$2.$ Gecko Insurance is planning to offer a new type of combined auto and renter$$s insurance product. Their chief statistician, Albert Gorithm, estimated the parameters of Bass$$s diffusion model for two potential markets. The results follow:

Market $1$:

Market $2$:

Remember that the general equation for sales in any time period t is:

Where S $($t$)=$ sales $(000$s$)$ in period t; p $=$ coefficient of innovation; q $=$ coefficient of imitation; m$=$ sales potential or saturation level; Yt$-1=$ total people who have ever bought $($cumulative sales$)$ by end of period t$-1$

a$.$ Without doing any calculations, which market would you guess had the higher sales potential m$?$ Briefly explain your answer.

b$.$ Draw the shape of the predicted sales curve for each market and explain your answer in each case. Show the starting sales level $($period $1)$ and draw the shape carefully.

c$.$ What diffusion effect is driving sales in market $1?$ What is driving sales in market $2?($Hint: It is either the innovation effect p or the imitation effect q$).$ Explain your answer.

$3$ i$)$ Provide an example of a product or service which follows a sales trajectory such as the one in Market $1$ of question $(2).$ Briefly explain why you have provided this example.

ii$)$ Provide an example of a product or service which follows a sales trajectory such as the one in Market $2$ of question $(2).$ Briefly explain the reasons why you provided this example.Gecko Insurance is planning to offer a new type of combined auto and renter's insurance

product. Their chief statistician, Albert Gorithm! estimated the parameters of Bass's diffusion

model for two potential markets. The results follow:

Market $1$: $S_t=2650+\mathrm{.}057Y_{t-1}-\mathrm{.}00022Y_{t-1}^2$

Market $2$: $S_t=14380-\mathrm{.}036Y_{t-1}-\mathrm{.}00065Y_{t-1}^2$

Remember that the general equation for sales in any time period $t$ is:

$S_t=p_{0}m+(q-p_0)Y_{t-1}-(\frac{q}{m})Y_{t-1}^2$

Where $S(t)=$ sales $(\text{'}000s)$ in period $t$; $p=$ coefficient of innovation; $q=$ coefficient of imitation;

$m=$ sales potential or saturation level; $Y_{t-1}=$ total people who have ever bought $($cumulative sales$)$

by end of period $t-1$

a$.$ Without doing any calculations, which market would you guess had the higher sales

potential $m?$ Briefly explain your answer.

b$.$ Draw the shape of the predicted sales curve for each market and explain your answer in

each case. Show the starting sales level $($period $1)$ and draw the shape carefully.

c$.$ What diffusion effect is driving sales in Market $1?$ What is driving sales in market $2?$

$($Hint: It is either the innovation effect $p$ or the imitation effect $q).$ Explain your answer.

$3$ i$)$ Provide an example of a product or service which follows a sales trajectory such as the one

in Market $1$ of question $(2).$ Briefly explain why you have provided this example.

ii$)$ Provide an example of a product or service which follows a sales trajectory such as the one in

Market $2$ of question $(2).$ Briefly explain the reasons why you provided this example.