Question 3: Pricing of Printers and Ink Cartridges

Your company has recently developed a cutting-edge new laser printer for hospitals that can print both documents and laminated wristbands. The latter are given to patients when they are admitted to hospitals for care. Currently, there is no competitor on the market selling a comparable printer. In addition, you have developed a customized ink cartridge for the printer. For the time being, owners of your printer would be required to purchase your dedicated ink cartridges. However, these cartridges are incompatible with any other printer model and, hence, they would only be purchased by an owner of your new printer. The basic printer is sold with an initial supply of ink cartridges. However, once this supply runs out, a customer would need to purchase additional cartridges from you.

The Table below summarizes the hospital market you serve. The market can be broadly segmented into 3 types of hospitals based on the value they obtain from your printer technology (printers and ink cartridges). Each type of hospital derives an inherent economic value from the purchase and usage of the printer itself. In addition, each hospital derives utility from purchasing one or more replacement ink cartridges. A hospital buys a year supply of ink cartridges at the beginning of each year over the lifespan of the printer but does not start buying replacement ink until the beginning of the second year. The table summarizes the willingness to pay for each ADDITIONAL ink cartridge during the course of a year. The last column details the number of hospitals of each type in the market. Assume that each hospital would purchase only one such printer for its emergency room. Assume also that a hospital does not anticipate the costs and utility associated with replacement ink cartridges when it makes the initial printer purchase decision (i.e. assume the hospital is not forward-looking). Finally, assume that the lifespan of the printer is 6 years.

Your job consists of recommending a price for the printer as well as for the replacement ink cartridges. The marginal cost of the initial printer package (with an initial supply of ink) is $400. The marginal cost of a replacement ink cartridge is $25. Assume that you must pre-commit to fixed, linear pricing for the printers and for the ink cartridge. In other words, you cannot change your

prices over time and you cannot target different prices to different hospitals. Assume also that your firm's cost of capital is 5% per year.

1)Derive the demand curve for the base product (i.e. a printer bundled with a single ink cartridge).

2)What is the profit-maximizing price of the printer if your firm decides not to sell replacement ink cartridges?

3)What is the profit-maximizing price of the printer and of each ink cartridge if your firm decides to sell both products as tied goods?

4)Does your pricing strategy in (3) achieve a form of price discrimination? Explain.