After years of training, Sara has landed a contract playing professional lacrosse. Eager to leverage her pro status by bringing in endorsements, she asks Jenny MacGuire to be her personal manager. Jenny has offered Sara a choice of two payment plans. Sara can engage Jenny's services for a flat fee of $100,000. Alternatively, Sara can pay Jenny 15% of all endorsement revenue.
Sara estimates that if Jenny expends modest effort ($20,000 worth) in her job, she will generate $600,000 in endorsement revenue for Sara. But if Jenny expends high effort ($50,000 worth), she'll bring in $1 million in endorsements. On the day Sara and Jenny are to sign their agreement, Jenny tells Sara, "I am 100% dedicated to you, and will always work as hard as humanly possible on your behalf no matter what payment plan you choose."
a. Sara has a choice of payment plans; Jenny has a choice of effort levels. Determine the relevant payouts for all of the possible outcomes, and draw the extensive form of the game Sara and Jenny are playing.
b. Find the equilibrium outcome to this game. Will Sara choose the flat fee or the 15% plan? Will Jenny expend modest effort or high effort?
c. Is Jenny's promise believable?
d. Discuss the implications of the type of payment scheme on the incentives and payoffs each player faces. Then, extend your analysis by discussing paying workers an annual salary versus paying them a certain amount for each finished product they produce (called "piece-rate compensation").