Suppose a market has two firms that compete by setting prices₁and₂simultaneously, with aggregate demand at, the lowest price, given by = 240 .

The marginal cost of production is $40 and there are no fixed costs.

Suppose prices can only be set in$10increments:$0, $10, $20, $30,...

1. Write down two Nash Equilibria in this market.
2. Write down all the remaining Nash Equilibria in this market.
3. The firms are considering forming a cartel. What price would maximize the cartel's profits? Denote this price_c.
4. Suppose this game is indefinitely repeated, and the associated probability- adjusted discount factor is.

-Consider the following "grim trigger" strategy for a firm:

If it's the first period, or if everyone in every previous period set a price of_c,set

price at_c.Otherwise, set a price of $40.

-Suppose it's the first period of the game. Compute thethat would ensure that this firm will not deviate in the first period of the game. Show your work.