Consider the following game. An incumbent decides whether to advertise at a cost or not. This action is observed by a challenger who has the option of entering the market at a cost or staying out. If the challenger stays out of the market, the incumbent firm remains a monopolist. If the challenger enters the market, the two firms compete a la Cournot. Assume that both firms have zero marginal cost. Advertisement increases demand at any given price. The inverse demand functions when the incumbent advertises and when not correspondingly are

()=60

() = 48

where denotes the total industry output.

1. (i) Calculate the profits of each firm when the challenger enters depending on
2. whether the incumbent advertises and not. (20 marks)
3. (ii) Draw the extensive form representation of the game. (20 marks)
4. Suppose = 350. Determine the values of for which the incumbent decides to advertise? (20 marks)
5. Determine how the range of values of that you calculated in part (b) would change if, upon entry of the challenger the two firms compete a la Stackelberg where the incumbent is the leader and the challenger is the follower. As before, if the challenger stays out of the market, the incumbent firm remains a monopolist. (40 marks)