The harvest arrives with the labor and the weather already mixed. The owner can weigh the grain, but its weight does not disclose every hour the tenant worked or every hour the rain withheld. A share of the harvest gives the tenant a reason to add his effort. It also makes his income fall when the season turns against him. The same rule reaches two things at once: the action the owner wishes to encourage and the uncertainty the tenant might pay to escape. The spur is therefore a bargain over exposure. Its strength determines how much the agent gains from doing more, and how much of what he cannot control he must carry with that gain.
The inherited field presents three ways of dividing that exposure. Under a fixed wage, the owner receives the crop and bears its fluctuation while the worker’s payment stays constant. Under a fixed rent, the tenant pays an agreed amount and keeps what remains, including the gain from an additional bushel. Under a share, each receives part of the crop and bears part of its variation. Where effort is privately costly, hidden and unrewarded by any other means, the wage provides no financial return to extra work; the rent provides the full marginal return; the share falls between. These statements describe the specified incentives, not the character of wage workers or a complete history of tenancy. Supervision, reputation, other productive inputs and the ability to finance a bad season can alter the comparison.
Risk returns to the principal through the terms on which the agent will accept it. Suppose the owner responds to weak effort by giving the tenant the entire crop and demanding a larger fixed payment. A risk-averse tenant values that uncertain remainder less than a certain sum with the same mean. He may require a lower rent, a reserve, or some other compensation before agreeing. The uncertainty has moved between the parties, but the cost of bearing it remains inside the bargain. A principal able to bear risk more cheaply can consequently gain by retaining part of it, even though doing so weakens the agent’s immediate financial stake. The question is what additional effort a sharper reward buys after the extra exposure has been paid for.
A small linear model makes that purchase visible. Keep the constructed example from the earlier Margin Incentive. Output equals effort plus mean-zero noise of variance three. Payment is a fixed amount plus a share of output, effort costs half its square, and the agent’s money-equivalent risk charge is half the variance of his pay. The principal is risk-neutral and transfers can be adjusted to secure participation. A share of one-quarter induces effort of one-quarter. After effort cost of one thirty-second and risk cost of three thirty-seconds, their combined certainty-equivalent gain is one-eighth. Giving the agent the whole output induces effort of one, but the half-unit effort cost and one-and-a-half-unit risk cost leave a combined return of minus one. More work has been bought at a greater loss.
The quarter share belongs to the assumptions that produced it. In this example the best share is one divided by one plus the noise variance. Raise the variance from three to seven, leaving everything else fixed, and the share falls from one-quarter to one-eighth. Remove the risk charge and the best share rises to one. Make the action directly contractible, and the principal may instead specify it while insulating the worker from an unrelated shock. These are different arrangements, not rival universal prescriptions. Holmström’s more general analysis also shows why the shape of optimal pay cannot be inferred from the familiar straight line alone. Particular distributions, restrictions on payment and the evidence a deviation leaves can change what a contract can achieve.
Better evidence can sharpen the reward without making the agent carry more of the same luck. Suppose two units of the model’s noise variance come from a common market disturbance and one from an independent local disturbance. A verifiable index records the common disturbance exactly. Pay the share on output minus that index, and an extra unit of effort still increases the measured result by one while the remaining noise variance falls to one. At the old quarter share, pay variance falls from three-sixteenths to one-sixteenth. Choosing the share afresh now gives one-half and a combined surplus of one-quarter. The improved measurement has enlarged the gain available to divide before the parties argue over its division.
Holmström’s informativeness principle asks what a signal adds to the evidence already in the contract. An index may contain no direct trace of a worker’s effort while helping to interpret an outcome that does. A second report of the same outcome may add nothing. Under the theorem’s conditions, informative additional evidence permits an improvement when it can be acquired and used without cost in a sufficiently flexible contract. This is a conditional test, not an instruction to put every statistic into pay. The signal must add information beyond what is already observed, and the value of using it must be weighed against collection, verification and administration. A monitor can be informative and still be an expensive way of learning too little.
The spur rewards the evidence through which effort can be reached, and inherits the defects of that evidence.
A perfectly measured result can still give the wrong direction to the work. A seller may spend an afternoon closing today’s order or preserving a relationship on which later orders depend. If the activities compete for attention, a commission on the counted sale can make the neglected service more costly for the seller to supply. Increasing the commission then does more than demand greater total exertion; it changes what the exertion is for. Holmström’s multitasking analysis makes that allocation central. Where task costs are independent, the same diversion does not follow merely because both tasks belong to one person. Where the tasks substitute for one another, a weaker reward on the clear number can protect valuable work that the number omits.
The contract consequently has to be read as a design for the whole job. The bonus, the fixed wage, the division of duties and the opportunity to review a decision affect one another. Assigning a task to a specialist may make its performance easier to assess; leaving judgment with an experienced worker may be worth more than a count that suppresses it. A salary can coexist with promotion prospects, professional obligations and the expectation of future work. It is therefore a mistake to infer from a low-powered payment alone that the arrangement has abandoned incentives. The more useful question is which actions the whole arrangement makes attractive, including the temptation to improve a measure while leaving the service worse.
The appropriate strength of the spur depends on what its point can reach. A reward should induce worthwhile action, secure participation and justify its cost in risk and displaced attention. The result is a settlement under a particular distribution of knowledge, rather than a natural price for virtue or a complete verdict on contribution. The principal’s side of the promise then comes into view. A worker will have little reason to pursue a promised bonus if the payer can withhold it after the work is done. To design the inducement is also to ask why it will be honored. The next plate places something at hazard on that side of the bargain: the pledge that makes a future obligation credible.