PROTECH Corporation produces advanced analytic software for computer simulations called Model Pro. Based on a regression analysis of product sales in the first year after launch, PROTECH’s marketing department estimates the demand for Model Pro to be:

Q_M = 1,200 - 8P_M + 4P_S

with adjusted R² = 0.65, and with all of the above coefficients statistically significant.  Here, Q_M denotes units sold of Model Pro software, P_M denotes Model Pro’s price, and P_S denotes the price of a best-selling statistical software package (with both prices in dollars).

 

a) Currently, P_M = $200 and P_S = $300. What is the predicted demand for Model Pro software? The price P_S has been unchanged (at $300) during the last 6 months. Given this information, write down the equation for Model Pro’s demand curve (with Q_M as the left-side variable and P_M as the only independent variable). Then, also determine the inverse demand curve (with P_M as the left-side variable). 

a)       An industry analyst comments that demand for Model Pro is not very sensitive to changes in the price of the statistical software package P_S. (This package does perform some of the same operations as Model Pro, but not as quickly or conveniently.) Carefully assess this contention. Do you agree or disagree? (Hint:  Calculate the cross-price elasticity) (5)

 

 

 

 

b)      As is true with many information goods, the marginal cost of producing Model Pro is negligible.  However, the company incurred significant costs in developing the product for market (estimated to be about $350,000).  Given the estimated demand of part a, determine the optimal price and output quantity for Model Pro. (5)

 

 

 

 

d).  A marketing department analyst realizes that a potentially important determinant of demand for Model Pro software is the price of computer workstations. The analyst reruns the regression model and now includes the price of workstations along with the other variables.  The new model differs from the original regression of part a in the following ways: The adjusted R²  increases from .65 to .78. The coefficient of P_M changes from -8 to -10, while the coefficient of P_S is essentially unchanged. The new regression coefficient for P_W (the workstation price) has a negative sign. Finally, all three price coefficients are highly significant.

        Is the new regression equation an improvement over the original? In the new regression, Q_M is observed to be more sensitive to changes in P_M than in the original regression. Explain why this might be the case?  (4)