You work for Titanic Products, a manufacturer of electric kitchen accessories, as an assistant in market research. Titanic is currently developing a new kitchen gadget, a combination coffee grinder-toaster oven, to be offered for sale at $50. The company estimates that long-run potential for this product is 25,000,000 households. Innovation rate and imitation rate for products in this category have tended to be in the ranges of 2% and 12% respectively in the the last, and management plans to use the same figures in their projections for the new gadget.

1) If these parameters are correct, how long will it take for cumulative sales of this product to reach 5 million units? 10 million units? Plot quarterly sales figures and interpret the shape of the graph you obtained. If initial price remained at $50, but price were gradually decreased to $45 over the next few years, what impact would this have on sales patterns?

2) You think that Titanic is heading for a major disappointment with this product. First, you believe the market potential estimate is greatly overstated. Second, you feel that the innovation and imitation rates are somewhat overly optimistic. Revise each of these parameters downward (use your own judgment on how much to decrease each one), and assess the impact on the quarterly and cumulative sales pattern.

Please show all work step by step. Thank you.

PROJECTING SALES WITH THE BASS DIFFUSION CURVEE The Bass model was first developed in 1969 by Frank Bass. It is a sales gowth model that predicts future product class sales for a durable good, using historical product sales levels. Managerial estimates of initial probability of trial (the probability that a purchase will be made early in the introductory phase of the Product Life Cycle) and of imitation or diffusion rate (reflecting the influence of positive word-of-mouth communication) are also required Given these estimates, the sales of the product class at time t are estimated by the model asn where p and q are the initial trial probability and diffusion rate parameters, m is the mumber of potential buyers, and Y(t) is the total (cumulative) number of purchases by time t This BASS spreadsheet can draw three gaphs 01-12 is a plot of the first 12 quarters of sales Q1-36 is a plot of the first 36 -|quarters ofsales. CUMUL is a plot ofcum ulative sales over 36 quarters. *Page down to contiue BASS INPUTS PROJECTIONS Cumulative QuarterSalesG25Sales Market Size(000s) 25,000 (At Start Price) 0.00 500.00 4651.80 230020 8856.77 5426.99 12 998.14 9240.34 16 1003.94 13296.47 20863.79 17000.35 24 644.35 19917.35 28 429.4321946.08 32 264 5523233.44 36 155.03 24002.10 88.1724444 17 0.00 500.00 Innovation Rate 0.02 (Parameter p) Imitation Rate 12 (Parameter r) Initial Price Final Price $50 $50 40 11 01-12 shows sales projections for the first 12 quarters 101-56 shows sales projections for the fiest 36 quartert PROJECTING SALES WITH THE BASS DIFFUSION CURVEE The Bass model was first developed in 1969 by Frank Bass. It is a sales gowth model that predicts future product class sales for a durable good, using historical product sales levels. Managerial estimates of initial probability of trial (the probability that a purchase will be made early in the introductory phase of the Product Life Cycle) and of imitation or diffusion rate (reflecting the influence of positive word-of-mouth communication) are also required Given these estimates, the sales of the product class at time t are estimated by the model asn where p and q are the initial trial probability and diffusion rate parameters, m is the mumber of potential buyers, and Y(t) is the total (cumulative) number of purchases by time t This BASS spreadsheet can draw three gaphs 01-12 is a plot of the first 12 quarters of sales Q1-36 is a plot of the first 36 -|quarters ofsales. CUMUL is a plot ofcum ulative sales over 36 quarters. *Page down to contiue BASS INPUTS PROJECTIONS Cumulative QuarterSalesG25Sales Market Size(000s) 25,000 (At Start Price) 0.00 500.00 4651.80 230020 8856.77 5426.99 12 998.14 9240.34 16 1003.94 13296.47 20863.79 17000.35 24 644.35 19917.35 28 429.4321946.08 32 264 5523233.44 36 155.03 24002.10 88.1724444 17 0.00 500.00 Innovation Rate 0.02 (Parameter p) Imitation Rate 12 (Parameter r) Initial Price Final Price $50 $50 40 11 01-12 shows sales projections for the first 12 quarters 101-56 shows sales projections for the fiest 36 quartert