Problem Set 4 -- Solutions
1. Consider a firm that sells vacuum cleaners door-to-door. The production process requires capital such as a personal computer (that salesmen can dial in to record orders, etc.), office space, brochures, etc. It also requires labor in the form of salesmen. Suppose one individual owns all of the capital, and employs five salesmen. Two of the salesmen are risk neutral, two are moderately risk averse, and one is extremely risk averse. Assume that salesmen's output (vacuum cleaner sales) is perfectly observable and separable, but imperfectly reflects effort due to factors outside of their control. Assume also that because they rotate regions every month, there is no reason for salesmen to lobby for the best territories. Assume also that each salesman only works for one year, and the capital owner can commit to an incentive scheme during the entire period.
The capital owner wishes to design compensation schemes which can combine salaries with performance incentives. He hires you as a consultant. What would you recommend as a compensation scheme toward the goal of total value maximization? Do you recommend that he use the same scheme to pay each of his workers? Why or why not? Would the workers be expected to earn the same amount? If not, why? If so, which would be expected to make the most, and which would be expected to make the least?
Since there is nothing in the description of the problem to suggest that you cannot use performance incentives (such as a budget constraint), a contract based with a fixed and variable components would be an efficient way of eliciting effort. This contract would take the form: where z is sales. From class, we determined that the efficient choice for , subject to the incentive constraint, is: Since '(e)>0, this expression is higher the less risk averse (lower r) the agent. Therefore, if you knew the salesmen's attitudes toward risk, it would be efficient to pay them differently. The risk neutral salesmen would get the highest performance incentives; the extremely risk averse salesmen would get the lowest ones. From the incentive constraint, this means that the risk neutral salesmen will put in the most effort and earn the highest bonuses.
The rest of this problem was very hard. However, they will not make the most overall. Why? Because when choosing the fixed part of the compensation scheme, the principal picks for each salesman to make him indifferent between selling vacuum cleaners and his next best alternative. Assume that each salesman's next best alternative nets him a certainty equivalent of C. Therefore, each vacuum cleaner salesman's certainty equivalent must equal C. Recall that: For a risk neutral agent, CEQ=E(y). For a risk averse agent to have the same CEQ, he must have a higher E(y), because he bears risk costs. Therefore, the more risk averse the salesman is, the more he must earn on the average. He earns less than risk neutral salesmen in bonuses, but much more in the fixed component.
2. Consider the two moderately risk averse salesmen in the above example. Suppose one sells a fancy vacuum cleaner that is extremely profitable and the other sells a more ordinary, less profitable one. How would this affect your recommendation? Now consider the two risk-neutral salesmen. Suppose one sells the fancy vacuum cleaner and the other sells the ordinary one. How would this affect your recommendation?
In both cases, you would wish to provide higher performance incentives to the salesman selling the more profitable machine, by the equation above. You would also want to rotate who gets to sell the more profitable machine in order to discourage influence activities.
3. Does efficiency wage theory provide a compelling description why CEOs might be paid wage premia? Why or why not?
Efficiency wage theory generally does not provide a compelling description why CEOs might be paid wage premia. Efficiency wage theory fits best in situations where one is for some reason unable to provide incentives through output based pay -- for example when the worker has a wealth constraint. This seems not to apply to CEOs, who are presumably wealthy people.
4. Imagine that you are consulting Henry Ford during the 1910s. He had successfully introduced the $5 day; his workers were earning well above what they could earn in their next best opportunity. Ford calls you in, and says that he is concerned about demographic changes in his workforce. The region's healthy economy was providing strong incentives for young men from Europe to immigrate near his auto plants in Michigan. While his workforce did not change in any other way, it was, on the average, two full years younger than it had been when Ford had initially (optimally) set wages for workers at $5/day and hired 100 supervisors to monitor workers. His policy, as always, was to fire (and never rehire) any worker who was found shirking.
In talking to Ford, you learn that he is particularly concerned about two matters. First, he is concerned that because his workforce is younger, if he happens to hire a shirker, this shirker may end up working at Ford for a very long time. So he is considering whether to hire more supervisor/thugs to monitor his workforce. He is also considering cutting the daily wage. Ford's reasoning is that it may make sense to do so because it would make the lifetime wage premium he would pay workers (on the average) the same as it was before this demographic change.
What do you recommend to Ford with respect to changes in the wage and the number of supervisors, given that he wants to minimize his total labor costs and deter shirking?
The number of periods "to go" in the relationship increased by two years. This means that the optimal wage premium decreases, and the optimal level of monitoring decreases, from the discussions in class and from Milgrom and Roberts. Ford should decrease the wage (although not for the reason he gave) and fire a few supervisors.
5. Consider the following situation. Raphael Bostic plays shortstop for the New York Mets. He is a good player, but he is by no means the best player in the league. Suppose the following:
Raphael's salary: $329,000 per year
The Mets' cost of replacing Raphael should he suddenly get injured or leave the team: $338,000 per year
Raphael's best offer at another team if he is able to offer his services to other teams in a competitive market: $300,000 per year
Raphael's best employment prospect outside of baseball: $30,000 per year
What, if anything, can you say about Raphael's economic rents, quasi-rents, and appropriable specialized quasi-rents?
Can't say anything about economic rents, because you don't know what Raphael's prospects were before he began to practice to become a ballplayer. Quasi rents equal payment to an asset in excess of the value of its next best use: $329,000-$30,000=$299,000. Appropriable specialized quasi rents equal payment to an asset in excess of the value to the next best user: $329,000-$300,000=$29,000.
A lot of people missed this one. Make sure you know these concepts. Confusion may well hurt you on the final.