Classroom Companion: Business

Fig. 18.8 The SIR model. (Authors’ own figure)
18.5 · Analysis of Real Markets

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18
Box 18.5 System Dynamic Models
System dynamics is based on essentially 
the same method as differential equa-
tions. However, instead of solving the 
equations using standard analytical or 
numerical methods, the equations are 
converted into a dynamic simulation 
model. The strength of system dynamic 
simulations is that the complete simula-
tion model can be compiled into exe-
cutable software programs directly 
from the graphical description of the 
model. There are several commercially 
available software packages for system 
dynamic modeling, all of them based 
on graphical description of the system. 
The task for the designer is then to 
develop the graphical model.
The method was developed by Jay 
Forester during the late 1950s (Forester, 
1971
). The first major application of 
the method was the project at MIT 
resulting in the book The Limits to 
Growth published in 1972 (Meadows 
et al., 
1972
).
The system dynamic model allows 
us to treat all system parameters as 
continuous or discrete functions of 
time and simulate cases that are far out-
of-reach using differential equations. 
.
Figure 
18.9
 shows a system dynamic 
model of the Bass equation, demon-
strating that the simulation model is 
identical to the differential equation in 
7
Sect. 
18.1
.
In system dynamics, the aggregates 
of people, things, or money are called 
stocks. In the Bass model, there are two 
stocks, potential adopters and adopters, 
and there is one flow from potential 
adopters to adopters. There are three 
functions:
5
Innovators having a flow rate of 
p(N − B). The function is realized 
by the multiplication operation × 
with inputs p and N − B.
5
Imitators having a flow rate of 
qB(N − B). The input to the multi-
plication function × is in this case q, 
N − B, and B.
5
New adopters which is the sum of 
innovators and imitators; that is, 
the flow rate of new adopters is 
(p + qB)(N − B).
Setting adopters equal to B, the flow of 
new adopters per unit of time equal to 
dB / dt,
and potential adopters equal to 
N − B, the Bass equation of
7
Sect. 
18.1
 is deduced. When the simulation 
starts, the stock of adopters may be 
empty or contain an initial number of 
adopters, B
0
. The initial stock of poten-
tial adopters is, then, either N or 
N − B
0
.