Imagine that you have acquired both the retailer and manufacturer discussed in Exercise 7. Your interests now are in maximizing profitability for your new firm and in setting up an incentive system to make this happen. You have chosen to keep the quantity flexibility contract in place to provide incentive to both your retailer and your manufacturer.
a. How does increasing α to 0.5 affect your firm’s profitability?
b. How does increasing β to 0.5 affect your firm’s profitability (keeping α at 0.2)?
c. Why does one of these changes have no effect on profitability?