WORLD TRADE
ORGANIZATIONTN/MA/S/3/Rev.1/Add.1
17 February 2003
(03-0992)
Negotiating Group on Market Access
FORMULA APPROACHES TO TARIFF NEGOTIATIONS
Note by the Secretariat1
Addendum
1. Introduction
1. This document has been prepared to assist Members to better understand the various
proposals for modalities that include a formula approach for tariff negotiations.  It adds to the material
contained in TN/MA/S/3/Rev.1 and complements the document TN/MA/6 entitled "Overview ofProposals Submitted".  It confines itself to illustrating the properties of several formulae using a
hypothetical tariff profile and with numerical examples presented in tables and graphs.
2. The document does not address the specifics of the various proposals such as the base period,
implementation, product coverage, treatment of non-ad valorem  duties and their application by
Members.  It also does not present all the formula proposals listed in document TN/MA/6 because notall of them include a clearly defined functional form and explicitly specified parameters or
coefficients. It is not possible to calculate the reductions for given initial tariff rates without such
information.
2. Methodology
3. The methodology for presenting the various proposals is similar to that used in
TN/MA/S/3/Rev.1.  A hypothetical tariff profile is used to evaluate the effect of implementing a
specific proposal, including the effects on a benchmark tariff escalation scenario.  This approachallows the reader to use the intuition behind the general formulaic expressions illustrated in
TN/MA/S/3/Rev.1 to interpret the proposals for formula modalities.  For  the proposals that include
the tariff average as a parameter, the average tariff of the hypothetical tariff profile is used.  This
means that the reductions calculated for the various initial duty rates do not apply to real tariff
profiles, where the average is lower or higher than the average of the hypothetical tariff profile.  Inthese cases, where possible, the properties of the formula with respect to the different profiles are
discussed.
4. It should be noted that for presentation purposes, the notation for the formulae in this paper
has been standardised.  In all cases the original tariff rate is denoted as t
0 and the final rate as t 1.  The
text does not distinguish between bound and applied rates, since the purpose of the document is toillustrate the use of different formula methodologies.
5. Formulae that propose a reduction of the average weighted tariff have to be distinguished
from those that propose a methodology for a line by line reduction.  Following the classification made
                                                     
1 This document has been prepared under the Secretariat's own responsibility and without prejudice to the
positions of Members and to their rights and obligations under the WTO.TN/MA/S/3/Rev.1/Add.1
Page 2
in document TN/MA/6 regarding weighted tariff average reductions and line by line reductions, they
have been presented in different figures and tables.
3. Proposals
(a) China2
6. The Chinese formula  is specified as:
()()
()020
1t Ptt PB tt
aa
+ +× ×+=
where,
ta is the simple average of the base rates ( A in TN/MA/20).
P is a peak factor defined as the ratio of the tariff rate over the average rate ( t0/ ta)
B is an adjusting coefficient for the year of implementation. B=1 for 2015 or B=3 for 2010.
7. The formula is very similar to the well known Swiss formula but instead of a fixed
coefficient, a variable factor based on the simple average of the base rates ta , a peak factor and an
additional parameter for the year of implementation has been used.  The properties of the Chineseformula are similar to what is known about the properties of the Swiss formula discussed in Section
III.B.2.b of TN/MA/S/3 Rev.1, such as higher cuts fo r higher rates.  Furthermore it can be shown that
for B=1 the formula reduces any initial tariff rate below a maximum level which is the current average
of the base rates.  This is equivalent in its effect to the standard Swiss formula using the tariff average
as coefficient.
8. The percentage cuts for any given tariff rate will depend on the tariff average of the Member
concerned. For the same tariff rate, Members with lower tariff averages will experience relativelyhigher reduction rates than Members with higher tariff averages.  Therefore, the overall result of
applying this formula will depend on the statistical properties of different Members' tariff profiles.
(b) European Communities
3
9. The EC proposal is within the class of linear tariff dependent formulae, however, with an
adjustment, which gives it the properties of a step-wise linear function. The formula is applied acrossa set of ranges and the overall cuts depend upon the upper and lower bound of the applicable range.
10. The formula is specified as:
() /g250
/g251/g249
/g234
/g235/g233
−−× − + =L UL U
L L
B BB BBt Bt
0 01 1
0 0 1 1
where i
jB are the upper and lower bounds of the respective bands.  The subscripted number
represents the applicable range.  The superscripted letters U and L are, respectively, the upper and
lower bounds of the range.  Technically, the number of ranges that can be specified is unlimited.  In
the most simple case two ranges could be used.
                                                     
2 TN/MA/W/20.
3 TN/MA/W/11/Add.1.TN/MA/S/3/Rev.1/Add.1
Page 3
11. The EC submission did not parameterise the formula but presented a chart showing a possible
'Duty Reduction Scenario.4  Nevertheless, it is still possible to examine the properties of the proposed
EC formula without precise, values given the specification of the formula.  For example, the term in
the first set of brackets must be greater than zero, since a given tariff within a range must be greater
than or equal to the value of the lower bound of the range within which it falls.5  The term in the
square brackets is simply a constant since the upper and lower bands of the ranges are given as
constants.  Furthermore, its value must be less than one, since the overall objective of the formula is to
'compress' the tariff rates.  That is, any given range will be smaller with the application of the
formula.6  The expression also indicates how the cut in th e tariff is sensitive to the specification of the
bands.  For example, high tariffs within the same band are reduced by more than low tariffs within the
same band.7  Technically, the number of ranges that can be specified is unlimited.  For the application
of the formula the upper and lower limits of the old and new ranges need to be clearly specified.
(c) Japan8
12. Japan proposes that each Member sets a target level of a trade-weighted tariff average
according to a formula and that each Member reduce its trade-weighted tariff average to that target
level.  Each Member will retain flexibility on ways to realize the target tariff level.  The formula is
specified as:
α++×=w
aw
a w
atAtAt
00
1
where, w
at0 is the weighted tariff average prior to the application of the formula and w
at1 is the
weighted average after the application of the formula.  A is a constant whose values varies as follows:
w
at0≤ 10%, A = 10
10% < w
at0 ≤ 20%, A = 20
20% < w
at0 ≤ 30%, A = 30
30% < w
at0, A = 40
13. The term α in this specification has been proposed as a constant equal to 0.3.
                                                     
4 Reproduced in document TN/MA/M/4.
5 Intuitively, if LBt00<it would be in another band.
6 Using this information the EC formula can be rewritten as:
()1 0 0 1 1 γ× − + =L LBt Bt     where  /g250/g251/g249
/g234/g235/g233
−−=L UL U
B BB B
0 01 1
1γ   and  1 01≤<γ
The above expression makes it easier to understand the intuition behind the EC proposal.  It says that the
new tariff is the sum of the lower bound of the new range (lower than the lower bound of the old range), plusweighted difference between the original tariff and the old lower bound.
7 The intuition behind this is that a unit increase in the original tariff rate will increase the new tariff rate
above the lower bound of a specified range by less than unity (since the constant is less than one).  Accordingly, thegreater the increase in the tariff rate, the smaller will be the proportionate increase to the lower bound of the specifiedrange.
8 TN/MA/W/15.TN/MA/S/3/Rev.1/Add.1
Page 4
14. The formula applies to the reduction of the trade-weighted tariff average  as opposed to a
reduction of the tariff rates on a line by line basis.  This means that the formula is used to determine
the end result, or the objective of the tariff negotiations.  A lower coefficient will yield a higher cut
and a higher coefficient a lower cut.  The Japanese proposal can, therefore, be summarised as
proposing that Members with higher weighted tariff averages face a lower reduction than those withlower rates.
9
(d) Republic of Korea10
15. The objective of this proposal is to lower the weighted tariff average of Members by
40 percent.  This is achieved by applying a reduction formula that results in a higher reduction of
tariff peaks.  The starting point is a 20 percent minimum reduction by tariff line, which is followed by
a further reduction aimed at harmonizing the tariff profile.  Two criteria are used to distinguish which
tariffs should be addressed and the applicable methodology.  These are twice the national average and25 percent.
16. For the case where tariffs are above twice the national average after  the minimum reduction
of 20 percent, the following formula is applicable which includes the initial 20 per cent reduction:
( ) ()()at t tt ×−× −×= 2 7.08.00 0 1
17. If the tariff rate is less than twice the national average, but still above 25 percent the following
formula is applicable which includes the initial 20 per cent reduction:
() ( ) () 25 7.0 8.00 0 1 − × − × = t t t
18. In cases where the tariff rate is above two times the simple national average and at the same
time above 25 percent, the final tariff rate shall be whichever is lower after the reduction.
19. The formula reduces higher tariff rates in a way that takes into account individual tariff
profiles since the cut is dependent on the tariff average.  This means tariff profiles that have dutiespredominantly below 25 percent but above twice the national average will still be subject to further
tariff reductions.  Alternatively, profiles with duties predominantly above 25 percent, but with high
overall averages will still be subject to reductions since the 25 percent rule will apply.
20. The overall result of applying this formula will, therefore, depend on the statistical properties
of each Members' tariff profile.  It should be noted though that for all tariff profiles with an average ofabove 12.5 percent the tariff rate reductions in percentage are identical for a given tariff rate because
the 25 percent rule applies in all cases where twice the national average is greater than 25 percent.
21. The Korean proposal is similar to the Japanese proposal in that both seek a reduction of the
weighted tariff average.  However, the application of the Korean  formula for the targeted reduction of
weighted tariff averages differs slightly from that of the Japanese proposal as illustrated in figure 3.
(e) United States
11
22. The United States has proposed a modality which includes the elimination of tariffs at or
below 5 percent and the application of a Swiss formula on the tariff profile for all other tariff rates.
                                                     
9 The high rates in the lowest band (up to 10%) would have a lower percentage reduction than the higher
rates in higher bands.
10 TN/MA/W/6/Add.1.TN/MA/S/3/Rev.1/Add.1
Page 5
The proposed coefficient is 8, which converts the general Swiss Formula into the following
specification:
00
188
ttt+×=
23. The general properties of this formula are described in TN/MA/S/3/Rev.1.  What is important
to note about the US proposal is the value of 8 for the coefficient.  This implies a maximum tariff rate
of 8 percent after tariff reductions for any tariff profile.
4. Tariff reduction simulations with hypothetical tariff profile
24. The reduction effects of the formulae presented above applied to a hypothetical tariff profile
similar to the one used in TN/MA/S/3/Rev.1 are illu strated in tables 1 to 3 and figures 1 to 3.  The
proposals using line by line reductions and those targeting reductions of average weighted tariff rates
are shown separately because they are not strictly comparable in their implications.
25. Table 1 shows, based on the hypothetical tariff profile, the base rates before and after
application of the various formulae.  For those formulae that use the tariff average as parameter theaverage of the hypothetical tariff profile has been used, i.e. t
a=30.  The application of the Chinese
proposal to tariff profiles with lower/higher tariff averages would, for a given tariff rate, result in a
higher/lower cut than that shown in the tables and figures.  In the case of the Korean proposal for line
by line cuts, tariff profiles with a tariff average below 12.5 percent would be subject to higher cuts
than those shown in the examples given in the tables and figures.  Descriptive statistics before andafter reduction highlight the overall effects of the application of the various proposals on the
hypothetical tariff profile.
26. Table 2 illustrates how the application of the formulae results in different percentage
reductions for the different tariff rates and indicates also the reduction of the simple average of the
hypothetical tariff profile.  For sake of comparison only, the tables and figures also include the effectsof a hypothetical 50% linear reduction.  Table 3 illustrates the same point for the formulae for
reductions of weighted tariff averages.
27. The information shown in the tables is also displayed in graphical form in figures 1 to 3
corresponding to tables 1 to 3.  In figures 1 and 2 for the Chinese formula only, the version with
coefficient B=1 has been included.
5. General Observations
28. Formulae by their very nature are technical.  Nevertheless, it is extremely important to
understand their properties in the context of their application to the tariff profiles of Members.  In this
regard, despite the diversity of innovative proposals on the use of formulae as a modality for market
access negotiations, some common elements can be highlighted.
29. The following general observations can be made:
• All the proposals make the reduction rate dependent on the initial tariff rate.
• All proposals reduce higher rates by proportionately more than lower rates.  This is accomplished
through different specifications.
                                                                                                                                                                    
11 TN/MA/W/18.TN/MA/S/3/Rev.1/Add.1
Page 6
• All proposals have similar effects at higher levels of tariffs, although with different absolute
impacts due to different parameters.
/g167 Some proposals take into account the diversity of the Members profiles via an explicit provision
in the functional design of the formula for the current level of base rates.
/g167 The treatment of the lower tariff rates differs significantly amongst the proposals.TN/MA/S/3/Rev.1/Add.1
Page 7
Table 1
Impact on tariff rates of various line by line formula proposals on the hypothetical tariff profile
Tariff line Initial
tariff rateChina
ta=30,  B=1China
ta=30, B=3European
CommunitiesKorea
ta=30USA Linear
cut 50%
Line 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Line 2 2.5 2.3 2.3 1.7 2.0 0.0 1.3
Line 3 5.0 4.3 4.4 3.3 4.0 0.0 2.5
Line 4 7.5 6.0 6.1 5.0 6.0 3.9 3.8
Line 5 10.0 7.6 7.7 6.7 8.0 4.4 5.0
Line 6 12.5 8.9 9.2 8.3 10.0 4.9 6.3
Line 7 15.0 10.1 10.4 10.0 12.0 5.2 7.5
Line 8 17.5 11.2 11.6 11.1 14.0 5.5 8.8
Line 9 20.0 12.2 12.7 12.1 16.0 5.7 10.0
Line 10 22.5 13.0 13.7 13.2 18.0 5.9 11.3
Line 11 25.0 13.8 14.6 14.3 20.0 6.1 12.5
Line 12 27.5 14.6 15.4 15.4 20.3 6.2 13.8
Line 13 30.0 15.2 16.2 16.4 20.5 6.3 15.0
Line 14 32.5 15.9 17.0 17.5 20.8 6.4 16.3
Line 15 35.0 16.4 17.7 18.6 21.0 6.5 17.5
Line 16 37.5 17.0 18.3 19.6 21.3 6.6 18.8
Line 17 40.0 17.5 18.9 20.7 21.5 6.7 20.0
Line 18 42.5 17.9 19.5 21.8 21.8 6.7 21.3
Line 19 45.0 18.3 20.1 22.9 22.0 6.8 22.5
Line 20 47.5 18.8 20.6 23.9 22.3 6.8 23.8
Line 21 50.0 19.1 21.1 25.0 22.5 6.9 25.0
Line 22 52.5 19.5 21.6 25.0 22.8 6.9 26.3
Line 23 55.0 19.8 22.1 25.0 23.0 7.0 27.5
Line 24 57.5 20.1 22.5 25.0 23.3 7.0 28.8
Line 25 60.0 20.4 23.0 25.0 23.5 7.1 30.0
Average 30.0 13.6 14.7 15.5 16.7 5.4 15.0
Maximum 60.0 20.4 23.0 25.0 23.5 7.1 30.0
Std. Dev 18.4 5.9 6.7 8.1 7.4 2.2 9.2
Coeff. Var. 61.3 43.5 45.5 52.0 44.6 40.7 61.3
Escalation
(line13/line5)3.0 2.0 2.1 2.5 2.6 1.4 3.0
Note:
Std. Dev:  Standard Deviation  is a measure of absolute dispersion of the tariff profile.  It is dependent
on the average level of the tariffs.
Coeff. Var:  Coefficient of Variation  is a measure of relative dispersion.  It is defined as the standard
deviation divided by the average and usually presented in percent, i.e. multiplied by 100.  It is not
affected by the average levels of tariffs.TN/MA/S/3/Rev.1/Add.1
Page 8
Table 2
Percentage reduction arising from the application of various line by line formula proposals
Tariff line Initial
tariff rateChina
ta=30,
B=1China
ta=30,
B=3European
Communitie
sKorea
ta=30USA Linear
cut 50%
Line 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Line 2 2.5 7.5 6.9 33.3 20.0 100.0 50.0
Line 3 5.0 13.9 12.9 33.3 20.0 100.0 50.0
Line 4 7.5 19.5 18.1 33.3 20.0 48.4 50.0
Line 5 10.0 24.4 22.7 33.3 20.0 55.6 50.0
Line 6 12.5 28.7 26.8 33.3 20.0 61.0 50.0
Line 7 15.0 32.6 30.4 33.3 20.0 65.2 50.0
Line 8 17.5 36.1 33.6 36.7 20.0 68.6 50.0
Line 9 20.0 39.2 36.6 39.3 20.0 71.4 50.0
Line 10 22.5 42.0 39.2 41.3 20.0 73.8 50.0
Line 11 25.0 44.6 41.6 42.9 20.0 75.8 50.0
Line 12 27.5 47.0 43.9 44.2 26.4 77.5 50.0
Line 13 30.0 49.2 45.9 45.2 31.7 78.9 50.0
Line 14 32.5 51.2 47.8 46.2 36.2 80.2 50.0
Line 15 35.0 53.0 49.5 46.9 40.0 81.4 50.0
Line 16 37.5 54.8 51.1 47.6 43.3 82.4 50.0
Line 17 40.0 56.3 52.6 48.2 46.3 83.3 50.0
Line 18 42.5 57.8 54.0 48.7 48.8 84.2 50.0
Line 19 45.0 59.2 55.3 49.2 51.1 84.9 50.0
Line 20 47.5 60.5 56.6 49.6 53.2 85.6 50.0
Line 21 50.0 61.7 57.7 50.0 55.0 86.2 50.0
Line 22 52.5 62.9 58.8 52.4 56.7 86.8 50.0
Line 23 55.0 64.0 59.8 54.5 58.2 87.3 50.0
Line 24 57.5 65.0 60.8 56.5 59.6 87.8 50.0
Line 25 60.0 66.0 61.7 58.3 60.8 88.2 50.0
Average 30.0 43.9 41.0 42.3 34.7 75.8 48.0TN/MA/S/3/Rev.1/Add.1
Page 9
Table 3
Applying different formulae to hypothetical weighted tariff averages
(Initial and final tariff rate and reductions by case in percent)
Initial Weighted average rates after
reductionReductions in percent
Hypothetical
cases weighted
averageJapan Korea
cut 40%Linear
cut 50%Japan Korea
cut 40%Linear
cut 50%
Case 1 0.0 0.3 0.0 0.0 n.a 0.0 0.0
Case 2 2.5 2.3 1.5 1.3 8.0 40.0 50.0
Case 3 5.0 3.6 3.0 2.5 27.3 40.0 50.0
Case 4 7.5 4.6 4.5 3.8 38.9 40.0 50.0
Case 5 10.0 5.3 6.0 5.0 47.0 40.0 50.0
Case 6 12.5 8.0 7.5 6.3 36.1 40.0 50.0
Case 7 15.0 8.9 9.0 7.5 40.9 40.0 50.0
Case 8 17.5 9.6 10.5 8.8 45.0 40.0 50.0
Case 9 20.0 10.3 12.0 10.0 48.5 40.0 50.0
Case 10 22.5 13.2 13.5 11.3 41.5 40.0 50.0
Case 11 25.0 13.9 15.0 12.5 44.3 40.0 50.0
Case 12 27.5 14.6 16.5 13.8 46.7 40.0 50.0
Case 13 30.0 15.3 18.0 15.0 49.0 40.0 50.0
Case 14 32.5 18.2 19.5 16.3 43.9 40.0 50.0
Case 15 35.0 19.0 21.0 17.5 45.8 40.0 50.0
Case 16 37.5 19.7 22.5 18.8 47.6 40.0 50.0
Case 17 40.0 20.3 24.0 20.0 49.3 40.0 50.0
Case 18 42.5 20.9 25.5 21.3 50.8 40.0 50.0
Case 19 45.0 21.5 27.0 22.5 52.3 40.0 50.0
Case 20 47.5 22.0 28.5 23.8 53.7 40.0 50.0
Case 21 50.0 22.5 30.0 25.0 55.0 40.0 50.0
Case 22 52.5 23.0 31.5 26.3 56.2 40.0 50.0
Case 23 55.0 23.5 33.0 27.5 57.3 40.0 50.0
Case 24 57.5 23.9 34.5 28.8 58.5 40.0 50.0
Case 25 60.0 24.3 36.0 30.0 59.5 40.0 50.0TN/MA/S/3/Rev.1/Add.1
Page 10
Figure 1: Comparison of formula proposals for line by line reductions
0102030405060
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70Initial Tariff Rate
to=t1
Linear 50%
EC
Korea
China B=1
USTN/MA/S/3/Rev.1/Add.1
Page 11Figure 2: Reductions in per cent of initial tariff rates
0%20%40%60%80%100%
0 1 02 03 04 05 06 07 0
Initial Tariff RateR
e
d
u
c
t
i
o
n
 i
n
 
p
e
r
 
ce
n
tUS
China B=1
Korea
EC
Linear 50%TN/MA/S/3/Rev.1/Add.1
Page 12
__________Figure 3: Comparison of formula proposal s for weighted average tariff reductions
0102030405060
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70Initial Weighted Tariff Average 
to=t1
Korea
Linear
50%
Japan