The profits of an incumbent monopolist, currently $20m,$ are threatened by a potential entrant. If

there is entry, and the incumbent and entrant decide to share the market, the incumbent will earn

profits of $12m$ and the entrant will earn $8m.$ However, if there is entry, and the incumbent and

entrant decide to engage in a price war, the incumbent will earn profits of $6m$ and the entrant will

earn $3m.$ Prior to entry, the incumbent can invest in extra productive capacity to improve its

competitive position in the event there is entry and a price war. The cost is $4m,$ but it will raise the

incumbent's profits in a price war by $7m$ to $13m,$ before the investment cost is deducted, and

lower the entrant's profits to a loss of $2m.$ Assume that the potential entrant earns zero profits if it

decides not to enter and that the incumbent's decision to invest is visible to the potential entrant.

a$)$ What are the equilibrium strategies of the incumbent and potential entrant if the investment

cost is sunk? Comment on the welfare implications to society of your solution.

$(25$ marks$)$

b$)$ What are the equilibrium strategies of the incumbent and potential entrant if the investment

cost is not sunk?

$(10$ marks$)$

c$)$ Critically discuss the role sunk costs play in business strategy.