By Shuo Zeng, Moshe Dror

This ebook examines contractual suggestions for a functionality established agreement among an proprietor of a profit producing unit and a fix agent for such unit. The framework of the research is that of economists' principal-agent challenge. The contractual techniques of a central and an agent are modeled as a Markov approach with an undetermined time horizon. For a probability impartial valuable, the authors determine the stipulations less than which a imperative contracts with a risk-neutral, risk-averse, or risk-seeking agent and derive the principal's optimum supply including the agent's optimum carrier potential reaction. In essence, the publication offers an intensive formulating research of principal-agent contracts given any exogenous parameter values. eventually a small variety of formulation conceal a wide spectrum of principal-agent conditions.

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12 depicts the shape of u. / when Á 1 and the value of p falls in different ranges. The proof when Á 1 is depicted in Fig. 13. 1, u. / is decreasing with respect to 0. 3) u. w; p// D w p. 0; p/: u. w; p// < 0, therefore the agent rejects the contract. 52 4 Risk-Averse Agent w ∈ (0, p) Reject. w≥p μ∗ = 0 p ∈ (0, 4p1 ] η≥1 w ∈ (0, p) Reject. w≥p μ∗ = 0 w ∈ (0, w4 ) Reject. p ∈ (4p1 , p4 ) p = p4 p > 4p1 μ∗ = 0 or μ∗ = w ≥ w4 w∈ 0, 2 (1 + η)pλ − λ (1 + η)p4 λ − λ Reject. p > p4 w≥2 Fig. 23 when Á Subcase w offered.

Du. / D p and lim D ! d 4 1 Á d 2 du. 1 Á/p D d . 1 Á/p . C /3 > : du. 1 C Á/p D d . C /2 du. C1 d lim 1, lim 1 and ! C  1CÁ du. / p D d 4 d2 u. 1 C Á/p <0 . C /3 The above derivatives indicate the direction of monotonicity and the concavity/convexity of function u. / over Œ0; / and . ; C1/. 1 summarizes b a à 3 ;1 5   1 1 4 Á 1CÁ ; Á p2 4 4 ; 1CÁ 1 Á  à 4 p2 ; C1 1 Á  4 p 2 0; 1CÁ  4 p2 ; 1CÁ 1 Á  4 p2 ; 1 Á 1 Á  à 4 p2 ; C1 1 Á  4 p 2 0; 1CÁ  à 4 p2 ; C1 1CÁ p2  p 2 0; b a Concave Concave Convex Convex >0 >0 <0 <0 Concave <0 Concave Concave >0 Ä0 Concave >0 Concave Concave Ä0 >0 u.

10) , then p in case the principal makes an offer, the agent accepts the contract and . 1 C Á/p . 1 C Á/p3 if r > p3 . Since @…P =@w D 1 < 0, therefore w D w3 . p3 / (see Eqs. 16)). 1 C 2Á/x C r=x/. 13, r3 > p3 > r1 , therefore we examine the following subcases. 17 part (a), p D p3 . w ; p // Ä 0, therefore the principal does not propose a contract. 17 part (a), p D p3 . 1 Á/p3 . 17 part (a), p D p3 . p3 / D p r1 /= p3 > 0, therefore the principal proposes a contract with w D w3 and p . 1 C Á/ C .

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