Modelling Systems Dynamics for
New Pastoral Industries
Keith B Woodford
School of Natural & Rural Systems Management
University of Queensland, Gatton Campus. Q443
tel 61754 601 320; fax 61 754 6010324
email: woodford @uqg.uq.edu.au
Abstract
New rural industries are often characterised by boom and bust cycles. These cycles
derive at least in part from long biological lead times between investment decisions
and production consequences. Also, for products that require animals to be
slaughtered there is a negative short-run supply response. This occurs because
female breeders are both capital goods and production goods. Accordingly, the
industry dynamics can be characterised as a complex two-way interplay over time,
where supply of product is a function of market prices, and market prices are a
function of product supply. A systems dynamics model of a developing venison
industry from farmed deer was constructed using ithink™ software. Production
cycles were unstable (i.e. had boom and bust characteristics) in situations where all
female progeny were retained as capital goods during industry expansion phases.
This occurred regardless of biological parameters, age of slaughter, rate of market
development, or form of price expectation model.
Introduction
One of the difficulties faced by many developing livestock industries such as deer,
ostriches and emu, is the ‘boom and bust’ syndrome whereby prices for breeding
animals reach very high values during the development phase, followed by a period of
declining product and livestock prices, and fluctuating product volumes. In this paper
these industry dynamics are modeled for farmed deer and the associated production of
venison, first conceptually and then quantitatively using ithink™ software. The
purpose of the modelling is to gain insights into bio-economic factors that contribute
to the boom and bust cycles and to explore strategies to minimise these effects.
The Conceptual Model
Venison can only be produced when animals are slaughtered. Accordingly, in
situations where individual animals are both capital goods (e.g. breeding females) and
production goods (e.g. a source of marketable meat), investment in breeding females
will lead to a negative short-run venison supply function. As a consequence, during
an initial herd buildup phase, supply of product is constrained to small volumes
which, under standard economic conditions of a backward sloping demand function,
will lead to high product prices. These high product prices provide further
encouragement for industry expansion. Eventually, the ongoing herd buildup will
result in increased product entering the market (because the Jong-run supply response
is positive). Given a finite market, this will lead to lower product prices, although the
timing of this price decline can be forestalled by market development. Once farmers
receive declining price signals they are likely to review their investment decisions, and
move towards a stable-sized herd. As soon as breeding herd numbers are stabilised
then venison supply will increase on account of increased females available to be
slaughtered. In addition, pipeline effects, resulting from the biologically determined
interval from conception to consumption, will cause the quantity of venison to
increase for several more years and this will lead to further pressure on prices.
If the industry responds to these lower prices by dis-investing in breeding hinds
(perhaps by reducing the intensity of operations, or by substituting other livestock
species), then the short term effect will be a further increase in venison output, leading
to a further price decline. Eventually the decline in breeding females will lead to a
lagged decline in venison production and output, and this could be expected to lead to
increased prices. In time these rising prices will lead to cessation of the dis-
investment in breeding hinds, but the decline in venison output will continue for
several years after this decision on account of the time lag from animal conception to
time of slaughter. This ongoing decline in venison output will produce a further
increase in prices, thereby setting the scene for a renewed ‘boom and bust’ cycle.
The above scenario of fluctuating volumes and price instability arises from the
interaction of three relationships. The first of these is the link between past prices and
expected future prices. The second is the biological lag between investment decisions
and outcomes. The third is the dual role of females as capital stock (i.e. breeders) and
as product (i.e. venison). There are strong similarities between this scenario and the
original cobweb model of Ezekiel (1938). However, Ezekiel’s cobweb model was
based on a one-period response function and did not consider the possibility of a
negative short-run supply response.
Price expectation models, whereby expected future prices are estimated as some
function of past prices, are known as adaptive expectation models following the work
of Nerlove (1958). They have been widely used in economic modelling for both crop
and animal industries (French & Mathews 1971; Rucker et al. 1984). The potential
lack of decision rationality associated with these models has been understood for a
long time (Muth 1961). However their explanatory capability in relation to empirical
outcomes is widely acknowledged (Shonkwiler 1982; Knapp 1987).
The role of female breeders as both capital goods and also production goods was
described by Jarvis (1974) in relation to cattle. Gordon (1990) has shown that the
sufficient condition for a negative short-run supply response is that the discounted
value of increased future profits from increased prices must exceed the profits
foregone from withholding animals from sale for breeding purposes. Subsequent to
the work of Jarvis (1974) there have been a number of studies for various species that
show how exogenous shocks to demand or supply can have persistent effects by
changing slaughter and breeding decisions (Chavas & Klemme 1986; Whipple &
Menkhaus 1989; Foster & Burt 1992; Rosen et al. 1994). These decisions affect the
age distribution of the herd and cause cyclical ‘echo’ responses as the herd converges
to a stable structure. However none of these studies have integrated the concept of
livestock inventory cycles and price expectation models with oscillating price cycles
that are themselves influenced by changing supply volumes.
The Systems Dynamics Model
The model was developed using ithink™ software based on the concepts of systems
dynamics as developed by Forrester (1968). Relationships are constructed and
displayed as interconnecting stocks, flows, converters and connectors.
The model was developed under simplifying assumptions of a one-product-market and
a single production system based on a closed herd. Accordingly, the potential
complexity associated with retaining males for velvet antler production was not
considered; nor was the potential impact of venison production from feral animals
considered. These issues are taken up in the discussion section of the paper.
The systems dynamics module was divided into four sectors (or modules) and one
sub-model for convenience of presentation. The four sectors operate at the same
level, whereas the sub-model is a component of one of these sectors. The sectors are a
female herd, a male herd, a venison production module and an economic module.
The female herd module is shown in Figure 1. The transfer of animals from one age
group to another is depicted by a flow from the younger to the older age group. This
occurs once per time period (defined as one year). Biological parameters such as
death rates and reproduction rates are defined as converters, and these are linked by
connectors to the flows that they regulate. Whereas flows occur per defined unit of
time, converters are transferred instantaneously. Flows originating from clouds imply
that the stock originates from outside the system boundary (although the size of this
flow is determined by one or more converters within the system). A flow exiting into
a cloud indicates that the stock is leaving the system under analysis.
63
breeder deaths
yearling death rate
83
az
yearling deaths
first year
> 63
QC) economic cults
breeding nin) 3
cull breeders for age
female\births
female yearli
i id expected price
young hind retention rate
birth rate
Figure 1 Female herd module
The decision as to the proportion of juvenile females to enter the herd, i.e. the young
hind retention factor, has been defined as a function of the long term expected price of
venison. When this price is high farmers will wish to build up their herds and
therefore the retention rate is high. Conversely, when long term prospects are
considered poor, then the retention rate is low. This expected price shows in Figure |
as a ‘ghost’ of the ‘real’ entity for price expectation which will be described later as
part of the economic module. This concept of ghosting allows links between various
sectors of the model to be represented more neatly by avoiding ‘spaghetti’ diagrams.
The specific characterisation of the stock for breeding females in Figure 1 indicates
that there is a sub-model associated with this stock. This breeder sub-model allows
females to progress through to successive age categories, with the number proceeding
to each successive year being determined by age-specific death rates and culling rates.
Further details are available in Woodford (1997).
The male herd module was constructed according to similar principles as the female
herd model. However, only a very small proportion of males are required for breeding
purposes (about 3% of breeding females) and hence nearly all males are slaughtered.
The venison production module converts slaughtered animals into tonnes of venison.
Details of both these modules are provided in Woodford (1997).
The economic module determines the current price of venison, the long term expected
price of venison, and the size of the market (Figure 2). The current price of venison is
determined by the demand function for venison and the current supply. The long term
expected price is a function of current and recent prices. The size of the market is
determined by the initial market size, the rate of market development, and the length
of time that market development has been occurring.
It was assumed that market demand could be represented by a downward-sloping
straight line demand function. Two alternative scenarios of market development were
explored. The first was where the point of intersection of the demand function with
the x-axis moved to the right but the point of intersection with the y-axis remained
fixed. This is consistent with a ‘scaling up’ model of development whereby the
number of people prepared to buy the product at a particular price increases. The
second scenario was where the slope of the demand function remained constant and
the point of intersection with both axes increased. This scenario is consistent with a
model of market development where both more people are prepared to buy the product
at a particular price and where some buyers are also willing to pay more than what any
buyers were previously willing to pay.
It was assumed that there was no carry-over of venison between periods. This was
considered realistic because, although it is feasible to freeze and store the venison,
there is a considerable price penalty associated with venison carrying a packing date
older than one year.
development rate
83
total venison supply
market size
future |expected price
price|2 years ago
tice flow 1
price flow priceniow2 price flow 3
Figure 2 Economic module
Investigations
Key biological parameters of this base model simulation are a reproductive rate of
80% (defined as the number of surviving progeny at three months divided by the
number of breeding females at the start of the year), annual death rates of 4%, and
slaughter of non-breeding animals at between one and two years of age.
The base model investment response function had two parts. The first, relating to
retention of young hinds for breeding, showed the proportion of hinds retained
increasing linearly from zero at an expected long-term price of $2 per kg carcass to
100% at $6 per kg. The second part of the function was that an additional 10% of
breeding hinds were culled (over and above those culled for age) when the expected
venison price dropped below $2.50. The initial market size was set by arbitrarily
fixing the y-axis point of intersection of the demand function at $8, and the x-axis
intersection at 100 tonnes.
The base model simulation was run over a 100 year period and focused on female
breeding numbers, venison production and venison price per kg of carcass. It was
found that all three variables have a very long cycle (28 years), that the cycle of
venison production follows the cycle of female breeding numbers with the lag being
greatest in the phase of herd build-up, and that price is counter cyclical to herd
numbers and venison supply. The cycles are ongoing without any tendency for
decline either in amplitude or cycle length.. Analysis of the tabulated model output
showed that the venison supply increased by approximately 80% over a two year
period after the decision was made to reduce female breeder numbers. Maximum
venison production was reached four years after the slaughter of young females
commenced.
Herd Productivity Factors
Initial investigations focused on whether these key attributes of long cycle length,
price instability and volume instability were an artefact of the chosen biological
parameters. Accordingly the model was rerun using different combinations of
parameters for reproductive rate and mortality rates. For reproductive rates within the
range of 50-90% there was a tendency for the amplitude of the cycles to be lower and
for the cycle lengths to be longer at the lower levels of performance. However this
trend was minor until the reproductive rate dropped below 60%. By combining very
high reproductive rates such as 130% with very low death rates such as 2%, the
amplitude of the breeding herd cycle increased to the point that the system ‘crashed’,
with no breeding animals retained. At the other extreme, by combining very low
reproductive performance levels such as 50% with high mortality rates such as 10%,
the cycle amplitude was not only smaller but declined over time such that production
and price would have eventually stabilised (although not for more than 100 years).
However, both these upper and lower performance levels are outside the range of
expected industry performance from farmed deer. In all situations the changes in
cycle length for one variable (e.g. breeder herd size, venison supply and price) were
mirrored by changes in the other two cycles.
Age of Male Slaughter
The second set of investigations addressed the impact on cycle characteristics of
delaying the age of slaughter to between 18 months and 30 months. This analysis was
undertaken assuming the original base model figures for reproductive rate and
mortality rates. In this situation the cycle length (all three variables) increased to 36
years, the amplitude of the price cycle was essentially unchanged, the amplitude of the
herd size cycle increased by 32%, and the amplitude of the venison supply cycle
increased by 16%. The reasons for these changes are that the increase in age-of-
slaughter increased the response time between farmer investment decisions on the one
hand and market supply responses and associated price information on the other hand.
Market Demand
Alternative market sizes were specified by alternative specifications of the downward
sloping demand function. This was first done by retaining the point of intersection
with the y-axis (set arbitrarily at $8), but allowing the point of intersection with the x-
axis to slide to the right. Not unexpectedly, the length of the initial herd growth
phase was a function of the relativity between the starting size of the herd and the size
of the market. However, once the initial herd growth phase ended the cycle
characteristics remained unchanged, with cycle length constant at 28 years, venison
price fluctuating between zero and close to $8 (i.e. the arbitrarily set point of
intersection with the y-axis). Subsequently, the demand function was reset with the y-
axis point of intersection increased to $16. The effect of this change was to markedly
increase cycle length to 38 years. Venison prices now fluctuated between zero and
almost $16. This increase in cycle length and amplitude arose directly from the higher
prices achieved during periods of low venison supply, and the associated longer time
period over which farmers retained all their female numbers.
Market Development
Most industries undertake market development to stimulate market demand. This
market development can focus on increasing the size of the market, increasing the
price that existing consumers will pay, or a combination of both. These respective
situations can be characterised in relation to the demand function by shifting the point
of intersection with the x-axis to the right, an upward shift of the point of intersection
with the y-axis, or a combination of both.
From initial simulations it soon became evident that an ongoing upward shift of the
demand function is unrealistic, creating a situation where, in the phase of the cycle
when venison supply was low, the prices in later years of the simulation rose to
thousands of dollars per kg. These results helped identify that sustained market
development inevitably flattens the demand function.
It was found that market development can reduce markedly the amplitude of all the
cycles. For example, at 15 % increase in market size per annum, the price fluctuated
between $3.33 and $6.35 on a 21 year cycle. The herd grew in all years but at
differing rates depending on the current expectation of future prices. There were short
periods of up to five years when venison production declined as a result of increasing
female retention rates, but the overall reduction in venison production during these
periods was less than 10%.
Analysis of the underlying relationships indicated that market development eliminated
the ‘boom and bust’ cycles only in situations where the rate of market development
approached the biological potential for herd growth. For the tested scenario (with
reproductive rate set at 80%, mortalities at 4 % and female longevity set at 10.5 years)
this biological potential is 24%. However, such high rates of market development
eventually become non-sustainable.
Price Expectations
Alternative price expectations models can be formulated by changing the number of
years of historical data in the model and also by changing the weightings applied to
each year. In a naive situation, future prices could be estimated solely from the price
in the most recent year. In this situation the cycle length declined by 10 years to 18
years, the amplitude of the price cycle remained unchanged, and the amplitude of both
the herd size cycle and the venison supply cycle declined by approximately 30%.
Changing the price expectation model to the average of the last five years price data
increased the cycle length to 40 years and increased the amplitude of the venison
supply cycle by approximately 30%. These results illustrate that price expectation
models based on a short set of historical prices produce faster responses to emerging
market situations than where a longer set of historical prices is used.
Random Shocks
All of the investigations reported so far assume that market demand is unaffected by
external factors such as general economic cycles or changes in the prices of competing
products. These assumptions can be relaxed by introducing a random element to the
current price of venison, which will transfer through into expected prices.
Accordingly, the model was run with the per kg price of venison subject in any year to
a random adjustment between negative $3 and positive $3. This was run for two price
expectation scenarios, namely that expected price was an average of prices over the
preceding three years, and that expected future price was the price obtained in the
most recent season. Each simulation was run five times using different seed values
for the random number generator. It was found that these shocks were sufficient to
produce short term disturbances to the herd size cycle and venison supply and this was
particularly evident with the one-year price expectation model. However, the
disturbances were insufficient to alter the key characteristics of these two cycles.
Herd Investment Response Function
The investigations to this point have shown that, except in situations where biological
productivity is well below the expected industry limits for farmed deer, or in situations
where ongoing market development is projected at an unsustainable level, that the
price of venison, the volume of venison produced, and investment in breeding females
all follow boom and bust cycles. Both the amplitude of these cycles and also their
length vary somewhat in response to biological parameters, age of slaughter, market
demand characteristics and the way in which price expectations are formed. However
none of these variations are sufficient to provide exceptions to the generalised finding
that venison prices and venison supply follow boom and bust cycles with long cycle
lengths. It appears therefore, that the only way to break these cycles is if the industry
has a much more conservative herd investment response function than in the base
model, and it is this issue that is now investigated.
Preliminary exploration indicated that the key issue was the low slaughter rate of
females during times of high venison prices. A higher rate of slaughter could be
achieved by either slaughtering a proportion of breeding hinds regardless of price, or
reducing the proportion of young hinds retained for breeding, or a combination of
both. For convenience, the analysis that follows focuses initially on increased
slaughtering of the existing breeding hinds.
With market development set at zero, the economic cull rate for breeder hinds had to
be set at a minimum of 19% before there was any trend towards stabilisation of prices,
stabilisation of venison output, and stabilisation of herd numbers. At 15% level of
economic culling the price of venison fluctuated between $2.08 and $6.67, which
avoided the extreme troughs and peaks but did not create stability. Small increases in
the economic cull rate above 19% had a marked impact on stability, such that at an
economic cull rate of 22% the venison price dropped to a minimum of $4.15 and
stabilised eventually at $4.98 (Figure 3).
Further investigation showed there was a strong link between the required culling rate
to achieve stability and the rate of market development. In a situation where market
size was increasing at 5% per annum then a culling rate of 17% produced a minimum
venison price of $4.52, and an eventual stable price of $5.08. If market size were to
increase at 10% per annum then an economic cull rate of 10% would be sufficient to
produce a minimum venison price of $4.49 and an eventual stable price of $5.09.
Similar effects were achieved by reducing the age of culling. For example, if all
females were culled at 6.5 years of age and assuming 10% market development, then
BBE: current price 2: Total venison supply 3) Breeding females
1:
2
3:
140.29) \ K
i / - 2 a
PV \ iN]
5.78
2 2.77 3.
3: 108.14
van e =
4 4.15)
ra 0.73
3 76.00
1.00 25.75 50.50 75.25 100.00
a Graph 1 Years 6:23 AM 10/24/29
Figure 3. Price cycles, venison production, and breeding herd cycles with
zero market development and a minimum annual cull rate of 22%
of breeding females
the venison price dropped to $4.50 after 15 years and then followed a 20 year cycle of
declining amplitude, eventually stabilising at about $5.20.
It was presumed that similar effects could be achieved by reducing the maximum
retention rate for young hinds but simulations indicated this was difficult to achieve.
The required reduction was large and had to be adjusted over time. For example, with
zero market development, a maximum retention rate of 25% was insufficient to
sustain herd numbers. However, when this was increased to 35% there was a very
slow but ongoing herd build up, a very slow but ongoing price decline, and very low
production of venison. At higher maximum rates of retention such as 50%, the cycles
showed all the elements of instability that were associated with the base model.
A range of alternative investment decision models were explored. These included
young females being retained for breeding only in years where the venison price was
higher than in the previous year, and young hinds only being retained when the
venison price was above a specified price such as $5 or $6. In all cases the price
information was received too late to avoid the occurrence of boom and bust cycles.
Discussion
The investigations undertaken in this paper have been based on assumptions of a
single market and a single production industry. In particular, it has been assumed that
all venison comes from farmed production, i.e. the supply of venison from wild and
feral deer has been ignored. Also, the possibility of commercial velvet antler
production from some species, and consequential culling of males based on the
relative price of velvet and venison, has not been considered. Under these simplifying
assumptions it has been found that, in situations where herd size grows at the
biological maximum (i.e. with all females retained as breeders), it appears inevitable
that there will at some point in time be a dramatic price collapse. This situation
prevails regardless of the biological parameters, age of slaughter, market size, or form
of price expectation model. Indeed the only way that a price collapse can be avoided
is if significant slaughter of females commences prior to the advent of price signals
providing information that further herd growth should be constrained.
The time taken for such a price collapse to occur depends on the initial size of the
production industry, the growth capacity of the herd, the initial size of the market, and
the rate of market development. In some situations, for example where there is a small
initial herd, low biological growth capacity, large market, and high rate of market
development, then the price decline may be forestalled for a considerable period.
However, long term market development at the same or similar rates as potential herd
growth would seem unsustainable.
In situations where future price expectations are derived from present and past prices,
then industry cycles for female breeding herd, venison production, and venison price
typically exceed 25 years and have high amplitudes. Both the amplitude of these
cycles and also their length vary somewhat in response to biological parameters, age
of slaughter, market demand characteristics and the way in which price expectations
are formed. However none of these variations are sufficient to provide exceptions to
the generalised finding that venison prices and venison supply follow cycles with large
amplitude and long length.
Industry attributes that contribute to the cycle characteristics include the capacity for
high rates of herd growth that exceed the Jong term sustainable rate of market
development, and the long lead times between investment decisions and venison
supply response. As a consequence, current and past prices are inappropriate
indicators on which herd investment decisions should be made. The key to avoiding
price crashes is to maintain a significant level of female slaughter during times of high
prices, combined with an ongoing market development program.
There appear to be two special factors that impact upon product supply and price
cycles for a developing deer industry that do not necessarily apply to other animal
species and other industry situations. The first factor is that developing industries are
seldom constrained in an absolute context by land resources, and hence there are
unlikely to be physical factors that prevent 100% female retention. For example, if a
farmer wishes to double the size of a small deer unit then typically this can be
achieved by reassigning land resources from a traditional activity such as cattle
raising. However the same pastoralist would often be prevented by overall carrying
capacity from making a similar upward adjustment with the herd of cattle. The
second factor is that deer have a longer breeding life than is usual for the traditional
domestic species. This reduces the number of animals that are culled-for-age. Both of
these factors tend to increase the amplitude associated with production cycles and
price cycles.
Relaxing the assumption in regard to a single farm-based production system is likely
to impact both on cycle amplitude and cycle length. In the case of venison production
from wild or feral animals it would seem much less likely than for farm-based
production that there would be a negative short term supply response. Also, feed
constraints create a situation where most of the wild and feral deer herds are unlikely
to be growing at anywhere near the biological rate that is possible with a developing
farm-based industry. The impact of these factors is likely to be similar to the modeled
situations where there was a forced minimum cull rate of breeding females; cycle
amplitude and length will be reduced.
The impact of incorporating velvet production into the model as a co-product could
lead to two potential impacts, depending on the correlation between venison price and
velvet price. To the extent that culling of stags is a function of velvet price, and if
velvet price is unrelated to venison price, then changes in velvet price are likely to
take the form of a random shock. However, to the extent that culling of the velvet
herd is influenced by venison prices, then increased venison price would lead to
increased male slaughter rates in the short-run situation.
The industry response function in regard to investment in breeding females is not a
simple additive function of the responses of individual farmers. This arises because of
the internal market within the industry for breeder females, which effectively prevents
the slaughter of females unless the market price for females as breeders is less than the
market value of female carcasses. This leads to a question as to whether counter-
cyclical production-focused investment strategies by industry entrepreneurs might
alter the overall industry decision response function. It would seem that any
entrepreneur acting alone would face a major problem as a consequence of the cycle
length being very long. However, if a large number of entrepreneurs undertook
counter-cyclical herd build-up and dis-investment activities, then the impact would be
to dampen the cycle amplitude and reduce the cycle length. This in turn would make
further counter-cyclical investment activities more attractive.
Concluding comments
The investigations presented in this paper provide insights in relation to the historical
volatility of the farmed deer industry both in Australia and New Zealand. In both
cases the industries expanded in the early years at the maximum biologically
constrained rate, and this was followed by a period of price decline for venison which
coincided with a major increase in the supply of product. The modelling has shown
that in situations where farmers use past and present prices to form expectation of
future prices, there is a short-run negative supply response that reinforces price cycles
and leads to industry instability. It is only where the investment in breeding females is
limited by other factors, such as availability of land resources or by counter-cyclical
investment activities, that the volatility reduces.
It is perhaps obvious to suggest that farmers are unlikely to make economically
efficient herd investment decisions unless they have appropriate information on
industry prospects. However, what was previously less obvious is the extent to which
past and present prices are seriously deficient as an information source on future
prices. Accordingly, there is a need for ongoing interpretation of market prospects
using models such as the one described within this paper. These models can only be
informative if there is an ongoing market research program that monitors both market
conditions and the herd cycle, and thereby provides the necessary model input data.
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