Consider an investor interested in a firm whose inverse demand equals: P = 800 - 2Q. The firm's marginal cost of output is constant and equals $160 per-unit. The profit- maximizing firm produces 180 units in each period (MR = 800 - 4Q = 160; so Q = 160, and sets its price at $480 (800 - 2x160)). At this level of output, firm revenue equals $76,800 (160 x $480) and its profit equals $51,200 (($480 - $160) x 160).

In return for an investment of cash, the firm and the investor are considering three different contractual arrangements that allow the investor to receive a return on her cash investment. The payoffs of the three plans under consideration are identical if we assume that the firm's price and quantity decisions are not affected by the plans under consideration. This exercise only considers the effects of the payment plan on the firm's incentives.

i.) A percentage royalty plan, where the investor receives 20 percent of the firm's revenue each period (0.20 x (160 x $480) = $15,360).