Signaling. There are two firms, A and B. There are two time periods, 1 and 2. There is one commodity, that can be produced by both firms, at linear cost. So, if firm i has marginal cost i, then the cost of producing q units of the commodity is ciq. The inverse demand for the commodity, at any given moment, is 100 − 4Q, where Q is the aggregate supply at that moment. In period 1, firm A is alone in the market. Firm A’s marginal cost is determined by Nature, either it is 10 or it is 2, each with probability 1/2. A knows it’s cost. Firm A produces some quantity in period 1 and firm B observes this. Between periods 1 and 2, firm B decides to enter the market or not. After making this decision, B is told firm A’s cost. It is too late at this point for B to change its action. In period 2, if B is in the market, then A and B compete on quantity. (1) In words, what are the steps to solving this problem? (2) There are two possible quantity-competition games that happen in this game. Solve them both. (3) Now solve the full game. (4) Now imagine that firm B never learns firm A’s cost. How does this change what you have done?
Signaling. There are two firms, A and B. There are two time periods, 1 and
2. There is one commodity, that can be produced by both firms, at linear cost. So,
if firm i has marginal cost i, then the cost of producing q units of the commodity
is ciq. The inverse
where Q is the
In period 1, firm A is alone in the market. Firm A’s marginal cost is determined
by Nature, either it is 10 or it is 2, each with probability 1/2. A knows it’s cost.
Firm A produces some quantity in period 1 and firm B observes this. Between
periods 1 and 2, firm B decides to enter the market or not. After making this
decision, B is told firm A’s cost. It is too late at this point for B to change its
action.
In period 2, if B is in the market, then A and B compete on quantity.
(1) In words, what are the steps to solving this problem?
(2) There are two possible quantity-competition games that happen in this game.
Solve them both.
(3) Now solve the full game.
(4) Now imagine that firm B never learns firm A’s cost. How does this change
what you have done?
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