24.12* Business Application: Carrots and Sticks: Efficiency Wages and the Threat of Firing Workers: In our treatment of labor demand earlier in the text, we assumed that firms could observe the marginal revenue product of workers, and thus would hire until wage is equal to marginal revenue product. But suppose a firm cannot observe a worker’s productivity perfectly, and suppose further that the worker himself has some control over his productivity through his choice of whether to exert effort or “shirk” on the job. In part A of the exercise, we will consider the subgame perfect equilibrium of a game that models this, and in part B we will see how an extension of this game results in the prediction that firms might combine

“above market” wages with the threat to fire the worker if he is not productive. Such wages, known as efficiency wages, essentially have firms employing a “carrot-and-stick” approach to workers: Offer them high wages (the carrot), thus making the threat of firing more potent. (Note: It is recommended that you only attempt this problem if you have covered the whole chapter.)

A. Suppose the firm begins the game by offering the worker a wage w. Once the worker observes the firm’s offer, he decides to accept or decline the offer. If the worker rejects the offer, the game ends and the worker is employed elsewhere at his market wage w*.

a. Suppose the worker’s marginal revenue product is MRP 5 w*. What is the subgame perfect equilibrium for this game when marginal revenue product is not a function of effort?

b. Next, suppose the game is a bit more complicated in that the worker’s effort is correlated with the worker’s marginal revenue product. Assuming he accepted the firm’s wage offer, the worker can decide to exert effort e . 0 or not. The firm is unable to observe whether the worker is exerting effort, but it does observe how well the firm is doing overall. In particular, suppose the firm’s payoff from employing the worker is 1x 2 w2 if the worker exerts effort, but if the worker shirks, the firm’s payoff is 1x 2 w2 . 0 with probability g , 1 and (2w)

with probability (1 2 g2. For the worker, the payoff is 1w 2 e2 if the worker exerts effort and w if he does not. What is the firm’s expected payoff if the worker shirks?