The Maple Sap Products Industry in Quebec:
An Economic and Production System Dynamics Model
L. Martin Cloutier
Department of Management and Technology
School of Management
University of Québec at Montréal
P.O. Box 6192, Downtown Station.
Montréal, QC H3C 4R2 Canada
Tel.: 514.987.3000, ext. 3732#
Fax.: 514.987.3343
E-mail: cloutiermartin@ugam.ca
Abstract
The SD model expounded in this paper characterizes the nonlinear and dynamic behavior
exhibited in maple sap production, and the potential hazard of long feedback delays involved in
fixed asset investments supporting sap collection and syrup production. Developed following the
structure introduced in Meadow s (1970) dynamic commodity cycle model, this model is adapted
to the specifics of maple syrup production, and integrates structural elements of price
expectations, supply response, demand substitution, and inventory fluctuation. As with most
conmodity production, maple sap collection and syrup production are subject to production,
Price, and stock pileup risks. All industry participants are subject to the uncertainty associated
with long time delays in the formation of price expectations, in the adjustment of the supply
response, seasonal production, and the demand for exports. Illustrative simulation results are
presented. Extensions to the current works are outlined in the conclusion.
Key Words: maple syrup, system dynamics, price expectations, feedback.
Introduction
The maple sap products industry has litle in common with its romantic origins still
perceived by consumers. In today’s marketplace industry, participants must coordinate, manage
dependencies, obtain information about demand and supply conditions in intemational markets,
and strive to bring the best quality product to consumers’ tables. The industry has become more
responsive to consumers through efforts such as the introduction of quality grades for the syrup
as a quality differential mechanism.
As with most commodities, maple syrup production has been subjected to production,
Piice risk, inventory buildups, and other uncertainties. These latter elements of uncertainty
include misperception in feedback among producers regarding the “expectation supply response
connection.” This uncertainty is reflected in large swings in inventory, stock buildups, and other
typical dynamic elements of behavior observed in commodity production (Meadows 1970;
Sterman 2001). Inventory buildups became an important problem during the 1979-1981 period.
Additionally, since 1988, the industry has adopted technology and management practices that
have contributed to more than 50% growth in production volume. Because of these factors, the
history of the industry in Quebec since the 1970s includes numerous cycles of excess supply and
inventory buildups, leading to episodes of production overshot relative to the market absorption
capacity as well as price collapses.
The objective of this paper is to report on the design of a system dynamics (SD) model
that integrates the structural elements of supply response, demand substitution, and inventory
fluctuation in the production of maple sap products in Quebec. Aside from govemment
monographs (MA PAQ 1996,1999), descriptive technical statistics reports (Gilbert et al. 2000),
and case studies (Dicaire 1985), there is a paucity of formal economic and quantitative modeling
of maple syrup production. The SD modeling approach is appropriate given the nonlinear and
dynamic behavior exhibited in production, and the long feedback delays involved in the
investment of the fixed assets necessary to support production. This paper is structured as
follows. The following section provides a brief background of the production and industry.
Using this background information, a dynamic hypothesis is presented using an influence
diagram as a means to describe the economic and production behavior of the industry. The
influence diagram sets the stage for the model development. Details are provided on the
development of the model and data source. Simulation results looking at the potential for growth
in export markets are presented to illustrate the potential of the model, and a conclusion follows.
Industry Background
The product at the origin of the maple products industry is the sap of a tree. Maple syrup
is the main product extracted from the sap. The evaporation of 34 liters of maple sap is necessary
to obtain 1 liter of syrup. Other maple sap products are obtained through further evaporation and
sometimes stirring; these products include maple butter, maple taffy, soft maple sugar, hard
maple sugar, and granular sugar.
The maple sap products industry in Quebec sells about $120 million annually worth of
maple sap products. Quebec production represents approximately 70% of the industry’s total
North American output, and 90% of Canada’s production. Quebec is the largest producer of
80 000 2.5
70 000 <
| \ 1?
60 000 ] a a
& 50000 ? ALY +15 £
2 40 000 A
A _ fey :
been a |
20 000 4
we ~ Perna 7 08
10 000 7
0 0)
1970 1974 1978 1982 1986 1990 1994 1998
(years)
-™ Production -*-CND Exports Price
Figure 1 Production, exports, and price trends - 1970-1999
80 000 3.00
70 000 2:80,
[ 2.60
60 000
= 2.40
2 swove Ma i \ P
= "f \ ro A | WY 220
g 40 000 os 2.00
% 30000 A | A\ aan [ : 1.80
5 1.60
20 000 +
- 1.40
10 000 Lion
0 IN 1.00
1970 1974 1978 1982 1986 1990 1994 1998
(years)
-*-Production —— Maple taps -@ Production yields
Figure 2 Production, maple taps, and yield trends - 1970-1999
maple sap products, and while domestic markets absorb a fair share of this production, domestic
output far exceeds local demand. Roughly 90% of production is destined for export markets.
Bulk maple syrup is the most important maple sap product exported. In fact, between 1993 and
1999, exports have increased by 115% percent. The bulk of exports is sold to the United States,
and, as well as to 32 other countries, including Germany, France, Australia, Japan and Taiwan.
Exports to the United States show a moderate steady upward trend, while exports to other
markets tend to fluctuate from one year to the next.
Production yields (Ibs./tap)
As seen in Figure 1, the trend in exports has increased dramatically since 1990. Maple
syrup production has dramatically increased as well. The production volume and price trends
clearly show opposite movement overtime. Prices tend to fall when production soars and vice
versa. Interestingly, both prices and production appear to cycle around an upward trend.
In Figure 2, the number of maple taps shows a moderate upward trend since the mid-
1980s. A ggregate gains in productivity arise from this trend as well as from improved
management practices and widespread adoption of the tubular sap collection technology, the
“SY SVAC.” This gain in productivity can be seen from the rising trend in yields. The production
of syrup also is subject to production risks, as is seen from the jigsaw pattem from one year to
the next. This pattem is highly correlated with production output and the evidence of ubiquitous
production risk.
Hypothesis of the Maple Syrup Production Behavior in Quebec
The influence diagram presented in Figure 3 consists of two balancing feedback loops
labeled B1 and B2. The balancing loop labeled B1 depicts the structure of supply response, and
the balancing loop labeled B2 represents the structure of demand substitution.
The balancing loop B1 comprises three variables, namely the price of maple syrup, the
expected price, and the supply response. The relationship between the price and the supply
response follows the principles of neoclassical economic theory as it relates to supply. As the
price rises (falls) producers tend to expand (contract) production. This can be accomplished
either by investing (disinvesting) in productive capacity or by using (idling) excess capacity. An
increase (decrease) in the supply response leads, with a time delay, to an increase (decrease) in
inventory. A growing (shrinking) inventory would result into a downward (upward) price
pressure, assuming everything else remains constant. This in tum leads to a lower (higher)
expected price for producers.
Itis important to note that long time delays are part of the structure of the supply
response feedback loop (B1). The annual production cycle means that producers have roughly a
year to form price expectations and then, after an investment decision is made, additional time is
needed to execute the adjustment and to bring this capacity online. A fter resources (in the form
of fixed assets) are committed to production capacity, these resources may contribute to excess
production capacity if producers over- expand, relative to the market absorption capacity, or if the
price takes a downward tum. In the case of over- expansion, fixed production costs per unit will
be higher, and in the case of the price drops, producers may keep production going over several
crop seasons in hope for higher prices and further exacerbating excess supply. The outcome is
inventory buildups. The supply expansion can have a lasting effect that extends through time due
to asset fixity and other govemment programs designed to ease producer cash flow.
Supply
Syrup
ce Price of Gc Denend
Smup Smup
Epeded
price
Figure 2 Influence diagram of maple syrup production dynamics
The balancing loop B2 represents the structure of demand substitution. As seen
previously, an increase (decrease) in the syrup inventory leads to a decrease (increase) in price.
Following economic theory, a lower (higher) price makes the product more (less) attractive for
consumers, relative to substitutes. An increase (decrease) in demand will deplete (maintain) the
inventory. As a result, a lower (higher) inventory results in a higher (lower) price.
The influence diagram described above does not account for the role of govemment or of
the producers’ federation that could play a role in influencing the extent of the supply response,
the management of the maple syrup inventory, and the stimulation for exports. These aspects are
to be further developed in subsequent work.
Dynamic Model of Maple Syrup Production
The SD model as seen in figure 4 was designed using the Powersim® software. The
model structure is adapted from the one developed by Meadows (1971) to study dynamic
commodity cycles. Although adjustments to the original model were conducted to account for
the specifics of maple syrup production, the economic and physical stock and flow variable
interactions of this model’s structure are similar.
Demand_Shock
Yields
Intial_inventor)
Pat
Syrup_ihventory
Local_Population
Piduction_rate
O
Initial_capacity
C Capital_depreciation
stment_rate __Depreciation_rate
1
Consumption)
Expected_consumption
coverage
2 Inventory
Capacity_ad Desired_coverage
Per_capit# consumption
Supply_response
Expected_price Price_of_maple_syrup
Figure 4 Stock and tlow diagram ot maple syrup demand substitution,
supply response, and inventory
Adjustment in the stock variable syrup inventory, denoted O, is augmented by the
production rate (r). The syrup inventory is diminished by the consumption rate (c) on the local
market, and exports (x). This relationship is captured in equation (1)
(1) © =0o+ftr—c—wat.
Equation (2) calculates the consumption rate that is the result of the per capita consumption,
denoted E, multiplied by the local population (1),
(2) c=Al
Equation (3) calculates exports as a residual of the inventory minus the consumption rate
multiplied by 6 a demand shock,
(3) x= -)Q
The production rate r, as calculated in equation (4) augments the inventory and is the
result of the production capacity (U) measured in maple taps multiplied by the maple syrup yield
per tap (a)
(4) r=Qy
Fluctuations in the maple syrup inventory change the inventory coverage (v). The
inventory coverage is the quantity of maple syrup that defines the equilibrium with expected
consumption (m). This is calculated in equation (5)
(5) v=0/m
A change in the inventory coverage influences the inventory ratio (w). The inventory ratio is
calculated by dividing the inventory coverage by the desired coverage (@) as in (6)
(6) w=v/6.
The inventory coverage drives maple syrup price movements. The price change influences price
expectations. Producers expectations are calculated using exponential smoothing (Weiner 1966),
also known as the ‘adaptive’ price expectation model (Arrow and Nerlove 1958; Nerlove 1958).
This method is frequently employed in SD models to account for the time delay in the
transmission of information “until persistent or stable delays are detected” (Lyneis 1980:435).
Technically, the adaptive price expectations assume that recent information has more influence
on the formation of price expectations than does less recent information. The time expectation
for the maple syrup price (6 = 1 / t) is a time span that producers are considering for making an
adjustment decision. Thus the integral component in (7) divides the difference between the
current price (P) and the exponential smoothed maple syrup price in the previous period (t- 1),
that is (Po), over a time span (6) necessary for producers to build their maple syrup price
expectation (EP). The adaptive maple syrup price expectation in the model is calculated as
follows
(7) EP=R +fr(P-B) at.
The price expectation is linked to the desired production capacity (number of maple taps) by
means of a table function.
The production capacity is the result of producer upward (downward) adjustments as a
response to economic incentives, that is, by the expansion of production when conditions are
favorable. In the event that economic conditions take a downtum, production could continue
because assets, in the form of equipment, are specific and assumed not transferable to altemative
use. The maple taps acquisition rate (a) in (8) incorporates the maple taps acquisition delay (4a)
associated with the difference between the desired maple taps (Ua) and the current level of maple
taps (U). The acquisition delay explicitly takes into account the time necessary for resources
acquisition associated with the adjustment of maple taps at the desired level, given by
(8) 4294-0) fou
The adjustment in the level of maple taps is stated in equation (9)
(9) Q=Q +flaty/t) dt,
where ais the adjustment in the number of maple taps as calculated in (8), and y is the
depreciation rate and t is the expected useful life of the equipment measured in years.
The maple syrup price also is used to determine consumer demand on the domestic
market using a table function. This table function is based on econometrically estimated
relationship between the price of maple syrup and the per capita consumption. This table
function calculates the consumption rate (c) seen in (2).
Data Sources and Model Calibration
The data employed to calibrate the model were obtained from publicly available time
series data, coefficients, and industry sources. There are two state variables in the model,
namely, the maple syrup inventory and the production capacity. These initial levels constitute the
baseline figure for the model. Table 1 summarizes the variable and parameter name, the value,
and the source for the state variables and the parameters of the model.
Table 1 Model state variable equilibrium (or initial) specification
Symbol State variables Specification Source
(0) Initial Maple syrup inventory (kiloliters) 16,599 Industry
U Initial production capacity (taps) 21,078 Calibrated
Table 2 contains the list of parameters that are included in the model, their calibrated
specifications, and their sources.
Table 2 Model parameter specifications
Symbol | Parameters Specification | Source
a Production yield (liter / maple taps) 0.74 Mean trend
v Desired inventory coverage (years) 1 Assumption
aa Adjustment of maple taps (years) 2 Industry
y Useful life of capital (years) 7 Industry
é Local population (individuals in thous.) 7,139 BSQ
Three table functions are specified in the model. First in Figure 5, the inventory coverage
in the model is a means to approximate the relative scarcity of maple syrup with respect to the
expected consumption equilibrium level in a given year. This information is transmitted to
determine the inventory ratio relative to the period of desired coverage. Variations in the
inventory ratio directly influence the price of maple syrup in the model. Industry sources have
indicated that the equilibrium price for the crop year 2000 crop was $2.00 for an output level of
60,000 pounds. The formula employed to determine the marginal price that follows a change in
the inventory ratio is $0.10 per 5,000 pounds of maple syrup. The minimum price that would be
set without causing massive pain to producers is $1.60 per pound for production output of 80,000
pounds. The equilibrium production level in inventory is used to calibrate relative coverage in
the model. The inventory ratio exercises expansion and contraction pressure on the price of
maple syrup. A relatively higher inventory ratio means less scarcity and thus lower prices, and
3.20
3.00
2.80
2.60
2.40 Equilibrium
relative coverage
2.20 price ratio
2.00 nwa
1.80
Price of maple syrup (P)
($/ Ibs.)
1.60 1.00
0.08 0.48 0.88 1.28 1.68
Inventory ratio (w)
Figure 5 Table function of the inventory ratio and the price of maple syrup
vice versa. Figure 3 shows the function table used to determine the maple syrup price as a
function of the inventory ratio as specified within the model.
Second, the supply response, represented by the desired capacity level, was estimated
using the univariate econometric equation (9). The dependent variable is the number of taps and
the independent variable is the price of maple syrup lagged by one period. These econometric
estimates provide the information needed for the calibration purposes of incorporating the supply
response in the model.
(9) Ua = 8285.8 +6528.8 Pe: ; R’ =0.5149.
The time series data used for estimating the regression parameters included years from 1974 to
1998 (Statistics Canada ; Bureau de la statistique du Québec). The fitted regression estimates can
be seen in figure A 1 in Appendix. The measure of goodness of fit is 0.515. This means that 51%
of the variance in the econometric model can be explained by the price lagged by one period.
34 000
32 000
30 000
28 000
26 000
24 000
22 000
Desired production capacity (U,)
(maple taps)
20 000
1.6 2 2.4 2.8
Expected price of maple syrup (EP) ($ / Ib.)
Figure 6 Table function for the supply response
This is quite high given there is only one variable in the model. The supply response in the
model, that is, the number of taps as a function of the lagged price expectations, was calibrated
using the econometric predicted value for the appropriate price range. The supply response to
price expectations is depicted in Figure 6.
The third table function is the demand curve for maple syrup consumption is seen in
Figure 7. This also was estimated using a univariate econometric model. The per capita
consumption is the dependent variable regressed on the price of maple syrup. The model
equation showing estimates is given in (10), and the fitted plot is displayed in Figure A 2 in the
Appendix,
(10) E =0.3726-0.1232P ; R?=.5166.
The goodness of fit measure (R2) is 0.52. This means that roughly 52% of the variance within the
econometric model is explained by the variation in the price of maple syrup alone. Other
methods could be employed to estimate the demand as a function of the price of maple syrup.
However, the results obtained are adequate within the context of this work.
Simulation Results
0.220
0.180
(Ibs. / capita)
Per capita consumption ( £)
0.020
16 2 24 28
Price of maple syrup (P) ($/lb.)
Figure 7 Table function for the demand
This section presents illustrative simulation results using the baseline SD model. Four
questions are asked to the model: What is the impact on the system if the demand for exports
grows by 4% per annum for the next 20 years, and:
(1) Everything else remains constant?
(2) The production yield varies according to a Gaussian- normal distributed stochastic
variable with a standard deviation 10% around the mean?
(3) The beginning inventory level for maple syrup is below and above the year 2000 level?
(4) The initial productive capacity for maple sap collection is below and above the year 2000
level?
The results are reported on graphs and depict the dynamic adjustment paths of the expected price
(line 1), exports (line 2), and the state variables production capacity (line 3) and syrup inventory
(line 4).
Simulation 1:
‘SSmiation 1: Aesunes everything ese is constant:
+
>
868) *
4
= 35 1 Expected_price
2 es 3 Beas
Ze inet Production capacty
se sm | Srameey
4
=e ie
a us il ‘
oe eae
ern
tex]
TF
i “tet pe
=e
+ a0 2 Exports
= 1460 =P roduction_capacity
= Be, IOAN a Synup_inventory
chs
> 10000
= 1650
Tom,
000 2005 2010 2015 2020
bei
The results of simulation 1 depict the dynamic adjustment path of a 4% growth per
annum in exports assuming the state variables production capacity and maple inventory are
calibrated to the year 2000 values. Ass seen, the initial growth in exports would take about two
years before the inventory begins to fall. This is because maple inventory surpluses are reflected
in the initial conditions of the model and growth in exports are initially too modest to
counterbalance the effect of excess capacity and syrup inventory. Because inventory remains
high (due in part to existing excess capacity) and continues to accumulate, and because
production assets are not removed from production, the expected price keeps falling to the
minimum level allowable by the model. Production capacity contracts until it reaches a low in
2005. This process of eliminating the industry excess supply in the form of existing inventory
and productive capacity (through the gradual wear and tear of the productive capital) would take
until about 2006, or five years following the introduction of the export program. At that point,
the expected price would start to rise from $1.60 per pound in 2005, the minimum allowable
price by the model to $2.60 per pound in 2020.
Simulation 2:
The results of simulation 2 exhibit dynamic adjustment paths similar to the ones of
simulation 1. The difference between the two sets of simulation results is the introduction of
stochastic production yield that follows a Gaussian- normal distribution (N~(0,1)) with a standard
deviation of 0.07 pound per maple tap, or approximately 10% around the mean. Note that
stochastic production yields do not overwhelm the dynamic behavior created by the structural
components of the stock and flow interaction, but rather are useful to introduce some elements of
production risk into the model.
Simulation 3a, b:
The results of simulation 3a were obtained by specifying the initial syrup inventory lower
than the year 2000 level in the model (6,599 kiloliters instead of 16, 599 kiloliters in the baseline
model). This means that at the beginning of the simulation the low inventory puts the expected
price at $2.70 per pound. The high expected price remains above equilibrium price until 2002. At
this point, producers contract production until 2006, time at which the export program leads to a
depletion of the syrup inventory. The depletion of the syrup inventory leads to a tise in the
expected price and this sends the incentive to producers to rebuild productive capacity as a
‘SSmiation 3a: Assures rape syup inventory lover than at equilibrium
27
15700
+4 p+
ont -t-Expected_price
n w=] —2- Exports
A -3-Production_capacity
X —-Syrup_inventory
FON S454
2.000 2005 2010 2015 2020
[yen]
‘SSmiation 3ix Assurres maple syup inventory higher than at equilibrium
26
209+
32000 td
XO
+ zi -t-Expected_price
Pa am] ~2- Exports
18360 —3-Production_capacity
+ weal 4 Syrup_inventory
a
a
-
Sa
2000 2.005 2010 2015 2020
response to the demand for exports. Note that the expected price of maple syrup at the beginning
of the simulation is $2.70 per pound, and that by 2020 the expected price remains lower at $2.62
per pound.
For simulation 3b, the initial maple syrup inventory is higher than the year 2000 level
(26,599 kiloliters instead of 16,599 kiloliters for the baseline model). This implies that this initial
condition of high inventory puts the expected price in the doldrums at $1.60 per pound, the
lowest price allowable by the model. Given this initial condition, the production capacity is
geared up to keep production flowing and inventory rising until it reaches nearly 32,000
kiloliters in 2002. This is the result of production pressures from not yet depreciated production
capacity, which keeps production going at a faster rate than the program for exports. The
inventory exercises downward pressure on the expected price that remains at $1.60 per pound
until 2007. By 2007, the rise in the demand for exports begins to put an upward pressure on the
expected price. As in the previous simulation 3a, the effect of the export program does not begin
to exercise pressure on the inventory until 2006. At that point, the syrup inventory and the
production capacity are sufficiently depleted to stimulate growth in the supply response.
Whether the inventory is over or lower than the year 2000 level, the export program for
maple syrup begins to show results after six years of growth. The pain for producers is less, of
course, if the expansion driven by the export program begins when the industry has lower
accumulated inventory level. Both simulations 3a and 3b reach near identical results by the year
2020. What differ is the adjustment paths of the variables in the system during the first five years
of the export program.
Simulation 4:
The results for simulation 4a were obtained by specifying an initial production capacity
lower than the one in the baseline model (11,078 maple taps rather than 21,078 taps). Initially,
the lower production capacity has no effect on the expected price. In addition, the production rate
is lower and the inventory does not replenishing as rapidly. In this scenario, however, the syrup
inventory reaches a new peak at approximately 17,000 kiloliters in 2005, most likely due to
capacity expansion overshot that sent the price to $1.75 per pound. By that time, the demand for
exports begins to be felt and as the syrup inventory depletes, the expected price begins to rise.
Production capacity expands to meet the program’s growth objectives.
Simulation 4b considers the case where the initial production capacity is higher than in
the baseline model (31,078 maple taps rather than 21,078 maple taps). With the existing excess
capacity, the syrup inventory continues to accumulate until 2003 at nearly 33,000 kiloliters. The
rising inventory leads to a declining production capacity and expected price. The price begins to
rise again by 2008, the point at which the export program provides a sufficient expansion
incentive from a declining inventory. This results in a production capacity expansion by 2009.
The results from simulations 4a and 4b show similar outcomes from growth in exports.
As for the results of simulation 3a and3b, the outcome is similar for the four dynamic paths
studied using the model. Adjustments in production capacity seem to add more delay in meeting
the export program objectives than adjustment in the maple syrup inventory.
‘SSmilalion 4zz Assures supply capacity lover than at equilibrium
+ 28
15700
498 =
Be
ae ? —rExpected_price
12260 2 Exports
15 400 -3-Production_capacity
70, —4-Syrup_inventory
+ 2.
15700
32 000 2
33 000 .
2
2
= 20 T —4- Expected_price
12280 —-2- Exports
3 22400 3 Production_capacity
18000 , 3 —4- Syrup_inventory
+ 1.6 ;
2 1000 3
3 16000 z
8000
2000 2005 200 20s 2020
[year]
Summary and Conclusions
The objective of this paper was to report on the development of a SD model that captures
the microstructure of maple sap collection and syrup production in Quebec and that can be used
to simulate the macrobehavior of the industry. An influence diagram was presented and the
microstructure of the stock and low interactions were characterized in a SD model. The model
was calibrated using publicly available information and data, and using univariate econometric
estimates of supply and of demand functions.
Simulation results were presented to illustrate the macrobehavior of the model. In recent
years, the industry has been plagued with inventory surpluses. The development of an export
program for the maple sap products industry is a privileged means to eliminate inventory pileups.
The results section of the paper presented basic simulation results looking at the time it would
take for the industry to receive an incentive to expand capacity following the introduction of the
program, assuming various degree of disequilibrium in the maple syrup and production capacity
state variables. In most cases it was found that the feedback from the export program takes
nearly five years before it can become significant to make a positive difference on price
expectations.
The limitations of the model are numerous. The following is an incomplete list of key
items that are currently being incorporated in the model:
= It would make sense to disaggregate the supply response according to the size of the
production capacity (per farm type) to account for scale economies. Individual farm
sizes have a different cost structure and profitability levels. This would allow us to
know the intensity of the supply response for each type of production unit. A study
has demonstrated that operating costs vary according to size (Bellegarde 2000).
«To help with cash liquidity, the Quebec Government has a program in place that
allows producers to borrow the money up to half the price of the maple syrup
production. This most likely plays a role in driving up production capacity.
= It would be important to disaggregate the maple syrup inventory. This disaggregation
would allow us to track where the syrup is the value chain between production and
the consumer.
= The policy an strategic components from large industry participants such as the
Fédération des producteurs acéricoles du Québec (FPA Q), and the Regroupement
pour la commercialisation des produits de l’Erable du Québec (RCPEQ). These
industry participants might have an impact on coordinating supply and demand.
+ The underground economy plays a role in the dynamics of the industry.
The model proposed in this paper constitutes an excellent platform towards addressing these
limitations and a first step for a greater understanding of the maple sap products industry
dynamics.
Literature Cited
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305.
Bellegarde, J.-P. 2000. Comment évaluer le prix d’ une érabliére ? Longueuil, QC: Fédération des
producteurs acéricoles du Québec.
Dicaire, N. 1985. Note sur |’ Industrie des Produits dela Séve del’ Erable. Montreal, QC :
Centrale de cas et de documentations pédagogiques, Ecole des HEC, 22 p.
Gilbert, D, Gouin, D.-M., and Dumas, G. (2000). Estimation dela production québécoise de
sirop d’ érable pour 1’ année 2000, Sainte- Foy, QC: GREPA, Université Laval.
Lyneis, J.M. 1980. Corporate Planning and Policy Design: A System Dynamics Approach.
Cambridge, MA: Pugh- Roberts Associates.
MAPAQ (Ministére de I’ agriculture des pécheries et de I’ alimentation du Québec). 1996.
Monographie de 1’ Industrie Acéricole du Québec. Québec, QC: Direction de I’ analyse et de
l'information économiques.
MAPAQ (Ministére de 1’ agriculture des pécheries et de |’ alimentation du Québec), 1999.
Portrait de I’ Industrie Acéricole du Québec. Québec, QC: Direction de la recherche économique
et scientifique.
Meadows, D.L. 1970. Dynamics of Commodity Production Cycles. Cambridge, MA: Wright-
Allen Press.
Nerlove, M. 1958. Adaptive expectations and cobweb phenomena. Quarterly J ournal of
Economics 72: 227-240.
Maple taps
35 000
30 000
25 000
20 000
15 000
10 000
0.3
° 2
£8
°
mn
a
Consumption (Ib. / individual )
o
a
0.05
Appendix
Ua = 8285.8 + 6528.2 Pe
R? = 0.5149
°
.2
4
Sd
2
0.5 0.7 0.9 11 1.3 15 1.7 1.9 21 2.3 2.5
Maple syrup price ($ / Ib.)
Figure A1 Econometric estimation of the supply response
E = 0.3726 - 0.1232 P
R’ = 0.5166 '
4
4
ee
+
i
0.5 0.7 0.9 11 13 15 17 19 21 2.3 2.5
Maple syrup price ( $/ Ib.)
Figure A2 Econometric estimation of consumer demand
