A manufacturer of inexpensive printers offers a model that retails for $150. Each sale of one of these models earns the manufacturer $60 in profits. The manufacturer is considering offering a $30 mail-in rebate. Assume that a randomly selected customer has probability p of purchasing this model of printer.
(a) Assume that the availability of a rebate increases the probability of purchase from p to p*. How much does the chance of purchase need to increase in order for the expected net profits to increase? (Assume that the manufacturer has plenty of printers to sell and that the cost to the manufacturer for the rebate is the stated $30.)
(b) Not all rebates that are offered are used, with the chance of the rebate being used hovering around 40%. If this is so, how much does the chance of purchase need to increase in order for the expected net profits to increase? Identify any assumptions you make.