A business firm F wishes to sell a unique kind of widget that no other firms sell. To sell this widget, it asks its supplier S to invest in building new equipment to produce this widget. Since the widget is unique, the equipment is only useful in producing it; the equipment has no other use. Selling the unique widget is worth $6 zillion to the Firm. The investment costs the supplier $2 zillion. F offers to pay S $4 zillion to make the investment, giving $2 zillion in "profit" to each party.

(a) After S makes the investment, but before F delivers the money for it, F can say that the investment isn't quite right for making the widgets and is worthless to F. (F would be lying, but all the experts are employed by it, so it cannot be proven in court.) F graciously offers $1 zillion instead of $4 zillion. S can either accept F 's gracious offer, or reject it and scrap the investment, in which case it is worth $0. What are the payoffs to S from accepting and rejecting F's gracious offer, and what is the sequentially rational choice?

(b) Now consider S's decision to make the investment in the first place. S can decline F's offer to make the investment at all, obtaining $0 zillion, or it can make the investment and subject itself to the manipulation described in the previous part. What is S's optimal choice?

(c) Suppose that, before making the initial proposal to S, F can develop an international market for used widget making equipment. If F develops this market, then S would be able to sell the widget making equipment for $3 zillion after building it. (It still costs $2 zillion for S to build the investment.) F incurs a cost of $1 zillion to develop the international market for used widget equipment. Assuming F maximizes its total profit (revenue from widget sales minus all costs of investment, widget equipment market develop- ment, etc.), should F do this? Why or why not?