Open Question 1: Lady Gaga's dancers The management team considers 3 alternative contract options for the dancers: Lady Gaga is an American pop artist who is famous for her extravagant live Contract 1: performances. Her shows typically Involve very specific choreographies, which Hiring the dancers as employees instead of free-lancers and paying them a fixed require Intense practice and training on the part of her accompanying dancers. salary of $4000 for the show. This training is not useful for other projects in which the dancers are Involved. As such, this training has the characteristics of a relationship-specific Investment. Contract 2: The support dancers operate as free-lancers, Le. they form individual one-person Proposing the free-lance dancers a contract paying them a fixed salary of $3500 firms that directly negotiate with the management team of Lady Gaga. The for the show and a share of 20% of the show's revenues. management team is concerned that the dancers may not put enough effort in training. For Lady Gaga's annual Las Vegas show, the team considers different Contract 3: options to organize its cooperation with the dancers and asks you for advice on Agreeing on an informal long-term relationship with the free-lance dancer, In which organizational form they should use. which the management pays $ 3500 per show, but credibly promises to re-hire the dancer under the same contract for next year's show if the routines are sufficiently These are the assumptions they provide you with: practiced (=100 training hours). If the dancer does not put in enough practice, the management will not renew the contract leaving the dancer with the second Practicing the entire choreography for the show takes 100 hours of individual best option. As the Gaga shows are annual, this renewal of contracts can go on training. One training hour (e) carries a cost of effort (C(e)) for a dancer given Indefinitely. The dancer discounts her earnings at a 10% discount rate. by the following function: Please answer the following questions about this case. = 2 (e -80) 2 First, analyse Contract 1: a: Mathematically describe how the pay-off of the dancer depends on the effort The revenue (R(e)) of a show depends on the effort of the dancer in the choice (e) under this contract. following way: State the profit/loss function of the management team under this contract. R(e) = 5000 + 100(e - 80) C: How much training hours will the dancer put in under this arrangement? Before the show, the management team cannot observe the amount of training hours the dancer practices. By observing the dancer during the show the What is the profit or loss of the management team and the pay-off for the management can observe whether or not the dancer has put in 100 training dancer in this case? hours and sanction the dancer ex-post if necessary. If the dancer does not work for Lady Gaga, the next best alternative is to dance Second, analyse Contract 2: in a generic show, such as Taylor Swift's. This pays $3200, but requires only 80 hours of training. e: Mathematically describe how the pay-off of the dancer depends on the effort choice under this contract For the management, the profits or loss on this contract () is the difference between the revenues (R(e)) and the cost of paying the dancer. f: State the profit/loss function of the management team under this contract. Forthe dancer, the pay-off of the contract is the difference between the salary and the cost of effort. How much training hours will the dancer put in under this arrangement? What is the profit or loss of the management team and the pay-off for the dancer in this case? 21 22