Home work for the market simulation topic (‘Emergence’ day)
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1. The agent-based simulation model has indicated resource (demand) release
at the market peripheries under a broad range of parameterizations. Recall
that resource release is the phenomenon when some dominant (here: large
sunk cost) firms relocate their niches closer to the demand-abundant market
center, after the deadly center competition chills out by outforcing a big deal
of competitors from the center. As a result of niche relocation, some demand
becomes uncovered at the so abandoned peripheries, which demand then can
be utilized by smaller, specialist firms, the ‘scavengers’ of the market.
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Studying the American beer industry, Carroll and Swaminathan (2000, see
attached) have described another center-periphery market partitioning
mechanism. In the late 20th century, the American beer market was
dominated by a few giant center players (Budweiser, Heineken) producing
pretty generic beers. Then, a microbrewery movement has emerged: some
people re-vitalized old, traditional beer production methods and produced
their own beers (small batch production) with fancy taste, color and alcohol
content. These new brewers defined their products in oppositional terms to
the (‘tasteless’, ‘uniform’, ‘dull’, etc.) generic beers produced by large-batch
industrial methods. The microbrewery movement, composed of microbrewers
and their fans, has developed an oppositional identity relative to the
industrial brewers. Their message was: ‘we produce authentic beers, you
don’t’. Importantly: authenticity is based on two things: (1) the specific
physical characteristics of the beer; and (2) the traditional methods how the
beer had been brewed. By emphasizing their authenticity, the microbrewers
could secure a solid market niche at the market peripheries. Just like in the
classical partitioning case (illustrated by the simulation), the market had a
center-periphery structure, with respective large and small firms. Still, the
two mechanisms of market partitioning differ substantially.
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Questions:
(i)
Was there a resource release in case of the beer producer story?
(ii)
Can we call the microbrewers ‘scavengers’?
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(iii)
It is a fact that large beer producers could fairly well reproduce the
tastes of microbrewery products with their high-tech industrial
production facilities. But then why could not they fully occupy the
prestigious microbrewery niche?
(iv)
The simulation assumed a market with two product dimensions. Can
we see authenticity as an additional new product aspect, which so
adds a new dimension to the ‘resource space’ representing the
market? How many scale elements this hypothetical new dimension
would have?
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2. The agent-based market simulation discussed in class operates with a
unimodal demand distribution over. According to the results, this feature entails
that large sunk cost firms have scale economies near the market center, while
small sunk players take advantage of product differentiation at the market
peripheries. This dual dynamics forces the small sunk cost firms to proliferate,
while the number of large sunk cost firms decline at the near center as a byproduct of scale-driven competition.
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Questions:
What the results would be if the demand distribution over the space was is either
(i)
flat (demand would distribute evenly along space cells);
(ii)
condensed (most demand would concentrate to a small number of
neighboring cells, so forming a ‘hyper-center’ for the market):
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Please fill your answers into the table below, - in the vein how the first line has
been filled in.
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Demand
distributi
on
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Unimodal
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Flat
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Condensed
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Number
Number
of large
of
sunk cost small
firms
sunk
cost
firms
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Low
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High
Explanation
Small sunk cost firms find it easy to
proliferate at the market fringe; large
sunk cost firm numbers decline as a
result of competition at the market
center; center-periphery scope
diseconomies makes it difficult for large
sunk cost firms to reach small sunk cost
ones.
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(v)
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Consider an (integer) n-dimensional space segment (frame space)
with m scale elements along each axis, yielding mn cells in the
segment. The fraction dimension DIM of the space constituted by the
occupied cells over this frame space was defined as
(1)
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DIM =
ln H
ln m
for m ≥ 1
with H denoting the count of ‘filled’ cells in the frame space.
Now, let’s relieve the assumption that the frame space has a uniform m ‘breadth’
along each axis. Let mi denote the number of scale elements along axis i. Then,
the generalized fraction dimension of the space spun by the occupied cells can be
defined as:
ln H
DIM =
(2)
1 n
∑ ln mi
n i =1
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Questions:
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(i)
for n, m ≥ 1.
Show that definition (2) can be re-written by replacing the single m
with the geometric mean of the mi values:
DIM =
ln H
n
ln n
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∏m
i
i =1
for n, m ≥ 1.
n
∏m
i
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where !
(ii)
is the number of cells in the n-dimensional frame space.
Show that (2) yields (1) for the special case when 1 ≤ mi = mj for
all i, j.
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(iii)
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i =1
Consider a two-dimensional space segment with m1 = 4 and m2 =
3. Demonstrate visually on the example of this specific frame space
that (2) does not yield integer dimensionality 1 as DIM for onedimensional fully saturated (fully ‘filled’) sub-spaces of the frame
space. (Recall that this property was an important feature of definition
(1)).
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