Problem 1. There are two firms, A and B. Each makes a hard drive and a monitor. Label the hard drive and monitor made by A as AH and AM respectively. Label the hard drive and monitor made by firm B as BH and BM respectively. Manufacturing costs of all products are zero. Buyers are interested in purchasing a system rather than individual components. That is, they want to purchase a hard drive and a monitor. We can divide buyers into 3 equally sized groups. The groups are labeled AA, BB and AB. They differ in the value they place on different hard drive and monitor combinations. These valuations are summarized in the table below:
Buyer Segment AH, AM BH, BM AH, BM AM, BH
AA $10 $5 $5 $5
BB $5 $10 $5 $5
AB $5 $5 $10 $0
So, the AA's prefer a system that is made up entirely of A components and the BB's prefer one that is made up of B components only. The AB's have a preference for systems that combine one component from each firm. Given the price of a system, buyers will buy the system that generates the largest surplus. For example if the price of an A system is $8 while that of a B system is $2, the AA's will buy the B system. There are two scenarios to consider.
In scenario 1, the hard drive of A is incompatible with the monitor of B and the hard drive of B is incompatible with the monitor of A. In this scenario, firms set prices on systems and sell only whole systems. In scenario 2, each firm's products are compatible with the other firms products. In this scenario, firms set prices on individual components and sell individual components.
1. In scenario 1 is both firms pricing their system at $10 an equilibrium?
2. What is an equilibrium price for components in scenario 2?
3. In the first scenario, incompatibility serves to segment the market in that Firm A's products are clearly different from
Firm B's products. Which scenario is more profitable for firm A
Problem 2. An incumbent and entrant face a market of 100 buyers. Each buyer has a RP of $100 for the incumbents as well as entrants product. At each round each buyer is interested in buying no more than one unit of the product. The incumbent has a $40 per unit of cost of production that is private information, i.e., the entrant does not know what the incumbents actual production costs are. The entrant does have a guess. Entrant believes that incumbents costs are either $40 per unit or $60 per unit (she assigns positive probability to either possibility and entertains no other possibilities). Incumbent knows entrants beliefs, entrant knows that incumbent knows and so on. Entrants costs are $50 per unit and incurs an entry cost of $1. If entrant enters, she enters with sufficient capacity to serve entire market.
1. In the first round, the incumbent alone is in the market. Incumbent sets a price and buyers choose to buy or not according to their surplus. Entrant can observe the price charged by incumbent.
2. In round two, entrant decides to enter market.
3. If entrant does not enter, incumbent sets price, buyers choose, game ends. If entrant enters, both incumbent and entrant set price simultaneously. Might incumbent want to signal its cost position to entrant? Is there a way to do so using the price in the first round?