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A Heuristic Decision Rule for Bufferstock Management
Copyright © IFAC Dynamic Modelling and Control of National Economies. Edinburgh.
9. I'LA"J"JING AND DECISION SYSTEMS
UK, 1989
A HEURISTIC DECISION RULE FOR BUFFERSTOCK MANAGEMENT W.
J.
H. Van Groenendaal
Titblng Ullivrrsih', PO Box 90153 , 5000 LE Tilblllg, The Netherlallds
Abstract. Most commodity agreements formulated rule out succes in advance because of the ridgit formulation of the gaol. Only recently a different view on agreement formulation has emerged. One of the agreements which aim is to be flexible with respect to changing market conditions is the new cocoa agreement, Using an annual model of the cocoa market this article will explore a heuristic rule for market intervention and compare it with the instruments agreed upon. Keywords. Commodity agreement, price stabilization, buffer stock policy, heuristic programming.
recent cocoa agreement was the collapse of the tin
1 INTRODUCTION
agreement in 1986. basically due to prolonged The new 1986 International Cocoa Agreement has
attempts to maintain the tin prices at an
(UNCTAD, 1986a). for the first time in history, as
artificially high level. As a direct consequence
its sole objective the reduction of price fluctua-
of this failure. the UNCTAD Committee on
tions around the long term market-determined trend
Commodities decided on new guidelines for
(see article one of the new cocoa agreement). The
commodity agreements. The major point of these
stabilization of income is regarded as a conse-
guidelines was that future agreements should be
quence of this objective of the agreement. From a
designed in such a way that they take into account
theoretical point of view there are objections
developments in market prices (Unctad,1986a).
against the use of the expected price trend if the market cannot be described by linear model. From
Incorporating this lesson in a model of a
the work of Turnovsky (1976.1978) and Nguyen (1979,1980) we know that the expected price trend
commodity market means that the decision rule for selling or buying by the buffer stock manager
can only be used if the Waugh-Oi-Masse1l model is
should not alter the market price trend and also
valid. In a general non-linear model with
should not ignore changes of prices induced by
multiplicative disturbances the arithmatic price
spill-over effects from other markets. The
trend will not lead to a realistic buffer stock
information which will influence the decisions of
policy. Realistic in the sence that it fulfills
the buffer stock manager can be seperated in
the requirements of (i) earnings stabilization and
information on the internal market and information
(ii) self-liquidation. In a realistic setting the
on the rest of the world economy. His objective
use of a price trend to guide the buffer stock
will be to stabelize the market prices for the
policy will lead to a failure of the policy
current year without inducing drastic shocks in
(Turnovsky.1976).
production. In a realistic setting the decisions of the buffer stock manager will not be influenced
The tin-disaster (and others like EEC inter-
by long term expectations on the development of
vention) confirms the theory. The main lesson is
the world economy.
that buffer stock intervention should not go against the general tendency of the market. The
In the literature two types of stabilization
decisive factor in shaping the caracter of the
policies are used. The first one is a band width
479
480
W.
J.
H. Van Groenendaal
rule or price range. This type of policy was
market. This can be formulated as:
mostly used in previuos commodity agreements. The band width rule does not take into account the PICCO *
spill over effects from other markets, it is
(2)
fl (0, O,FOM:)
t
restricts the price variations to a pre-specified range, the band width. In most agreements the band If the only instrument available to the buffer
is formulated in absolute prices and based on
stock manager is the buffer stock, this implies:
outdated information (ICCO,1984). Such a policy uses neither information on the internal market,
t.(BST
nor information on external developments.
f (PICCO *
)
2
t
PICCO
-
t
(3)
) t
The second type of rule results from the optimal control formulation of the problem; the buffer The advantage of this rule is that the only target
stock manager has to keep the price as close as
price needed is the actual one, and only short
possible to a pre-specified price path. The pre-
term expectations on future developments are
specified price path is based on information on
needed. This seems more realistic given the
the internal and external market conditions till the previous period. However, in this formulation
practical situation the buffer stock manager has
of the problem the objective function has to be
to deal with. A disadvantage is that in a rea-
modelled explicitly, and is mostly of a quadratic
listic model we will not be able to prove that the
function. The model used is nearly always a linear
agreement leads to optimal results, it can only be
model (Lee and Blandford,1980;Ghosh et al. ,1982
shown that over a longer period of time it is
and 1987).
satisficing. For our model this implies that two conditions should met:
The objective of this article is to formulate a flexible heuristic decision rule for the buffer stock manager and to compare it to the 1986 cocoa
g(QR - GR ) - t.BST1 t
t
t
o
(4 )
o
(5)
agreement. The heuristic will be formulated in ST
such a way that it does not violate the general
t-l
- STd
t-!
- t.BST2 t
principles stated above. In section 2 the heuristic will be discussed. In
The total buffer stock mutation necessary to
section 3 the the new cocoa agreement will be
achieve the target price PICCO * is t
reviewed. In section 4 the intervention heuristic will be compared to the agreement using an annual t.BST
model of the cocoa market. Section 5 contains
t.BST1
t
+ t
t.BST2
(6)
t
conclusions and an outline for practical use of the heuristic. This condition is the target for the buffer stock manager to achieve every period. Implementation in 2 A HEURISTIC RULE FOR INTERVENTION
the model of appendix A leads to the following target price for the buffer stock manager:
It is assumed that the actual price PICCO on supply and demand g(QR
t
depends
l
- GR ), the difference t
between stocks and desired stocks (ST
_ t
1
ST:_
-
I
),
and expectations about forces from outside the
PICCO * t
market FOM: (see the appendix): where CPI
t
covers FOM e t
•
Since 6BST
t
is based on
production, consumption and stocks of cocoabeans PICCO
t
f (g(QR 1
t
- GR ) ,ST t
t-l
- STd
t-l
,FOM e t
)
(1)
only, this rule is referred to as the rule of internal growth.
The aim of the buffer stock manager is to formulate a short term target price PICCO * , which t
implies that excess demand or excess supply is taken out of the market. In this way his policy will not react on influences from outside the
A Heuristic Decision Rule for Buflerstock Management
3 THE 1986 COCOA AGREEMENT
481
Taking both semi-automatic adjustments into account it turns out that the 1986 cocoa agreement
The 1986 cocoa agreement consists out of two
contains the most flexible adjustment of the price
stabilization instruments and two semi-automatic
range that has ever been incorporated in a com-
adjustment rules for the reference price (UNCTAD,
modity agreement.
1986b). These two types of semi-automatic adjustment of the reference price to the price trend (and thus the intervention prices) are the
Implementation of the Agreement
most important new features of the 1986 cocoa agreement.
The agreement contains two instruments and two
The 1986 agreement is characterized by:
section 2) which have to be translated in terms of
- a relatively large band width of 80 US-dollar
the model of appendix A.
adjustment mechanisms for the price range (see
cents. This implies that the lower and upper intervention price are at a distance of 40 US-
- The buffer stock can be implemented in equation
dollar cents from the reference price of 227 US-
(A.7), since it effects world supply of
dollar cents per kilo.
cocoabeans QRWT.
- a buffer stock of 250,000 mt (as in the
cents per kilo if the buffer stock manager has to
agreement of 1980). Should, after three years, the
sell or buy 75,000 mt within six months. was
- The adjustment of the reference price by 13 U$
agreement be extended for a period of more than
translated into an adjustment of the reference
one year the maximum buffer becomes 350,000 mt.
price each time the buffer stock manager sells or
The stock resulting from the old agreement
buys 75,000 tons within one year. After one
(100.000 mt) and a capital of 250 million US-
adjustment within a year, the adjusted reference
dollar have been transferred to the new agreement.
price was used. The computer program used allows
Additional funds for buffer stock operations will
for two of these adjustments within one year.
continue to come from a levy of 2 US-dollar cents
- Withholding has the same effect on prices as a
per lb (recently changed to 1.36 US-dollar cents
buffer stock mutation, and was implemented in the
per lb).
same way (without tranches). Withholding starts when the maximum buffer of 250,000 mt has been
- a withholding scheme. The bufferstock manager
reached. Withholdings are sold whenever the actual
keeps national stocks in store up to a maximum of
cocoa price exceeds the reference price. The
120,000 mt. The withholding scheme becomes
amount sold will keep the actual price equal to
operative once the buffer has reached 200,000 mt
the reference price.
or the manager runs out of funds. The effect of
- Implementation of the annual price review is
withholding is the same as buying by the buffer
straightforeward.
stock manager. The main difference between a
- The reference price is adjusted each calender
buffer stock operation and withholding is that
year instead of each cocoa year.
withholdings are released at the reference price. This implies that only the lower half of the price range is relevant for this instrument.
Implications of the Model
- an annual price review. In case the average
Only the main effects of the model of appendix A
price over the preceding year has been outside the
are reported. These main effects within the model
range, the reference price will be increased
are elucidated by the effect of changes in the
(decreased) such that the indicator price comes
world cocoa price PICCO on production and
within the band width at a distance of 6 US-dollar
consumption, and by the effect of a change in real
cents from the upper (lower bound) of the band,
gross national income per capita. These effects
with a maximum adjustment of 13 US-dollar cents
are given in table 1 and table 2 respectivily (see
per kilo.
also Van Groenendaal and Vingerhoets,1989). Compared to other studies of the cocoa market by
- a price review during the year. If the size of
the World Bank (Akiyama and Duncan, 1982) and The
the actually held buffer stock changes 75,000 mt
International Cocoa Organization ICCO (1984) the
within a six month period, the reference price is
results for North America and Western Europe are
adjusted 13 US-dollar cents per kilo.
of the same magnitude. For Eastern Europe and the
W.
482
J.
H. Van Groenenclaal
USSR the price elasticities obtained differ. This
4 THE EFFECT OF THE DIFFERENT POLICIES
is partially due to differences in the definition of the region. With respect to the rest of the
Since the rule of internal growth and the cocoa
developed world the results are close to those of
agreement do not effect the average production and
the ICCO, but differ from the results of the world
consumption over the total simulation period when
bank. There are, however, no real anamolies
compared with the free simulation results, they
between the various results, only differences in
are both neutral with respect to the development
magnitude.
of supply and demand. The conclusion that the market trend is not altered is valid under all three the assumptions with respect to inflation
Simulation Exercises
(see tables 3,4, and 5). (The same goes for the world income, which is not reproduced here.)
In order to compare the application of the
However, in case of one or three percent inflation
heuristic rule and the effect of the policy
the agreement becomes ineffective after period
instruments of the 1986 cocoa agreement, a number
sixteen and period thirteen respectively (see
of simulation experiments were performed, based on
tables 7 and 8). The only instrument used is the
the following assumptions. A zero growth and an
annual price review, but this instrument is to
annual one and three percent growth over a period
restrictive to restore the effectiveness of the
of 25 years of the Commodity Price Index CPl. The
agreement, the adaption of the price trend is too
one and three percent growth rate are introduced
slow. The main reason for this is the fact that
to test both policies in an inflationary enviro-
spill over effects from other markets are ignored
ment. Fluctuations are introduced by taking the
in the adaption of the price trend. This in
historical differences of the actual values of the
contrast to the rule of internal growth, which
commodity index CPI and its geometrical mean. The
remains active during the total simulation period
so obtained fluctuations are added to the trend in
regardless the experimental setting due to the
CPI used for the different experiments. Exchange
flexibility with respect to spill-over effects
rates are assumed to be constant over the
which is build into the rule of internal growth.
simulation period. This implies that the US-dollar
In all experimental settings the rule of internal
can be used as currency instead of SDR's, the
growth is more effective than the agreement. In
denominator used in the agreement. The consumption
case of zero percent inflation the opportunity
prices are linked to the development in the
costs and the operational result are comparable.
commodity price index to avoid unneccessary
In the other cases the costs of the rule of
complications due to increasing differences in the
internal growth still remain moderate, with a
development of exogenous variables.
maximum of 40.2 million US-dollars over twenty five periods in case of three percent inflation.
As was shown by Van Groenendaal and Vingerhoets (1989) the 1986 cocoa agreement is to flexible. Reducing the band width from 80 to 40 US-dollar cents leads to better results. Therefore this reduced band was used as a reference for the rule of internal growth.
If we take into account the contributions of the members of the International CoCoa Organization, the funds of the ICCO are sufficient to finance the policy, as the opperational result of 211.5 million US-dollar teaches us.
Since the aim is to compare the price trend of the rule of internal growth and the price trend used in the agreement, a maximum buffer of 250,000 mt and withholdings up to 120,000 mt were used in both cases. A range of
~
5% is used in case of the rule of
internal growth. This was done because in practice only larger differences in demand and supply can be taken into account, since minor differences cannot be identified.
5 CONCLUSIONS The heuristic rule formulated here performs better than the policy rules formulated in the 1986 cocoa agreement. The price adjustment part of the agreement is not flexible enough, to adjust to even a moderate inflation of one percent over a longer period. Application of the rule of internal growth shows that price and income stabilization is possible over a longer period of time. It also shows that only recent information is necessary to do so. No predictions of future developments are necessary.
483
A Heuristic Decision Rule for Bufferstock Management Using the most recent information on production
Van Groenendaal W.J.H. and J.W.A. Vingerhoets
and consumption, and on forces from outside the
(1989). The new cocoa agreement analysed .
market it is possible to formulate a decision
Working Paper FEW 339, Tilburg University.
support sytem for the buffer stock manager for every day practice since the rule is independent of the model used to validate the rule. The principle of neutrality with respect to the market trend, and quantification of the spill-over
TABLE 1 Price Elacticities of Cocoa Production
effects, although difficult, can be used to formulate such a decision support system, where
Short Run
the model is replaced by information from the market and the price equation by its short term equi valen t .
REFERENCES
Long Run
Cameroon Ghana Ivory Coast Nigeria Brazil Rest Latin America Asia and Oceania
.13 .10 .42 .20 .25 . 14 .0
·73 .38 .82 .47 .29 .28 ·50
World Total
.23
.54
Akiyama, T. and R.C. Duncan (1982). Analysis of the world cocoa market. World Bank Staff Commodity Working Papers, §. Ghosh, S., C.L. Gilbert and A.J. Hughes Hallett (1982). Optimal stabilisation of the copper
Remark: Short Run means current and 1 year lag. Long Run means steady state elasticity. For Africa Rest we used a dummy equation which describes the development of production over time.
market: The problem of information. Resources Policy, §, 201-214. ICCO (1984). An Analysis of the World Cocoa
TABLE 2 Price and Income Elasticities of Cocoa Consumption
Economy. International Cocoa Organization PCA/3/6, London.
price short run long run
Lee, S. and D. Blandford (1980) . An analysis of international buffer stocks for cocoa and copper through dynamic optimisation. Journal of Policy Modelling,
~,
371-388.
Nguyen, D.T. (1979). The implications of price stabilization for short-term instability and
North America Western Europe Eastern Europe Rest World
-.19 - . 14 -.26
-.25 -.15 -.26 -.40
-.16
-.23
- .11 +
USSR
World Total
long-term level of ldcs' export earnings. The income
Quarterly Journal of Economics, 149-154.
short run
Nguyen, D.T . (1980) . Partial price stabilization and export earning instability . Oxford Economic Papers, 341-352. Turnovsky, S.J. (1976). The distribution of welfare gains from price stabilization: The case of multiplicative disturbances. International Economic Review, 21, 133-148 . Turnovsky, S . J. (1978). The distribution of welfare gains from price stabilization: A survey of some theoretical issues. In F.G . Adams and S.A . Klein (Eds.) .Stabilizing world commodity markets. Lexington Books, Lexington. UNCTAD (1975). An integrated programme for commodities. UNCTAD TD / B/ C.1 / 198, Geneva. UNCTAD (1982) . International cocoa agreement 1980. UNCTAD TD/Cocoa 6/7/rev. 1, Geneva. UNCTAD Bulletin (1986a) no. 224 July/ August. UNCTAD (1986b). The international cocoa agreement. UNCTAD.
North America Western Europe Eastern Europe Rest World World Total
+
USSR
long run
.21 .25 .44 .42
.25 .30 . 66 .57
. 30
·39
W . .J. H. Van Groenendaal
484
TABLE 3 The Effect of the Rule of Internal Growth and the Agreement on the Stability of Prices and Income in Case of Zero Percent Inflation
instability index*) simulation
internal growth
agreement
36.9% 29.1%
16.6% 15.7%
20.9% 19.6%
Brazil Rest Latin America Cameroon Ghana Ivory Coast Nigeria Rest Africa Asia & Oceania
20.4% 24.5% 27·2% 47.7% 21.5% 53.0% 30·9% 9.4%
13.0% 18.9% 19.9% 31.0% 14.1% 40.8% 23.0% 9.8%
13.5% 21.2% 23.3% 41.6% 17.6% 47.6% 27.4% 8.1%
World total
20.1%
15.4%
Prices: PICCO PICCO/CPI Income in 1985 U$:
In million U$ **) Operational result**) Opportunity costs Average in 10 3 metric tons of World production World consumption
*) defined as
II =
[ll:n n
16.4%
-
102.6 11.9
101.8 12.9
2406 2375
2408 2375
2405 2376
(x - x
1=1
t
0
(1+X)t)2]/~ mean
.
**) See the appendix for the definition of these concepts.
TABLE 4 The Effect of the Rule of Internal Growth and the Agreement on the Stability of Prices and Income in Case of One Percent Inflation
instability index*) simulation
internal growth
agreement
37. 1% 28.8%
16.0% 16.1%
24.3% 21.5%
Brazil Rest Latin America Cameroon Ghana Ivory Coast Nigeria Rest Africa Asia & Oceania
19.7% 23.6% 27.5% 47.9% 21.5% 52.9% 30.7% 9.2%
12.9% 18.3% 20.5% 31.5% 14.3% 41.4% 23.0% 9.9%
15.6% 21.1% 26.2% 43.4% 20.0% 49.7% 28.3% 7.6%
World total
19.8%
15.4%
Prices: PICCO PICCO/CPI Income in 1985 U$:
18.7%
In million U$ **) Operational result**) Opportunity costs
136 .6 16.1
160.5 -7 .1
Average in 10 3 metric tons of World production World consumption
2405 2370
2399 2371
*) and **) See table 3.
2402 2370
485
A Heuristic Decision Rule for Bufferstock Management TABLE 5 The Effect of the Rule of Internal Growth and the Agreement on the Stability of Prices and Income in Case of Three Percent Inflation
instability index*) simulation
internal growth
agreement
38.1% 28.4%
18 .6% 18.6%
23.2% 19.6%
Brazil Rest Latin America Cameroon Ghana I vory Coast Nigeria Rest Africa Asia & Oceania
18.5% 21.9% 28.2% 48.2% 21.6% 52.8% 30.3% 9.0%
14.5% 18.4% 22.9% 35.7% 16.4% 45.4% 23.4% 11.0%
14.6% 19.6% 27.0% 42.4% 20.1% 48.8% 27·9% 8.3%
World total
19.1%
16.9%
Prices: PICCO PICCO/CPI Income in 1985 U$:
18.2%
In million U$ **) Operational result**) Opportunity costs
211.5 40.2
291.9 -36.2
Average in 10 3 metric tons of World production World consumption
2396 2360
2390 2360
*) and **) See table
2393 2359
3.
TABLE 6 The Use of the Available Instruments in Case of Zero Percent Inflation internal growth period
1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17
18 19 20 21 22 23 24 25
!>BST
0 -14 0 -86 250 0 0 0 - 250 0 0 52.8 -52.8 40 . 7 79.4 45 .4 -86.0 0 0 74.6 93.4 2 .7 -13.1 -168.2 21. 3
agreement
!>WTH
P
0 0 0 0 82.3 0 0 -82.3 0 0 0 0 0 0 0 0 0 0 0 0 0 88.3 - 88.3 0 0
210.4 196.3 196.6 196.7 206.7 188.2 173.3 158 .4 160.8 170.8 180.8 180.1 181.4 226.5 206.3 206.6 220 .0 228 .4 241.9 251.1 242.3 228.6 226.1 241.9 235 .7
rd
!>BST
!>WTH
0 0 0 0 22.4 0 0 -0.7 120 128.3 0 0 0 0 0 0 -40.8 -120 0 -75 0 0 0 75 0 -75 0 0 0 0 0 0 -125.2 0 0 0 0 0 0 0 0 5.2 0 74.3 0 -25 .3 0 -54.2 14.4 0
!>P
re f
1,/) 2 2 2 1 1 1
1,2 2 2
2
P
re f
227 227 227 227 227 201 191.8 179.5 179.5 179 . 5 192.5 192 ·5 179.5 192.5 192·5 192.5 192.5 213.5 226 . 5 234 . 1 234.1 234 . 1 234.1 234.1 247.1
*) 1 implies a correction reference price of 13 US-dollar cents due to !>BST > 75,000 mt . 2 implies that the end of year price is out of range and the reference price is corrected in order to bring the actual price at a distance of 6 US-dollar cents of the intervention price. The maximum intervention is 13 US-dollar cents.
J.
W.
486
H. Va n Groen endaal
TABLE 7 The Use of the Available Instruments in Case of One Percent Inflation internal growth period
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
t.BST
t.WTII
0 -27.3 0 -72.7 250 0 0 0 -250 0 0 49.4 -49.4 42.7 83.0 49 . 4 -80.2 0 0 80.6 74.5 0 0 -164.5 30·3
0 0 0 0 79.6 0 0 -79 . 6 0 0 0 0 0 0 0 0 0 0 0 0 29.0 91.0 -120 . 0 0 0
agreement P
rer
211. 3 199.8 201 . 4 205.8 221.3 201.9 187.4 172 . 9 177.5 190 . 4 204.2 205 · 9 209.2 264.8 243.5 246.5 265.4 278 . 9 297.7 312.2 305·5 292 . 2 290.7 311. 3 309.3
t.BST
t.WTII
0 0 0 -54.1 173.7 0 0 0 -116.0 -30.7 0 75 -75 25·5 0 -25 . 5 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
t.P
re f
P
ref
227 227 227 227 227 201 201 201 201 214 214 214 201 214 214 214 214 227 240 253 261.2 261 . 2 261 . 2 274 . 2 287 . 2
1
1 1 1
2 2 2 2 2 2 2
TABLE 8 The Use of the Available Instruments in Case of Three Percent Inflation internal growth period
1 2 3 4 5 6 7 8 9 10
11
12 13 14 15 16 17 18 19 20 21 22 23 24 25
t.BST
0 -53 . 2 -33 . 4 -13.4 250 0 0 0 -250 0 0 39·1 -39.1 49 . 9 95.0 61.4 -65.3 0 0 71.9 17·5 0 0 -163 . 3 52.3
I'.WTH
0 0 0 0 79 . 4 0 0 -82 . 3 0 0 0 0 0 0 0 0 0 0 0 0 105·3 14.7 -120.0 0 0
agreeme nt P
re f
213 . 1 207 .0 211.5 220.1 257 . 1 234.1 218 . 4 205.2 214 . 1 235 . 3 259.3 268.3 277·5 361.2 338.3 349.6 384.7 413 . 4 447 . 8 479.1 482.3 473 . 6 460.4 517·3 531.8
I'.BST
0 0 0 -100.0 163.4 0 0 0 -163 . 4 0 0 75 -75 0 0 0 0 0 0 0 0 0 0 0 0
t.WTH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
I'.P
re f
1 1
1,2 2 1 1 2 2 2 2 2 2 2 2 2 2
P
re f
227 227 227 227 250 224 224 224 224 262 275 275 262 288 301 301 310 . 5 323 · 5 336.5 349 . 5 362 . 5 375.5 388.5 401.5 414.5
487
A Heuristic Decision Rule for Bufferstock Management Appendix: A Model of the Cocoa Market
factor .99 accounts for transportation losses). The desired level of stocks for production of
Cocoabeans are produced in less developed
cocoa products is set equal to the avarage level
countries and cocoa products are mainly consumed
of stocks over the period 1962-1982 (O.30 x GRWT).
in developed countries. This dichotomy was used in
In as far as last years stocks STWT differ from
formulating a model of the world cocoa market,
the desired level this difference will have a
where the producers and consumers are countries or
negative effect on the price for cocoa. If demand
regions. The regions are arranged in such a way
increases or decreases over a longer period of
that the amount of beans imported by producing
time a change in the demand for stocks by
regions, and the amount of beans exported by
O. 30 x t.GRWT will be induced. This has to be added
consuming regions, can be neglected. Instead of
to the demand for consumption in order to obtain
beans bean equivalents were used, since all
total demand (GRWT
exports and imports of intermediary products were
price index CPI is included in order to seperate
transformed into bean equivalents.
the effect of differences in supply and demand on
The producing countries or regions are Cameroon,
other markets.
+
O.30t.GRWT). The commodity
the cocoa market from spill-over effects from Ghana, Nigeria, Ivory Coast, Africa Rest, Brazil, Rest South America and Asia and Oceania. QRWT GRWT
t.(ln(QRt ))
+
f3 In(QR 9
t -
1
(A.1)
)
STWT
t
2: 8i= 1 QR ti
t
4 2: Jd GR tJ
t
In(PICCO The consuming regions are North America, Western Europe, Eastern Europe (including the USSR) and
STWT ) t
)
[~gp]
f3
o
+
CCRR
(A.8)
t
+
[.99 x QRWT
'"0
+
"'1 In(CPl t )
GRWT ] t
t
'" [QRWTt - (GRWT t
+ '"
+
4
(A.9)
In(PICCO t
-
1
)
.3 0 t.GRWT)]
GRWT
2
t-l
- '"3
t
+
t-l
Rest of the developed World .
In(
(A.7)
f3 ln ([GNPR!PC] ) 1 POP
+
f3 In ([PI] ) 2 PC
STWT t-! - . 30 x GRWT t-l ] [
GRWT
.
(A.10)
t - 1
t
t
(A.2)
The mode l also includes a submodel for the calculation of costs of buffer stock operations.
The price system contains relations for producer
These costs are based on the possible profit from
prices PFI in home-currency, and for export prices
buying and selling cocoabeans by the buffer stock
PE and import prices PI in US-dollar cents.
manager, the interest costs of an annual loan to finance the buffer stock for this year, and the costs of keeping the beans in a warehous in the
PFI PE PI
t
t
United Kingdom. The costs of keeping 1000 MT of t
cocoabeans in stock are based on information K
1
K
1
PICCO PICCO
+ K t
2
+ K t
2
PICCO PICCO
t - 1
t -
1
+ K
3
+ K
3
PE PI
t - 1
t -
1
(A.5)
correspondence with the ICCO. (A.6)
The world market cocoa price PICCO depends on the difference between world supply QRWT and demand for grindings GRWT. The definitional equation for total demand for grindings GRWT also includes an autonomous component CCRR to account for imports in countries or regions, which are not modelled explicitly. Differences in supply and demand will also induce changes t.STWT in free stocks (the
gathered by UNCTAD (UNCTAD. 1975) and private
9. I'LA"J"JING AND DECISION SYSTEMS
UK, 1989
A HEURISTIC DECISION RULE FOR BUFFERSTOCK MANAGEMENT W.
J.
H. Van Groenendaal
Titblng Ullivrrsih', PO Box 90153 , 5000 LE Tilblllg, The Netherlallds
Abstract. Most commodity agreements formulated rule out succes in advance because of the ridgit formulation of the gaol. Only recently a different view on agreement formulation has emerged. One of the agreements which aim is to be flexible with respect to changing market conditions is the new cocoa agreement, Using an annual model of the cocoa market this article will explore a heuristic rule for market intervention and compare it with the instruments agreed upon. Keywords. Commodity agreement, price stabilization, buffer stock policy, heuristic programming.
recent cocoa agreement was the collapse of the tin
1 INTRODUCTION
agreement in 1986. basically due to prolonged The new 1986 International Cocoa Agreement has
attempts to maintain the tin prices at an
(UNCTAD, 1986a). for the first time in history, as
artificially high level. As a direct consequence
its sole objective the reduction of price fluctua-
of this failure. the UNCTAD Committee on
tions around the long term market-determined trend
Commodities decided on new guidelines for
(see article one of the new cocoa agreement). The
commodity agreements. The major point of these
stabilization of income is regarded as a conse-
guidelines was that future agreements should be
quence of this objective of the agreement. From a
designed in such a way that they take into account
theoretical point of view there are objections
developments in market prices (Unctad,1986a).
against the use of the expected price trend if the market cannot be described by linear model. From
Incorporating this lesson in a model of a
the work of Turnovsky (1976.1978) and Nguyen (1979,1980) we know that the expected price trend
commodity market means that the decision rule for selling or buying by the buffer stock manager
can only be used if the Waugh-Oi-Masse1l model is
should not alter the market price trend and also
valid. In a general non-linear model with
should not ignore changes of prices induced by
multiplicative disturbances the arithmatic price
spill-over effects from other markets. The
trend will not lead to a realistic buffer stock
information which will influence the decisions of
policy. Realistic in the sence that it fulfills
the buffer stock manager can be seperated in
the requirements of (i) earnings stabilization and
information on the internal market and information
(ii) self-liquidation. In a realistic setting the
on the rest of the world economy. His objective
use of a price trend to guide the buffer stock
will be to stabelize the market prices for the
policy will lead to a failure of the policy
current year without inducing drastic shocks in
(Turnovsky.1976).
production. In a realistic setting the decisions of the buffer stock manager will not be influenced
The tin-disaster (and others like EEC inter-
by long term expectations on the development of
vention) confirms the theory. The main lesson is
the world economy.
that buffer stock intervention should not go against the general tendency of the market. The
In the literature two types of stabilization
decisive factor in shaping the caracter of the
policies are used. The first one is a band width
479
480
W.
J.
H. Van Groenendaal
rule or price range. This type of policy was
market. This can be formulated as:
mostly used in previuos commodity agreements. The band width rule does not take into account the PICCO *
spill over effects from other markets, it is
(2)
fl (0, O,FOM:)
t
restricts the price variations to a pre-specified range, the band width. In most agreements the band If the only instrument available to the buffer
is formulated in absolute prices and based on
stock manager is the buffer stock, this implies:
outdated information (ICCO,1984). Such a policy uses neither information on the internal market,
t.(BST
nor information on external developments.
f (PICCO *
)
2
t
PICCO
-
t
(3)
) t
The second type of rule results from the optimal control formulation of the problem; the buffer The advantage of this rule is that the only target
stock manager has to keep the price as close as
price needed is the actual one, and only short
possible to a pre-specified price path. The pre-
term expectations on future developments are
specified price path is based on information on
needed. This seems more realistic given the
the internal and external market conditions till the previous period. However, in this formulation
practical situation the buffer stock manager has
of the problem the objective function has to be
to deal with. A disadvantage is that in a rea-
modelled explicitly, and is mostly of a quadratic
listic model we will not be able to prove that the
function. The model used is nearly always a linear
agreement leads to optimal results, it can only be
model (Lee and Blandford,1980;Ghosh et al. ,1982
shown that over a longer period of time it is
and 1987).
satisficing. For our model this implies that two conditions should met:
The objective of this article is to formulate a flexible heuristic decision rule for the buffer stock manager and to compare it to the 1986 cocoa
g(QR - GR ) - t.BST1 t
t
t
o
(4 )
o
(5)
agreement. The heuristic will be formulated in ST
such a way that it does not violate the general
t-l
- STd
t-!
- t.BST2 t
principles stated above. In section 2 the heuristic will be discussed. In
The total buffer stock mutation necessary to
section 3 the the new cocoa agreement will be
achieve the target price PICCO * is t
reviewed. In section 4 the intervention heuristic will be compared to the agreement using an annual t.BST
model of the cocoa market. Section 5 contains
t.BST1
t
+ t
t.BST2
(6)
t
conclusions and an outline for practical use of the heuristic. This condition is the target for the buffer stock manager to achieve every period. Implementation in 2 A HEURISTIC RULE FOR INTERVENTION
the model of appendix A leads to the following target price for the buffer stock manager:
It is assumed that the actual price PICCO on supply and demand g(QR
t
depends
l
- GR ), the difference t
between stocks and desired stocks (ST
_ t
1
ST:_
-
I
),
and expectations about forces from outside the
PICCO * t
market FOM: (see the appendix): where CPI
t
covers FOM e t
•
Since 6BST
t
is based on
production, consumption and stocks of cocoabeans PICCO
t
f (g(QR 1
t
- GR ) ,ST t
t-l
- STd
t-l
,FOM e t
)
(1)
only, this rule is referred to as the rule of internal growth.
The aim of the buffer stock manager is to formulate a short term target price PICCO * , which t
implies that excess demand or excess supply is taken out of the market. In this way his policy will not react on influences from outside the
A Heuristic Decision Rule for Buflerstock Management
3 THE 1986 COCOA AGREEMENT
481
Taking both semi-automatic adjustments into account it turns out that the 1986 cocoa agreement
The 1986 cocoa agreement consists out of two
contains the most flexible adjustment of the price
stabilization instruments and two semi-automatic
range that has ever been incorporated in a com-
adjustment rules for the reference price (UNCTAD,
modity agreement.
1986b). These two types of semi-automatic adjustment of the reference price to the price trend (and thus the intervention prices) are the
Implementation of the Agreement
most important new features of the 1986 cocoa agreement.
The agreement contains two instruments and two
The 1986 agreement is characterized by:
section 2) which have to be translated in terms of
- a relatively large band width of 80 US-dollar
the model of appendix A.
adjustment mechanisms for the price range (see
cents. This implies that the lower and upper intervention price are at a distance of 40 US-
- The buffer stock can be implemented in equation
dollar cents from the reference price of 227 US-
(A.7), since it effects world supply of
dollar cents per kilo.
cocoabeans QRWT.
- a buffer stock of 250,000 mt (as in the
cents per kilo if the buffer stock manager has to
agreement of 1980). Should, after three years, the
sell or buy 75,000 mt within six months. was
- The adjustment of the reference price by 13 U$
agreement be extended for a period of more than
translated into an adjustment of the reference
one year the maximum buffer becomes 350,000 mt.
price each time the buffer stock manager sells or
The stock resulting from the old agreement
buys 75,000 tons within one year. After one
(100.000 mt) and a capital of 250 million US-
adjustment within a year, the adjusted reference
dollar have been transferred to the new agreement.
price was used. The computer program used allows
Additional funds for buffer stock operations will
for two of these adjustments within one year.
continue to come from a levy of 2 US-dollar cents
- Withholding has the same effect on prices as a
per lb (recently changed to 1.36 US-dollar cents
buffer stock mutation, and was implemented in the
per lb).
same way (without tranches). Withholding starts when the maximum buffer of 250,000 mt has been
- a withholding scheme. The bufferstock manager
reached. Withholdings are sold whenever the actual
keeps national stocks in store up to a maximum of
cocoa price exceeds the reference price. The
120,000 mt. The withholding scheme becomes
amount sold will keep the actual price equal to
operative once the buffer has reached 200,000 mt
the reference price.
or the manager runs out of funds. The effect of
- Implementation of the annual price review is
withholding is the same as buying by the buffer
straightforeward.
stock manager. The main difference between a
- The reference price is adjusted each calender
buffer stock operation and withholding is that
year instead of each cocoa year.
withholdings are released at the reference price. This implies that only the lower half of the price range is relevant for this instrument.
Implications of the Model
- an annual price review. In case the average
Only the main effects of the model of appendix A
price over the preceding year has been outside the
are reported. These main effects within the model
range, the reference price will be increased
are elucidated by the effect of changes in the
(decreased) such that the indicator price comes
world cocoa price PICCO on production and
within the band width at a distance of 6 US-dollar
consumption, and by the effect of a change in real
cents from the upper (lower bound) of the band,
gross national income per capita. These effects
with a maximum adjustment of 13 US-dollar cents
are given in table 1 and table 2 respectivily (see
per kilo.
also Van Groenendaal and Vingerhoets,1989). Compared to other studies of the cocoa market by
- a price review during the year. If the size of
the World Bank (Akiyama and Duncan, 1982) and The
the actually held buffer stock changes 75,000 mt
International Cocoa Organization ICCO (1984) the
within a six month period, the reference price is
results for North America and Western Europe are
adjusted 13 US-dollar cents per kilo.
of the same magnitude. For Eastern Europe and the
W.
482
J.
H. Van Groenenclaal
USSR the price elasticities obtained differ. This
4 THE EFFECT OF THE DIFFERENT POLICIES
is partially due to differences in the definition of the region. With respect to the rest of the
Since the rule of internal growth and the cocoa
developed world the results are close to those of
agreement do not effect the average production and
the ICCO, but differ from the results of the world
consumption over the total simulation period when
bank. There are, however, no real anamolies
compared with the free simulation results, they
between the various results, only differences in
are both neutral with respect to the development
magnitude.
of supply and demand. The conclusion that the market trend is not altered is valid under all three the assumptions with respect to inflation
Simulation Exercises
(see tables 3,4, and 5). (The same goes for the world income, which is not reproduced here.)
In order to compare the application of the
However, in case of one or three percent inflation
heuristic rule and the effect of the policy
the agreement becomes ineffective after period
instruments of the 1986 cocoa agreement, a number
sixteen and period thirteen respectively (see
of simulation experiments were performed, based on
tables 7 and 8). The only instrument used is the
the following assumptions. A zero growth and an
annual price review, but this instrument is to
annual one and three percent growth over a period
restrictive to restore the effectiveness of the
of 25 years of the Commodity Price Index CPl. The
agreement, the adaption of the price trend is too
one and three percent growth rate are introduced
slow. The main reason for this is the fact that
to test both policies in an inflationary enviro-
spill over effects from other markets are ignored
ment. Fluctuations are introduced by taking the
in the adaption of the price trend. This in
historical differences of the actual values of the
contrast to the rule of internal growth, which
commodity index CPI and its geometrical mean. The
remains active during the total simulation period
so obtained fluctuations are added to the trend in
regardless the experimental setting due to the
CPI used for the different experiments. Exchange
flexibility with respect to spill-over effects
rates are assumed to be constant over the
which is build into the rule of internal growth.
simulation period. This implies that the US-dollar
In all experimental settings the rule of internal
can be used as currency instead of SDR's, the
growth is more effective than the agreement. In
denominator used in the agreement. The consumption
case of zero percent inflation the opportunity
prices are linked to the development in the
costs and the operational result are comparable.
commodity price index to avoid unneccessary
In the other cases the costs of the rule of
complications due to increasing differences in the
internal growth still remain moderate, with a
development of exogenous variables.
maximum of 40.2 million US-dollars over twenty five periods in case of three percent inflation.
As was shown by Van Groenendaal and Vingerhoets (1989) the 1986 cocoa agreement is to flexible. Reducing the band width from 80 to 40 US-dollar cents leads to better results. Therefore this reduced band was used as a reference for the rule of internal growth.
If we take into account the contributions of the members of the International CoCoa Organization, the funds of the ICCO are sufficient to finance the policy, as the opperational result of 211.5 million US-dollar teaches us.
Since the aim is to compare the price trend of the rule of internal growth and the price trend used in the agreement, a maximum buffer of 250,000 mt and withholdings up to 120,000 mt were used in both cases. A range of
~
5% is used in case of the rule of
internal growth. This was done because in practice only larger differences in demand and supply can be taken into account, since minor differences cannot be identified.
5 CONCLUSIONS The heuristic rule formulated here performs better than the policy rules formulated in the 1986 cocoa agreement. The price adjustment part of the agreement is not flexible enough, to adjust to even a moderate inflation of one percent over a longer period. Application of the rule of internal growth shows that price and income stabilization is possible over a longer period of time. It also shows that only recent information is necessary to do so. No predictions of future developments are necessary.
483
A Heuristic Decision Rule for Bufferstock Management Using the most recent information on production
Van Groenendaal W.J.H. and J.W.A. Vingerhoets
and consumption, and on forces from outside the
(1989). The new cocoa agreement analysed .
market it is possible to formulate a decision
Working Paper FEW 339, Tilburg University.
support sytem for the buffer stock manager for every day practice since the rule is independent of the model used to validate the rule. The principle of neutrality with respect to the market trend, and quantification of the spill-over
TABLE 1 Price Elacticities of Cocoa Production
effects, although difficult, can be used to formulate such a decision support system, where
Short Run
the model is replaced by information from the market and the price equation by its short term equi valen t .
REFERENCES
Long Run
Cameroon Ghana Ivory Coast Nigeria Brazil Rest Latin America Asia and Oceania
.13 .10 .42 .20 .25 . 14 .0
·73 .38 .82 .47 .29 .28 ·50
World Total
.23
.54
Akiyama, T. and R.C. Duncan (1982). Analysis of the world cocoa market. World Bank Staff Commodity Working Papers, §. Ghosh, S., C.L. Gilbert and A.J. Hughes Hallett (1982). Optimal stabilisation of the copper
Remark: Short Run means current and 1 year lag. Long Run means steady state elasticity. For Africa Rest we used a dummy equation which describes the development of production over time.
market: The problem of information. Resources Policy, §, 201-214. ICCO (1984). An Analysis of the World Cocoa
TABLE 2 Price and Income Elasticities of Cocoa Consumption
Economy. International Cocoa Organization PCA/3/6, London.
price short run long run
Lee, S. and D. Blandford (1980) . An analysis of international buffer stocks for cocoa and copper through dynamic optimisation. Journal of Policy Modelling,
~,
371-388.
Nguyen, D.T. (1979). The implications of price stabilization for short-term instability and
North America Western Europe Eastern Europe Rest World
-.19 - . 14 -.26
-.25 -.15 -.26 -.40
-.16
-.23
- .11 +
USSR
World Total
long-term level of ldcs' export earnings. The income
Quarterly Journal of Economics, 149-154.
short run
Nguyen, D.T . (1980) . Partial price stabilization and export earning instability . Oxford Economic Papers, 341-352. Turnovsky, S.J. (1976). The distribution of welfare gains from price stabilization: The case of multiplicative disturbances. International Economic Review, 21, 133-148 . Turnovsky, S . J. (1978). The distribution of welfare gains from price stabilization: A survey of some theoretical issues. In F.G . Adams and S.A . Klein (Eds.) .Stabilizing world commodity markets. Lexington Books, Lexington. UNCTAD (1975). An integrated programme for commodities. UNCTAD TD / B/ C.1 / 198, Geneva. UNCTAD (1982) . International cocoa agreement 1980. UNCTAD TD/Cocoa 6/7/rev. 1, Geneva. UNCTAD Bulletin (1986a) no. 224 July/ August. UNCTAD (1986b). The international cocoa agreement. UNCTAD.
North America Western Europe Eastern Europe Rest World World Total
+
USSR
long run
.21 .25 .44 .42
.25 .30 . 66 .57
. 30
·39
W . .J. H. Van Groenendaal
484
TABLE 3 The Effect of the Rule of Internal Growth and the Agreement on the Stability of Prices and Income in Case of Zero Percent Inflation
instability index*) simulation
internal growth
agreement
36.9% 29.1%
16.6% 15.7%
20.9% 19.6%
Brazil Rest Latin America Cameroon Ghana Ivory Coast Nigeria Rest Africa Asia & Oceania
20.4% 24.5% 27·2% 47.7% 21.5% 53.0% 30·9% 9.4%
13.0% 18.9% 19.9% 31.0% 14.1% 40.8% 23.0% 9.8%
13.5% 21.2% 23.3% 41.6% 17.6% 47.6% 27.4% 8.1%
World total
20.1%
15.4%
Prices: PICCO PICCO/CPI Income in 1985 U$:
In million U$ **) Operational result**) Opportunity costs Average in 10 3 metric tons of World production World consumption
*) defined as
II =
[ll:n n
16.4%
-
102.6 11.9
101.8 12.9
2406 2375
2408 2375
2405 2376
(x - x
1=1
t
0
(1+X)t)2]/~ mean
.
**) See the appendix for the definition of these concepts.
TABLE 4 The Effect of the Rule of Internal Growth and the Agreement on the Stability of Prices and Income in Case of One Percent Inflation
instability index*) simulation
internal growth
agreement
37. 1% 28.8%
16.0% 16.1%
24.3% 21.5%
Brazil Rest Latin America Cameroon Ghana Ivory Coast Nigeria Rest Africa Asia & Oceania
19.7% 23.6% 27.5% 47.9% 21.5% 52.9% 30.7% 9.2%
12.9% 18.3% 20.5% 31.5% 14.3% 41.4% 23.0% 9.9%
15.6% 21.1% 26.2% 43.4% 20.0% 49.7% 28.3% 7.6%
World total
19.8%
15.4%
Prices: PICCO PICCO/CPI Income in 1985 U$:
18.7%
In million U$ **) Operational result**) Opportunity costs
136 .6 16.1
160.5 -7 .1
Average in 10 3 metric tons of World production World consumption
2405 2370
2399 2371
*) and **) See table 3.
2402 2370
485
A Heuristic Decision Rule for Bufferstock Management TABLE 5 The Effect of the Rule of Internal Growth and the Agreement on the Stability of Prices and Income in Case of Three Percent Inflation
instability index*) simulation
internal growth
agreement
38.1% 28.4%
18 .6% 18.6%
23.2% 19.6%
Brazil Rest Latin America Cameroon Ghana I vory Coast Nigeria Rest Africa Asia & Oceania
18.5% 21.9% 28.2% 48.2% 21.6% 52.8% 30.3% 9.0%
14.5% 18.4% 22.9% 35.7% 16.4% 45.4% 23.4% 11.0%
14.6% 19.6% 27.0% 42.4% 20.1% 48.8% 27·9% 8.3%
World total
19.1%
16.9%
Prices: PICCO PICCO/CPI Income in 1985 U$:
18.2%
In million U$ **) Operational result**) Opportunity costs
211.5 40.2
291.9 -36.2
Average in 10 3 metric tons of World production World consumption
2396 2360
2390 2360
*) and **) See table
2393 2359
3.
TABLE 6 The Use of the Available Instruments in Case of Zero Percent Inflation internal growth period
1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17
18 19 20 21 22 23 24 25
!>BST
0 -14 0 -86 250 0 0 0 - 250 0 0 52.8 -52.8 40 . 7 79.4 45 .4 -86.0 0 0 74.6 93.4 2 .7 -13.1 -168.2 21. 3
agreement
!>WTH
P
0 0 0 0 82.3 0 0 -82.3 0 0 0 0 0 0 0 0 0 0 0 0 0 88.3 - 88.3 0 0
210.4 196.3 196.6 196.7 206.7 188.2 173.3 158 .4 160.8 170.8 180.8 180.1 181.4 226.5 206.3 206.6 220 .0 228 .4 241.9 251.1 242.3 228.6 226.1 241.9 235 .7
rd
!>BST
!>WTH
0 0 0 0 22.4 0 0 -0.7 120 128.3 0 0 0 0 0 0 -40.8 -120 0 -75 0 0 0 75 0 -75 0 0 0 0 0 0 -125.2 0 0 0 0 0 0 0 0 5.2 0 74.3 0 -25 .3 0 -54.2 14.4 0
!>P
re f
1,/) 2 2 2 1 1 1
1,2 2 2
2
P
re f
227 227 227 227 227 201 191.8 179.5 179.5 179 . 5 192.5 192 ·5 179.5 192.5 192·5 192.5 192.5 213.5 226 . 5 234 . 1 234.1 234 . 1 234.1 234.1 247.1
*) 1 implies a correction reference price of 13 US-dollar cents due to !>BST > 75,000 mt . 2 implies that the end of year price is out of range and the reference price is corrected in order to bring the actual price at a distance of 6 US-dollar cents of the intervention price. The maximum intervention is 13 US-dollar cents.
J.
W.
486
H. Va n Groen endaal
TABLE 7 The Use of the Available Instruments in Case of One Percent Inflation internal growth period
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
t.BST
t.WTII
0 -27.3 0 -72.7 250 0 0 0 -250 0 0 49.4 -49.4 42.7 83.0 49 . 4 -80.2 0 0 80.6 74.5 0 0 -164.5 30·3
0 0 0 0 79.6 0 0 -79 . 6 0 0 0 0 0 0 0 0 0 0 0 0 29.0 91.0 -120 . 0 0 0
agreement P
rer
211. 3 199.8 201 . 4 205.8 221.3 201.9 187.4 172 . 9 177.5 190 . 4 204.2 205 · 9 209.2 264.8 243.5 246.5 265.4 278 . 9 297.7 312.2 305·5 292 . 2 290.7 311. 3 309.3
t.BST
t.WTII
0 0 0 -54.1 173.7 0 0 0 -116.0 -30.7 0 75 -75 25·5 0 -25 . 5 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
t.P
re f
P
ref
227 227 227 227 227 201 201 201 201 214 214 214 201 214 214 214 214 227 240 253 261.2 261 . 2 261 . 2 274 . 2 287 . 2
1
1 1 1
2 2 2 2 2 2 2
TABLE 8 The Use of the Available Instruments in Case of Three Percent Inflation internal growth period
1 2 3 4 5 6 7 8 9 10
11
12 13 14 15 16 17 18 19 20 21 22 23 24 25
t.BST
0 -53 . 2 -33 . 4 -13.4 250 0 0 0 -250 0 0 39·1 -39.1 49 . 9 95.0 61.4 -65.3 0 0 71.9 17·5 0 0 -163 . 3 52.3
I'.WTH
0 0 0 0 79 . 4 0 0 -82 . 3 0 0 0 0 0 0 0 0 0 0 0 0 105·3 14.7 -120.0 0 0
agreeme nt P
re f
213 . 1 207 .0 211.5 220.1 257 . 1 234.1 218 . 4 205.2 214 . 1 235 . 3 259.3 268.3 277·5 361.2 338.3 349.6 384.7 413 . 4 447 . 8 479.1 482.3 473 . 6 460.4 517·3 531.8
I'.BST
0 0 0 -100.0 163.4 0 0 0 -163 . 4 0 0 75 -75 0 0 0 0 0 0 0 0 0 0 0 0
t.WTH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
I'.P
re f
1 1
1,2 2 1 1 2 2 2 2 2 2 2 2 2 2
P
re f
227 227 227 227 250 224 224 224 224 262 275 275 262 288 301 301 310 . 5 323 · 5 336.5 349 . 5 362 . 5 375.5 388.5 401.5 414.5
487
A Heuristic Decision Rule for Bufferstock Management Appendix: A Model of the Cocoa Market
factor .99 accounts for transportation losses). The desired level of stocks for production of
Cocoabeans are produced in less developed
cocoa products is set equal to the avarage level
countries and cocoa products are mainly consumed
of stocks over the period 1962-1982 (O.30 x GRWT).
in developed countries. This dichotomy was used in
In as far as last years stocks STWT differ from
formulating a model of the world cocoa market,
the desired level this difference will have a
where the producers and consumers are countries or
negative effect on the price for cocoa. If demand
regions. The regions are arranged in such a way
increases or decreases over a longer period of
that the amount of beans imported by producing
time a change in the demand for stocks by
regions, and the amount of beans exported by
O. 30 x t.GRWT will be induced. This has to be added
consuming regions, can be neglected. Instead of
to the demand for consumption in order to obtain
beans bean equivalents were used, since all
total demand (GRWT
exports and imports of intermediary products were
price index CPI is included in order to seperate
transformed into bean equivalents.
the effect of differences in supply and demand on
The producing countries or regions are Cameroon,
other markets.
+
O.30t.GRWT). The commodity
the cocoa market from spill-over effects from Ghana, Nigeria, Ivory Coast, Africa Rest, Brazil, Rest South America and Asia and Oceania. QRWT GRWT
t.(ln(QRt ))
+
f3 In(QR 9
t -
1
(A.1)
)
STWT
t
2: 8i= 1 QR ti
t
4 2: Jd GR tJ
t
In(PICCO The consuming regions are North America, Western Europe, Eastern Europe (including the USSR) and
STWT ) t
)
[~gp]
f3
o
+
CCRR
(A.8)
t
+
[.99 x QRWT
'"0
+
"'1 In(CPl t )
GRWT ] t
t
'" [QRWTt - (GRWT t
+ '"
+
4
(A.9)
In(PICCO t
-
1
)
.3 0 t.GRWT)]
GRWT
2
t-l
- '"3
t
+
t-l
Rest of the developed World .
In(
(A.7)
f3 ln ([GNPR!PC] ) 1 POP
+
f3 In ([PI] ) 2 PC
STWT t-! - . 30 x GRWT t-l ] [
GRWT
.
(A.10)
t - 1
t
t
(A.2)
The mode l also includes a submodel for the calculation of costs of buffer stock operations.
The price system contains relations for producer
These costs are based on the possible profit from
prices PFI in home-currency, and for export prices
buying and selling cocoabeans by the buffer stock
PE and import prices PI in US-dollar cents.
manager, the interest costs of an annual loan to finance the buffer stock for this year, and the costs of keeping the beans in a warehous in the
PFI PE PI
t
t
United Kingdom. The costs of keeping 1000 MT of t
cocoabeans in stock are based on information K
1
K
1
PICCO PICCO
+ K t
2
+ K t
2
PICCO PICCO
t - 1
t -
1
+ K
3
+ K
3
PE PI
t - 1
t -
1
(A.5)
correspondence with the ICCO. (A.6)
The world market cocoa price PICCO depends on the difference between world supply QRWT and demand for grindings GRWT. The definitional equation for total demand for grindings GRWT also includes an autonomous component CCRR to account for imports in countries or regions, which are not modelled explicitly. Differences in supply and demand will also induce changes t.STWT in free stocks (the
gathered by UNCTAD (UNCTAD. 1975) and private