Question

A company is considering the development of several new products. Their chief statistician estimated the parameters of Bass's diffusion model for two potential markets. The markets are represented as: Market 1: S(t) 2.2484 .476Y(t-1) 0.0048728Y (t-1) Market 2. S(t) = 2.0500 + .01 1 Y(t-1)_ 0.0001024%2 (1-1) where S(t)sales (1,000s) in period t Y(t-1) total people who have ever bought by end of period t-1 a) For each market, what are the parameters of the Bass model (market size, initial probability of adoption and diffusion rate)? b) In a few sentences, explain the tradeoffs between entering each market.

Answer 1

a) For market 1, the Bass diffusion model equation

S(t) = 2.2484+.476Y(t-1) - 0.0048728Y² (t-1) which can be compared with standard Bass diffusion model equation,

S(t) = a + bY(t-1)-cY² (t-1) where a= 2.2484, b=.476 and c= -0.0048728

therefore, parameters of market 1 are as follows:

the size of market 1(m₁ ) = -b-$\sqrt{}$(b² -4ac)/2c = (-.476- ((.476)² -4*2.2484*-0.0048728)^0.5)/ (2*0.004872)

                                                      =-102.21= 102.21 (As market size cannot be a negative value)

initial probability of market adoption(p₁ ) = a/m₁ = 2.2484/102.21= 0.021

and diffusion rate (q₁ ) = p₁ +b= 0.021+.476= 0.497

For market 1, the Bass diffusion model equation

S(t) = 2.0500+.011Y(t-1) - 0.0001024Y² (t-1) where

   a= 2.0500, b = .011 and c =-0.0001024

therefore, parameters of Bass diffusion model for market 2,

market size( m₂) =( -0.011- ((0.011)² -4*2.0500*-0.0001024)^0.5 ) /(2*0.0001024)= -205.05= 205.05 (Ignoring the negative sign)

Therefore, probability of market adoption (p₂ ) = 2.0500/205.05 = 0.0099

and diffusion rate (q₁ ) = p₂ +b =0.0099 +.011 = 0.0209

b) For companies, the trade-offs for entering market is determined by analyzing the market and credit risks. A firm can opt for market entry with low risk option such as making business partners in a new market and marketing products through the business partners. For market of large size, probability and diffusion rate, it is always better for companies to opt low risk market entry option. However, if market size, behaviors, probability of market adoption and diffusion rate are less, companies can choose high risk market entry option that entails massive capital investment, aggressive marketing compaign and supply chain activities in a target market.