The market for gizmos have two firms operating in it. The demand curve in the market is Q = 100.2P, where Q = Q1 +Q2. The firms' cost functions are C1(Q1) = 20+10Q1 and C2(Q2) = 20 + 12Q2.

1. (a)(2 mark) What are the firms' marginal-cost functions?
2. (b)(7 marks) First, assume that the two gizmo producers are behaving noncooperatively. Using the Cournot model, find how much each firm would produce and what its profits would be? Draw the firms' reaction curves and show the equilibrium.
3. (c)(6 marks) Now assume that firm 1 announces its output decision publicly before firm 2 decides on its output level. Find the rollback equilibrium of the game that represents this strategic situation. How much would each firm produce and what would its profits be?
4. (d)(3 marks) Discuss how the profits of each of the two firms change between parts (a) and (b). Explain why you are seeing these differences. What is this an example of?
5. (e)(7 marks) Finally, assume that the two gizmo producers are colluding instead of competing. They can freely share their profits so they are attempting to maximise their joint profit (i.e. their total combined profit). Given the firms' cost functions, would both firms produce positive quantities? Why or why not? What is the joint- profit-maximising level of output? How much would each firm produce and what would its profits be?