Classroom Companion: Business

 
Chapter 18 · Digital Market Modeling

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18
2. Bass equation for q = 0.
(a) For q = 0, the solution of the Bass equation is B(t) = N − (N − B
o
)e
−
pt
.
(b) We easily find that d
2
B/dt
2
= − p
2
(N − B
0
)e
−
pt
< 0 for all t. Therefore, there 
is no inflexion point in this case.
(c) Expanding the equation for B(t) as a series, and only keeping terms to the 
first order in t gives:
B t
N
N
B
pt
B
n
B
pt
 













0
0
0
1
.
This is the equation for a straight line.
3. The correct answer is B
1
> B
2
.
References
Bass, F. M. (1969). A new product growth model for consumer durables. Management Science, 15(5), 
215–227.
Cannarella, J., & Spechler, J. A. (2014) Epidemiological modeling of online social network dynamics. 
ArXiv 1401.4208.
Forester, J. (1971). Counterintuitive behavior of social systems. Theory and Decisions, 2, 109–140.
Mahajan, V., Muller, E., & Bass, F. (1995). Diffusion of new products: Empirical generalizations and 
managerial uses. Marketing Science, 14(3), G79–G88.
Meadows, D. H., Meadows, D. L., Randers, J., & Behrens, W. (1972). The limits to growth. Potomac 
Associates – Universe Books.
Murray, J. D. (2002). Mathematical biology. I: An introduction (3rd ed.). Springer.
Øverby, H., & Audestad, J. A. (2019). Temporal market evolution of interactive games. SSRN.
Roberts, P. (2017). The most important Facebook statistics for 2017. Our Social Times, Cambridge.
References

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© The Author(s), under exclusive license to Springer Nature 
Switzerland AG 2021
H. Øverby, J. A. Audestad, Introduction to Digital Economics, 
Classroom Companion: Business,
https://doi.org/10.1007/978-3-030-78237-5_19
281