariff-rate, the
firm exports some of its output; in the second case the equilibrium at the
maximum exploitable tariff-rate is autarkic.
3.1. Exports
In fig. 2 equality between marginal revenue MR (derived from domestic
demand D) and marginal ccst MC obtains at a value less than the
exogenous world price D*. In the free-trade equilibrium the firm produce> ~~~
(determined by p* = UC) and the quantity (q4--yz) is imported. The
so
G. Fishelson and AL. Hillman, Domestic monopoly,
imposition of a imarginal tariff raises the maximum price which the firm may
receive for its output, and as such moves the point F on the demand function
in the direction of H. Along the segment FIY of the demand function, the
firm’s response in its price and output Idecisions to further successive
marginal indrements in the tariff yields outcomes equivalent to those which
would occur, ‘were the domestic industry competitive: domestic output
increases, c:onsumption is reduced, and import.s fall. A tariff rate tI yielding a
domestic price p*(1 + E,) supports an autarkic equilibrium wherein the firm
supplies total domestic demand d3.
MC
O--I?g. 2.
Beyond H, increases in the tariff rate from tl up to t2 maintain successive
autarkic equilibria. The firm contracts output (from q3 towards qz) and
raises domestic price by the full extent of tariff jncreases, from p*(l +t, )
towards p*(t +t2). Hence the tariff over this range is countervailing the
output-raising incentive effects of the initial tariff increases up to tl. At J,
ulherc the tariff reaches the height t,, output contraction ceases; output has
then returned to its free-trade equilibrium level q2. Since here the world price
1s o’nce rrore equal to MC, further increases in the tariq beyond t2 (towards
t3) occasion mcvement of domestic consumption demand from J towards L
but maintain output at J. Domestic consumption contracts, and the difference bt:tween it and qa is exported.
This process a! substitution of foreign for domestic sales halts at L, where
the tarifr t, leads to domestic consumption q1 and exports of (q2 -ql ). Were
the firm free of (tariff-inclusive) import-competition, it would satisfy its profitmaximizing condition MR = p* = MC by choosing to produce output q2
and allocating this output between domestic and foreign markets in the
manner indicated at Land J. Hence, at the tariff t, supporting equilibrium at
L, revenue fro-n domestic sales is maximized. The firm would accordingly
G. Fishelson and A.L. Hillmuv, Domestic monopoly
ignore tariff increases to protective levels beyond
in excess of t, would yield redundant protection.
t3,
51
and consequen?!y a tariff
3.2. Autarky
In fig. 2 the effect of tariff-rates between t2 and the maximal exploitable
rate t3 is to cause the domestic industry to switch from an import-competitor
in the free-trade equilibrium to an exporter in the protected equilibrium. This
transition from imports to exports is, however, not a necessary consequence
of the tariff. The equilibrium at the maximum exploitable tariff rate may be
autarkic. Such an equilibrium is depicted in fig. 3, which in distinction to fig.
2 is characterized by the equality of MR and MC above the world price p*.
p’(l+
p”Cl+
Fig. 3.
For initial departures from the free-trade equilibrium up to the minimum
autarkic tariff-rate t,, the firm’s response in fig. 3 is no different from the case
described in fig. 2. And in departing from H in response to tariffs in excess of
t,, the firm maximizes profits by contracting its output from q3 in successive
autarkic equilibria. But there now exists no tariff which will lead the firm :o
export: as the tariff is increased from t, and domestic demand contracts from
H, a tariff t, is reached which sustains an autarkic profit- naximizing
equilibrium where MR = MC > p*. This equilibrium, depicted at R is
attained before the point .I, where p* .= MC and from which further
contractions in domestic demand would lead to exports. The price ~"(1 + tz)
and quantity q, chosen by the domestic monopolist at 12 ma+mize profits
without regard to the world market; so t2 is the maximum exploitable rate,
and for tariff-rates beyond tz there is water-in-the-tariff.
4. A necessary condition for water-in-the-tar;
Our approach
in the above sections has been to establish the maximum
tariff utilized by considering the consequences of successive tariff increases
52
G. Fishelson and A.L. Hiilman,
Domestic mortopol)
!n this section we focus on a given tariffaway from a free-trade equilibri
rate and ask the question., untDet what circumstances will that tariff yield
redundant protection?
Given a tariff-rate 6 we are able to construct an effective marginal revenue
function as STUVZ in fig. 4. The segment ST is the consequence of importcompetition at the tariff-inclusive domestic price; UV is a segment of the
actual marginal revenue function derived from the domestic demand function: and the unbounded segment VZ reflects exports at the world price. In
all, the effective marginal revenue function is composed of four segments (the
above plus the connecting segment TU), hence there are four categories of
equilibria with marginal cost.
gP(l ti)
P3
PI
P”
qoq?,
92
Fig. 4.
Should marginal cost be of the form of MC, (so that equality with
effective marginal revenue is on the segment Vi?), the monopalist maximizes
profits by producing output CJ,, exporting (4, --(I*) and selling (I~ domestically a* price pI_ Since p, is less than p*(l +F), there is water-in-the-tarif
At marginal cost MC2 (on segment UV) the profit-maximizing equilibrium
is autarkic. The equality of MC and MR yields an output y3, which iu sold
domestically at price p3. This price is again less than p*(l -t-9, and so there is
once more water-in-the-tarifS:
On the other hand, for marginal cost functions MC3 and MC4 (with
marginal cost-marginal revenue equalities respectively on the segments TU
and ST), the monopolist’s domestic profit-maximizing price incorporates the
full level of tariK protection. With MC3 the monopolist supplies the entire
dom.estic market (and since p* < MC does not era*ort), while with MC, the
domestic market is shared with imports.
Consider now fig. 5. This is a repetition of fig. 4 except that the effective
marginal revenue function consist; of but three (linear) segments. Tine
segment UV (composed of the actual marginal revenue function derived from
G. Fishelson and AL. flillmzn, Domestic monopoly
53
domestic demand) is missing. Effective marginal revenue consists of p*( 1 + F)
for domestic sales (the segment ST), and of p* for exports (the segment VZ).
In each of the three characteristic equilibria established by the marginal cost
functions MCI, MC2 and MC, the domestic profit-maximizing price is p*(l
-1-0~ so no part of the tariff is redundant. In the case of MC,, the firm
exports: with MC2 the equilibrium is autarkic; and wrth MC3 there is
import competition. This confirms that all possible trading situations are
consistent with full utilization of tariff protection,
Fig. 5.
The comparison afforded by the outcomes in figs. 4 and 5 indicates a
necessary condition for the existence of water-in-the-tariff: the effective
marginal revenue function (as derived for the given tariff rate) must contain
as one of its segments a part of the actual domestic marginal revenue
function. Let qO denote domestic demand at the full tariff-inclusive domestic
price. Then this condition will be satisfied if NR(q,)
> p*; that is, marginal
revenue derived fron; domestic demand at the full tariff-inclusil;e price must
exceed the world price if water-in-the-tariff is to be a possibility.
5. Concluding summary
III this paper we have investigated the circumstances of redundant tariff
protectron when domestic output is produced by a sole profit-maximizing
firm.’ Our conclusions are sllmmarized in the following propositions:
‘Our cm.xm has been exclusively with tariffs. Given perfect competition [and also certainty,
see Fishelson and Flatters (1975)], tariffs and quotas have a well-established
equivalence
relation. This equivalence
is, however, compromised
by the introduction
of monopoly
[see
Shibata (1968). Bhagwati (1968)‘J, and hence the above analyses of water-in-the-tariff
will not be
symmetrically appropriate
when a quota is the instrument of protection. The specification of a
quota equtlibrtum is further complicated by the variety of domestic market structures that may
in prmcipk obtain as d consequence of the procedure for quota allocation. As Bhagwati (1965)
54
G. Fishelson and AL. Hillman, Domestic
monopol)
(a) If in free trade the firm has a comparative advantage in the world
market (and so exports and ser rices the entire domestic market) then as the
tariff is raised fror- zero the firm maintains its level of production but shifts
its sales from tht- Jiomestic to the foreign market; the sales-shift ceases when
the tariff supports that domestic price at which domestic marginal revenue
equals the world price (both of which equal dome&ic marginal cost), and
increases in the tariff beyond this rate yield water-in-the-tariff.
(b) Ii’ in free-trade the firm has a comparative disadvantage in the world
market (and so does not supply the entire domestic market), then as the
tariff is raised from zero, the firm raises its output and imports simultaneously contract until the tariff eliminates imports completely; further
increase., in the tariff maintain successive autarkic equilibria while contracting the firm’s output. If a tariff-rate supports a domestic price at which
marginal revenue equals marginal cost at a level above the world price, then
this tariff yie!ds maximum exploited protection and it establishes an autarkic
equilibrium: on the other hand, if tariff increases lead successive autarkic
equilibria to culminate in a tariff level at which, as a consequence of output
contraction, marginal CDS?equals the world price, then this places a lower
bound on output contraction. Further increases in the tariff maintain the
latter output, but lead to a substitution of exports for domestic sales (as in
Proposition
la). ‘This process continues until the tariff raises marginal
revenue to the level of marginal cost Tnd the world price. Increases in the
tariff beyond this rate are redundant.
(c) A necessary condition for a given tariff-rate to support an equilibrium
with water-in-the-tariff is that the domestic monopolist’s effective marginal
revenue function contain as one of its parts a segment of the actual marginal
revenue function derived from the domestic demand curve.
notes, the post-quota outcome may be competition, monopoly, or duopoly; Bhagwati’s
classification of outcomes is further extended in F’shelson and Hillman (1978). where the
circumstances of redundant :iuota are iuvestigated for the case of a monopoly-dominant firm
domestic market structure.
References
Bhagwati, Jagdish N., 1965, On the equivalence oi’ tariffs and quotas, in: R.E. Baldwin et al.,
eds., Trade, growth and the balance of paymerits (Rand McNally, Chicago).
Bhagwati, Jagdish N., 1968, More on the equivalence of tariffs dnd quotas, American Economic
Review 58, 142-146.
Bhagwati, Jagdish N., 1971, The generalized theory of distortions and welfare, in: J.N. Bhagwati,
R.W. Jones, R.A Muntlcll and J. Vanek, eds., Trade, the balance of payments and growth
(North-Holland, Amsterdam), 69-90.
G. Fish:!sb,l
and A.L. Hillman, Domestic monopoly
51’
Craves, Richard E. and Ronald W. Jones, 1977. World trade and payments (Little, Brown,
Boston).
Orden, W. Max, 1974, Trade policy and economic welfare (Clarendon Press, Oxford).
Fishelson, Gideon and Frank Flatters, 1975, The non-equivalence of tariffs and quotas under
uncertainty, Journal of International Economics 5, 385-393.
Fishelson, Gideon and Arye Hillman, 1978, Utilization of protective quotas when domestic
production is monopolized, Foerder Institute for Economic Research, Paper No. 3-78.
Melvin, James R. and R.D. Warne, 1973. Monopoly and the theory of international trade.
Journal of International Economics 3, 117-134.
Shibata, H., 1968. A note on the equivalence of tariffs and quotas. American Economics Review
58, 137-142.