Analyze a two-period model for the market of computers in which two firms operate. Firm 1 only produces in period 1 and is endowed with an old technology providing a quality level vO to consumers. Firm 2 is a potential entrant in period 2 and it is able to produce an old technology, vO, and a new technology, vN . However, the production of new technology requires an innovation cost of I > 0. Note that old and new technology can be nondurable (only last one period) or durable (it lasts for two periods). Hence, the cost of producing nondurable technology, cND = 0, is considerably lower than the cost of durable technology, CD = 3. There is only one consumer in period 1 who seeks to buy a computer for the two periods of her life. In period 2, one additional consumer enters the market and seeks to buy a computer. Both consumers have the same gain from the quality of the technology embedded into the product they buy in period t. That is, VN = 7 and VO = 5 for new and old technology, respectively. The structure of the two-period, two-firm game is as follows: In period 1 firm 1 sells the old technology product and therefore has to decide which price to charge (p1) and whether to produce a durable (D) or a nondurable (ND) product. In the second period, firm 2 obviously chooses to produce a nondurable good (since the world ends at the end of period 2) and hence has to decide whether to invest in adopting the newer technology and price (p2).
(a) Illustrate the extended form game of the two-period, two-firm game.
(b) Describe the second-period pricing for the case in which the first-period product is nondurable and durable.
(c) Identify the first period durability choice.
(d) Calculate the social-welfare function and discuss whether or not Proposition 12.8 is satisfied.