Mos-Def Corporation has recruited Bobcat Consulting (BC) to build a sales forecasting model for their new line of headphones, which features a new technology for wirelessly shifting from one music source to another. After collecting sales data for the first 5 quarters after introduction, BC estimated a Bass diffusion model of the form:

Where S_t is sales units (in thousands) in period t and Y_t-1 is cumulative sales up to the end of t-1.

The sales for the first 5 quarters look like this:

Quarter	Sales (000)
1	275
2	345
3	380
4	390
5	350

What is the forecast for quarter 6 using the Bobcat model? Show all your calculations (do not use 000s in your calculations, only remember to include them in the final answer). You can use an Excel spreadsheet, in which case the spreadsheet should be submitted as an attachment to email, and the cell formulae should be visible.

Was the Bass model able to predict the downturn in sales when it occurred? Explain.

2. Gecko Insurance is planning to offer a new type of combined auto and renters insurance product. Their chief statistician, Albert Gorithm, estimated the parameters of Basss 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 (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

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

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.

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.