Question 1. Suppose initial adoption of an innovation follows the bellshaped curve implied by the

Bass Model (BM). Suppose further that each adopter repeat purchases the innovation every 3

periods after initial adoption. Plot the sales curve for this innovation, i.e., unit sales versus time (if

necessary, you may assume p = 0.04, q = 0.4, M = 5 million). DATASET USED - 2B-BASSMODELPRELAUNCHFORECASTING.XLS

Since there is repeat purchase every 3 periods,

Sales in period N=Adoptions in period N+ Adoptions in period (N-3) + + Adoptions in period 1

E.g. Sales in period 7 = Adoptions in period 7 + Adoptions in period 4 + Adoptions in period 1

Plotting the adoptions from the calculated values, we find:

Figure: New adoptions per time period. Does not account for repeat purchase and hence not a sales curve

Figure: Indicates total sales per time period. Accounts for repeat purchase and hence is a sales curve

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

1 5 9 1 3 1 7 2 1 2 5 2 9

NO

. OF

AD

OP

TIO

NS

TIME PERIOD

NEW ADOPTIONS BY T IME PERIOD

0.00

0.50

1.00

1.50

2.00

1 5 9 1 3 1 7 2 1 2 5 2 9

SALE

S

TIME PERIOD

SALES BY T IME PERIOD

Question 2. Estimate the Generalized Bass Model (GBM) for VCRs using the provided data on

annual adoptions and prices. Employ the Nonlinear Least Squares (NLS) technique for this purpose

(you may use the OLS technique to obtain good starting values for p, q, M). Report the estimated

parameters: p, q, M and b. Interpret the coefficients qualitatively. Forecast the adoptions for the

next quarter (not next year) following the period of data.

In order to formulate the Generalized Bass Model for VCR sales, the following steps were

followed:

The data was used to find p, q and M using the OLS method.

The values obtained were used as base values for Solver to calculate the values for the NLS

method.

Parameters OLS Values NLS Values

p 0.009066 0.002584

q 0.707071 0.593173

M 62.625644 68.556014

b - -0.552455

Interpretations

The NLS value of p parameter is comparatively low. It indicates that innovation driven

adoption is low and slow. Therefore the time required for achieving peak adoption will be

long and slow.

The NLS value of q parameter is high which implies that imitation is high and that the

adoption curve of the sales would be flat.

The negative value of the b parameter is indicative of the fact that adoption of product has

high negative correlation with price. Adoption will be accelerated if there is a relatively small

drop in price.

Forecast for Next Quarter

To forecast for the next quarter, the parameters were altered accordingly by dividing p and q by

4 with the b and M values remaining the same. The altered quarterly parameters for forecasting

are outlined in the table below.

Assumption: The prices do not change from the 48th quarter to the 49th quarter (first quarter of the 13th year)

When the above values are substituted in Generalized Bass Model for VCRs the following

results was obtained: Total Sales (Quarter 49) 1.1797 Million Units

Parameter Quarterly NLS Values

p' 0.000646

q' 0.148293

M 68.556014

b -0.552455