Question 1: Let demand for car batteries be such that Q = 100 - 2P. Assume constant marginal costs of 25. Compute the equilibrium price, quantity, consumer surplus, producer surplus and if relevant deadweight loss for:

1. A perfectly competitive firm

2. A monopoly

3. Two firms engaged in Cournot Competition.

4. Two firms engaged in Bertrand Competition.

You should explain your work and define all relevant concepts. 

Question 2: Show graphically a case where increasing the number of firms can speed up the arrival of innovation. Show a case where it can slow the arrival of innovation down. What is the key difference in terms of firm level incentives from adding additional firms in each scenario? 

Question 3:  Assume that if a pair of oligopolists fail to collude, their profits are equal to 1 unit each per period of un-attempted collusion. Assume that if they collude, their profits are equal to 10 units each per period of successful collusion. Suppose that if one monopolist attempts collusion while the second attempts deviation, that the deviator's profits are 12 and the colluder's profits are 0 in such a period. Assume an interest rate of r

1. Assume in an infinitely repeated game both players attempt to collude until one player deviates. Once this happens both players no longer attempt collusion. Find the values of r such that the above strategies constitute an equilibrium.

2. Explain why it is still an equilibrium to not attempt collusion once a deviation was recorded. (Hint what has changed about each players expectations?) This is important in economic theory, because it means that our theory of collusion does not depend on bluffs.

Question 4: How can increasing competition aid innovation? How can increasing competition hinder innovation? Explain via a diagram. 

Question 5:  How would your ideal anti-trust law differ in its analysis and handling of implicit and explicit collusion? Justify your answer. Explain the differences in how these types of collusion may present themselves to the courts. Are there any issues with handling implicit collusion more aggressively than the current law does?