8

The term principal-agent problem is due to Ross (1973) (per Stiglitz, 1989). Other early contributions to this literature include Mirrlees (1974, 1976) and Stiglitz 1974, 1975).


5

I found "Contract Theory" by Patrick Bolton and Mathias Dewatripont to be a very nice and thorough book. It, however, might be too advanced, although you can skip the formalism and just read the intuitions provided. Let me quote how the book is advertised: The book emphasizes applications rather than general theorems while providing self-contained, ...


5

In my PhD program everyone was using The Theory of Incentives: The Principal-Agent Model by Jean-Jacques Laffont and David Martimort. It offers a formal and relatively complete treatment without being too technical. I haven't read any other book on the topic, so unfortunately I cannot compare. If you want to avoid any mathematical formalism, a good ...


5

Just a model that can be used to state how (in)complete a particular contract is, whatever the reason. I remember a debate at the end of the 90's on Incomplete Contracts: Where do We Stand? by Jean Tirole and Foundations of Incomplete Contracts by Hart and Moore, where they develop a model that provides a rigorous foundation for the idea that contracts are ...


4

A thing that bothers me here is the following: the Incentive Compatibility constraint is $$IC: w'p(a') + w(1-p(a')) - 1 \geq w'p(a) + w(1-p(a))$$ $$\implies w'-w \geq \frac {1}{p(a')-p(a)} \tag{1}$$ ...since by assumption $p(a')-p(a) >0$. We are told that we should find that at the optimum, $$x'-w' = x-w \implies x'-x = w'-w \tag{2}$$ Combining $(1)...


3

Notice that MWG choose a wage function $w(\pi)$ to maximize profit, not a wage level $w$. As footnote 6 on p.481 of MWG says: The first-order condition for $w(\pi)$ is derived by taking the derivative with respect to the manager's wage at each level of $\pi$ separately. In other words, you'd treat the wage function as a variable, e.g. $w(\pi)=z$, and ...


3

This answer shows three things: We do not need the Lagrangian approach to solve your maximization problem. We do not need the assumption that $x'-x=\frac{1}{p(a')-p(a)}$ either. The condition $x'-w'=x-w$ is not necessarily satisfied for the optimal contract. Fix indeed the payment $w$. The problem can be written \begin{equation*} \max_{w'}{u(x'-w')p(a')} \...


3

It is true that when both principal and agent are risk neutral, the first best can be obtained despite asymmetric information. You should refer to a textbook, such as MWG (ch.14), for the technical details of such models. I'll give an intuitive explanation here. The intuition of the result lies in optimal risk sharing between the principal and the agent. ...


3

We are given that $u$ is increasing and concave, and $u(0) = 0$. This implies that $\dfrac{u(t)}{t}$ is decreasing in $t$, and also, $\dfrac{u(t)}{t} > u'(t)$ for all $t$. Nicole's maximization problem : \begin{eqnarray*} \max_{x} \ q(x)(w-t(x))\end{eqnarray*} FOC : $q'(x)(w-t(x)) = q(x)t'(x)$ Suppose $x_N$ solves Nicole's problem. Therefore, it ...


2

"The Economics of Contracts" by Bernard Salanié is nice and concise. Like the Bolton and Dewatripont book suggested by Bayesian (and most other books on this topic) it is pitched at a graduate level and certainly does not fall into the "popular science" category. The theory of contracts grew out of the failure of the general equilibrium model to account ...


2

I think its not a complex issue: a) You need to keep the high type agent from pretending to be the ow type agent, so you give him an extra compensation from showing his high type. But this nice deal pays him more than necessary to keep him in the game so his IR is more than satisfied, i.e. not binding. b) Similarly, you will make it painful to show that ...


2

In direct mechanism agents directly report their preferences (preferences are observable). In indirect mechanism agents don’t report their preferences directly. Preferences can be observed only indirectly through signals or behavior. By Revelation Principle if some outcomes can be implemented in indirect mechanism they must be also implementable in the ...


2

Not all principal-agent problems are the result of incomplete contracts, no. In fact, in most principal-agent problems, complete contracts are assumed. An incomplete contract is one that cannot be contingent on every possible outcome that could occur after the contract is signed. You can't write a contract that gives out a different payment to each party ...


1

From Bolton and Dewatripont Contract Theory (2005, p.135): "In the absence of risk aversion on the part of the agent and no wealth constraints, the first best can be achieved by letting the agent "buy" the output from the principal." This quote is in the context of a simple two outcome model.


1

Moral hazard models feature agents' hidden actions (or these actions are not contractible). For example, a manager's contract cannot determine a wage contingent on the manager's effort, only contingent on other observable outcomes such as "success" / "no success" of a project. The next two classes of models assume that actions are observable/contractible, ...


1

If we try to directly optimize with respect to $t$, given this system (two unknwowns, one equation), we get a nonsensical result. $$\frac{\partial P}{\partial t}: -s = 0$$ Which may not be true, and I'm assuming you are taking $s$ as given, not something to choose. You can only optimize with respect to $x$. $$\frac{\partial P}{\partial x} = 1 - sx = 0 \...


1

I believe this is the basic case discussed in the Laffont-Martimort textbook "The Theory of Incentives". The choice of the agent is either 0 or 1. You can find a complete description in "The Moral Hazard" chapter, section 4.2. The results are listed later, and while I am not sure, I do not think there should be qualitative differences.


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