Two firms A and B control the market for mouth guards and face a market demand curve for mouth guards given by

 

Q = 320  4P

 

where Q is the total sales of mouth guards. The short-run cost curves of the two firms are given by

SRTC_A = 2090 + (q²A)/4

SRTC_B = 1045 + (q²B)/2

1. a) If the two firms agree to collude in order to maximize their joint profits, what will be output of each firm and the price of mouth guards? What will be the profit of each firm?

2. b) If instead the two firms act as price takers, what will be the output of each firm and the price of mouth guards? What now will be the profit of each firm?

3. c) What is the deadweight loss associated with the collusive outcome?

4. d) Show that at the collusive outcome, each firm has an incentive to

   cheat by raising its output.