1. Introduction

The recent book by Bolton and Dewatripont (2005) contains details of contract design. However, they did not deal with the details of the principal agent models.

Jensen and Meckling (1976) is the most influential specification of agency costs. On the other hand, Williamson (1988) contains a succinct exposition of the distinctions between transaction costs and agency costs.

Note that vertical integration and circumventing the market lead to contracts within the firm. The labor market literature predominantly deals with this. Contracts with agents outside the firm, e.g., subcontractors, franchisees etc., is equally dominant. The first set of studies is closer to the transaction cost argument of Coase while the latter are more concerned about agency costs. They also differ with respect to the duration of contracts. The present study concentrates mostly on the second type of contracts.

The literature on mechanisms design is rather extensive. Many useful concepts of efficient contract design are discernible. The principal agent model is one among the several alternatives. To the extent I am aware of it no formal comparisons, among the alternatives, has been attempted so far. The basic reason is that the econometric problems involved in such an enterprise are formidable. The reader may refer to Masten and Saussier (2002) for a review of econometric studies dealing with the choice of markets versus contracts.

Though somewhat dated, the early exposition by Rees (1985a, b) contains very useful insights about the principal agent models.

Two aspects of this specification should be noted clearly. First, that the principal would spend more to achieve the same result. It is not possible to justify delegation to the agent otherwise. Second, the cost reduction y must exceed y ²/2δ. For, otherwise, there is no point in entrusting the job to the agent.

No specific effort, to categorize randomness as external to the contracting individuals or endogenous to their functions, has been discernible expect when some specific details have been incorporated.

As the model implies σ ² is a constant independent of p. Hence, it would be necessary to clarify the form that this improvement takes. An obvious approach is to make σ ² a function of p.

Two aspects of this specification should be noted clearly. First, that the principal would spend more to achieve the same result. It is not possible to justify delegation to the agent otherwise. Second, the cost reduction y must exceed y ²/2δ. For, otherwise, there is no point in entrusting the job to the agent.

In this formulation u may be purely exogenous. In such a case, an agent who is made to share risk feels that he is being punished for something he did not do. There is then a possibility that he will reduce y if σ ² increases. This was noted in Borenstein et al. (2007). Alternatively, Baker (2006) suggested the following. The agent may use more resources and incur greater costs, given his risk aversion, in order to be sure that he may deliver the promised output. This can also give rise to the possibility that y depends on λ and/or σ ². However, note that in this formulation it is independent of σ ² ex ante given p. Ex post p will depend on σ ² and hence the observed y is not independent of σ ². By way of contrast, based on some experimental evidence, Sloof and vanPragg (2008) noted that y does not depend on σ ² even ex post. Some basic adaptations will be necessary to replicate this result in principal agent models of this vintage.

Clearly, delegation would be beneficial whenever

It would be reasonable to suggest that the labels principal and the agent are for analytical convenience only. Their functional roles determine the nature of the contract.

Cooper and Ross (1985), Emons (1988), and Dybvig and Lutz (1993) acknowledged that the consumers can adjust the care with which they use the product. Thus, the consumers can exert some influence on the failure of the product depending on the way they use it. The issue is this. What determines the adjustments in δ? λσ ² is surely one of the determinants. Emons (1988) argued that p, viz., the warranty offered, may itself determine the choice of δ. Similarly, following the argument of Murty and Blischke (2000), it can be argued that even the firm makes adjustments in several characteristics of its product when it recognizes the pertinent dimensions of consumer risk aversion. This may include the warranty and the σ ² itself. We will not consider these alternatives in detail here.

This argument holds only for a given λσ ². In such a case the resulting p is the minimum rather than a maximum. There will be a simultaneous choice of λσ ² that the agent would exhibit. This is entirely plausible if σ ² is a result of the agent’s action instead of its being fixed exogenously.

Jullien et al. (1999) pointed out that the costs to the agent, of making such adjustments in his efficiency levels, will not be negligible. Hence, he must weigh the advantages due to an increase in p against such costs. This may be the primary reason why we do not expect η > 1 in practice. Secondly, there may be limits on the extent to which he would be willing to take increased risk. In the limit, even the maximum p may not be attainable.

An increase in C beyond 2 will increase the value of the contract to the agent. However, it would be realistic to expect that the principal wishes to maintain as large a share of output as the agent will concede. Note that any C ≥ 2 will be acceptable to both of them if both of them maximize their respective value and disregard the share of output.