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, V N = 7 and V O = 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).
- Illustrate the extended form game of the two-period, two-firm game.
- Describe the second-period pricing for the case in which the first-period product is nondurable and durable.
- Identify the first period durability choice.
- Calculate the social-welfare function and discuss whether or not Proposition 12.8 is satisfied.