Task-specific effort costs and the trade-off between risk and efficiency

This paper considers a principal-agent model in which an agent chooses the level of effort on two tasks that determine two separate outputs. The level of effort is private information to the agent. We examine the relationship between risk and incentives when the agent has a preference towards one of the two tasks. This is modelled by the assumption that the cost of effort is task specific. We show that when outputs are not perfectly measurable, even if the measurement errors have the same variance, the principal has to set different marginal incentives. This is because the agent tries to spread the risk, created by imperfect output measurement, by distributing more evenly his effort between the two tasks, thereby moving away from an efficient allocation of effort. If the two outputs are measured with different precision, it can be optimal for the principal to set higher marginal incentives on the output measured with less precision. Hence the standard result of the negative correlation between risk and incentives does not necessarily hold.uncertainty, risk spreading, efficiency, incentives

A note on the Almansi property

The first goal of this note is to study the Almansi property on an m-dimensional model in the sense of Greene and Wu and, more generally, in a Riemannian geometric setting. In particular, we shall prove that the only model on which the Almansi property is verified is the Euclidean space R^m. In the second part of the paper we shall study Almansi's property and biharmonicity for functions which depend on the distance from a given submanifold. Finally, in the last section we provide an extension to the semi-Euclidean case R^{p,q} which includes the proof of the classical Almansi property in R^m as a special instance.Comment: Dedicated to Prof. Renzo Caddeo, to appear in Mediterranean Journal of Mathematic

A generalisation of the Hopf Construction and harmonic morphisms into \s^2

In this paper we construct a new family of harmonic morphisms \varphi:V^5\to\s^2, where $V^5$ is a 5-dimensional open manifold contained in an ellipsoidal hypersurface of \c^4=\r^8. These harmonic morphisms admit a continuous extension to the completion ${V^{\ast}}^5$, which turns out to be an explicit real algebraic variety. We work in the context of a generalization of the Hopf construction and equivariant theory.Comment: 10 page

A general approach to equivariant biharmonic maps

In this paper we describe a 1-dimensional variational approach to the analytical construction of equivariant biharmonic maps. Our goal is to provide a direct method which enables analysts to compute directly the analytical conditions which guarantee biharmonicity in the presence of suitable symmetries. In the second part of our work, we illustrate and discuss some examples. In particular, we obtain a 1-dimensional stability result, and also show that biharmonic maps do not satisfy the classical maximum principle proved by Sampson for harmonic maps.Comment: 13 pages, final version to appear in Mediterranean Journal of Mathematic

Optimal Audit Policy and Heterogenous Agents

Frauds can be explained not only in terms of individual willingness to cheat, but may also be driven by opportunities to behave dishonestly. The audit policy should therefore be different for different categories of agents. This paper focuses on the optimal audit policy when there are two categories of agents and shows that the auditor adopts different policies depending on its budget. When resources are quite limited, the auditor sets identical audit probabilities for both types. On the other hand, in most of the cases, the authority should first ensure that people with lower opportunities choose not to commit an offence.Fraud, audit, opportunities, budget allocation.

Too Few Cooks Spoil the Broth: Division of Labour and Directed Production

How can a manager influence workers' activity while knowing little about it? This paper examines a situation where production requires several tasks, and the manager wants to direct production to achieve a preferred allocation of effort across tasks. However, the effort that is required for each task cannot be observed, and the production result is the only indicator of worker activity. This paper illustrates that in this situation, the manager cannot implement the preferred allocation with a single worker. On the other hand, the manager is able to implement the preferred allocation by inducing a game among several workers. Gains to workers from collusion may be eliminated by an ability-dependent, but potentially inefficient, task assignment. These findings provide a new explanation for the division of labor, and bureaucratic features such as "over"-specialization and "wrong" task allocation.specialization, job design, moral hazard, multitasking

Division of Labour and Directed Production

We examine a situation where efforts on different tasks positively affect production but are not separately verifiable and where the manager (principal) and the worker (agent) have different ideas about how production should be carried out: agents prefer a less efficient way of production. We show that by dividing labour (assigning tasks to different agents and verifying that agents do not carry out tasks to which they are not assigned), it is possible for the principal to implement the efficient way of production. Colluding agents can undermine this implementation. However, if agents have different abilities, collusion can be prevented by a specific assignment of agents to tasks.hidden action, moral hazard, specialisation, job design