HIDDEN ACTIONS (MORAL HAZARD )

HIDDEN ACTIONS (MORAL HAZARD )
Imagine that the owner of a firm ( the principal) wishes to hire a manager (the agent) for a one time project . When manager actions are not observable , the owner must design the manager’s compensation scheme in a way that indirectly gives him the incentive to take the correct action s. Let Π denotes the project’s profit ( observable profit) and e denotes the manager’s decision choice or measuring the managerial effort . Two possible choice : 1- High effort level ( eH ) leads to high profit level. 2- Low effort level ( eL ) leads to low profit level . profits can take values in the domain [Π1 , Π2 ] that is stochastically related to e in a manner described by a density function f(ΠIe) , with f(.) >0 for all e and Π. Any potential realization of П can arise following any given effort choice by manager . For example if f(ΠIe) =2e+3, and e=2, then Π=6 . this means that when effort level is 2 , the probability of any profit level happening is 6. Levels of expected profits when the manager chooses eH is larger than from eL : ∫ Π f(ΠIeH) dΠ > ∫ Π f(ΠIeL) dΠ the manager is a expected utility maximizer U(w,e) = v(w) – g(e) Vw (w) >0 , and Vww(w) ≤ 0 , g(eH )>g(eL) . Mas-collel CH 14 priciple agent problem

the owner is risk neutral , and his objective is to maximize his expected return. The idea behind this is that the owner may hold a well diversified portfolio that allows him to diversify away the risk from the project . THE OPTIMAL CONTRACT ;WHEN EFFORT IS OBSERVABLE ; the owner chooses to offer a contract to manager that the manager can reject or accept . We also assume that U0 is the reservation utility level and w(Π) is the wage offered as a function of profit level . If the manager rejects owner’s contract offer , the owner receives a payoff of zero . The optimal contract for the owner is to maximize his compensation cost (net expected profit): Choosing w(π) to maximize ; ∫(π – w(π)) f(πIe) d π=(∫ π f(πIe) d π) – (∫w(π) f(πIe) d π ) is equivalent to minimizing the expected value of the owner’s compensation cost , ∫w(π) f(πIe) d π .because profit level is given based upon the effort level. So the optimal compensation scheme could be written as follows ; Mas-collel CH 14 priciple agent problem

Min ∫w(π) f(πIe) d π with respect to w(π ) s.t. ∫ v(w(π)) f(πIe) d π - g(e) ≥ U0 . The first order condition is -f(πIe) + γv’(w(π))f(πIe)=0 or If the manager is strictly risk averse , so that v’(w) is strictly decreasing in w , the implication of the above condition is that optimal compensation scheme w(π) is a constant . v(w)=w1/2 , v’(w)=1/2w -1/2 =1/ γ , w* = (γ2 )/4 =fixed .This means that the risk neutral owner should fully insure the risk averse manager against any risk in the income stream . Hence the owner offers a fixed wage of we* ( for each e there is a we* ) such that the manager receives his reservation utility level v(we* ) – g(e) = u0 . Since g(eH) > g(eL) , the manager’s wage will be higher if the contract calls for effort eH than if it calls for eL . If the manager is risk neutral , the above condition holds for any compensation since , v’(w)= constant. So any compensation function w(π) that gives the manager an expected wage payment equal to u0 + g(e) is also optimal Mas-collel CH 14 priciple agent problem

the owner optimality specifies the effort level e € ( eH , eL ) that maximizes his expected profits less the wage payment . [∫ π f(πIe) d π) ] - [v-1 (u0 +g(e))] [ v(w) = utility obtained from w ] Gross profit wages that must be paid to compensate the manager this will be the unique optimal contract if v” (w) <0 for all w . Preposition 14.b.1. : in the principle agent model with the observable managerial effort , an optimal contract specifies the effort level e* that maximizes [∫ π f(πIe) d π) ] - [v-1 (u0 +g(e))] and pays the manager a fixed wage of w* = v-1 (u0 +g(e*) . This is the uniquely optimal contract if v” (w) <0 at all w . the optimal contract when effort is not observable ; The optimal contract accomplished in the observable case accomplishes two goals ; it specifies an efficient effort choice by the manager, and it fully insures him against income risk . Mas-collel CH 14 priciple agent problem

When the effort is not observable , these two effect often came into conflict because the only way to get the manager to work hard is to relate this pay to the realization. We will study two cases ; 1- when the manager is risk neutral , the owner can still achieve the same outcome as when effort is observable . 2- when manager is risk averse , and when the first best contract involve the high-effort level , the efficient risk-bearing and efficient incentive provision come into conflict , and the presence of non-observable action leads to welfare loss . 1- risk neutral agent . The optimal effort level e* when effort is observable solves MAX ∫π f(πIe) d π – g(e) – u0 with respect to e .In which; v(w)=w= g(e)+u0 π f(πIe) d π – g(e) – u0 = owner’s profit . And U0 = the expected utility that the manager receives Preposition 14.b.2 : in the principle agent model with unobservable managerial effort and a risk neutral manager , an optimal contract generates the same effort choice and expected utilities for the manager and the owner as when effort is observable . Mas-collel CH 14 priciple agent problem

Suppose that the owner offers a compensation schedule of the form W(π)= π - α , (manager is risk neutral dW(π))/dπ = 1) , when α is some constant. This compensation schedule can be interoperated as “ selling the project to the manager “ because it gives the manager the full return π except for the fixed payment α , the sales price . If the manager accepts the contract , he chooses e to maximizes his expected utility ; ∫w(π) f(πIe) d π – g(e) = ∫ π f(πIe) d π – α – g(e) , comparing this maximization with MAX ∫ π f(πIe) d π – g(e) – u0 reveals that a unique e* will maximizes both of them . The condition for manager to accept the contract ; ∫ π f( πIe ) d π – α – g(e* ) ≥ u0 . If the manager is risk neutral , the problem of risk-sharing disappears . Efficient incentives can be provided without incurring any risk-bearing losses by having the manager receive the full marginal returns from his effort. Mas-collel CH 14 priciple agent problem

2- Risk-averse manager In this case incentives for high-effort can be provided only at the cost of having the manager face risk. We should consider two steps ; 1- first ; we characterize the optimal incentives scheme for each effort level that the owner might want the manager to select ‘ 2- second ; we consider which effort level the owner should induce . The optimal incentive scheme is that e which minimizes the owner’s expected wage subject to two constraints; Min ∫w(π) f(πIe) d π with respect to w(π) s.t. (i) ∫v(w(π)) f(πIe) dπ – g(e) ≥u0 (ii) e maximizes ∫v(w(π)) f(πIe) dπ – g(e) over all the values of e Suppose that there are two levels of efforts eH , eL . How does the owner optimality implement each of these two possible levels of e . 1- implementing eL : the owner optimality offers the manager the fixed wage payment w*e = v-1 (u0 +g(eL )) , the same payment he would offer if contractually specifying effort level eL when effort is observable , because this is the least payment which is required to induce the manager to enforce effort level eL whether effort level is observable or not . . priciple agent problem

2- implementing eH ; the owner decides to induce the effort level eH . In this case the second constraint indicates that ; (ii) ∫v(w(π)) f(πIe) dπ – g(eH ) ≥ ∫v(w(π)) f(πIe) dπ – g(eL ) W(π) must satisfy the following Kuhn-Tucker F.O.C condition in between the lower and upper bound of π . ( page 3 f.o.c.) Consider for example , the fixed wage payment such that ; According to the above condition and v’(w)>0 , v”(w)<0 : Mas-collel CH 14 priciple agent problem

What these relations says is that the compensation scheme pays more than for outcomes that are statistically relatively more likely to occur under eH than under eL in the sense of having a likelihood ration less than one . likelihood ratio the compensation package has this form because of its incentive effects. That is by structuring compensation in this way , it provides the manager with an incentive for choosing eH instead of eL . It is clear that the likelihood ratio is decreasing in π . That is as π increases , the likelihood of getting profit level π if effort is eH relative to the likelihood if effort level is eL must increase . This property is known as monotone likelihood ratio property . Finally , note that given the variability that is optimally introduced into the manager’s compensation , the expected value of the manager’s wage payment must be strictly greater than his fixed wage payment in the observable case: . Intuitively because : Mas-collel CH 14 priciple agent problem

The manager muse be assured an expected utility level of , the owner must compensate him through a higher average wage payment for any risk he bears. Since the manager is a risk averse person with concave utility function and knowing that utility of expected wage is less than expected utility of wages. From the preceding analysis , we know that the wage payment when implementing eL is exactly the same as when effort is observable , whereas the expected wage payment when the owner implements eH under non observability is strictly larger than his payment in the observable case . Thus , in this model , non observability raises the cost of implementing eH and does not change the cost of implementing eL . The implication of this fact is that non-observability of effort can lead to an inefficiency low level of effort being implemented and welfare loss. Hidden Information and (Monopolistic Competition) Post contractual information asymmetry takes the form of hidden information . Manager’s effort level denoted by e, is fully observable . What is not observable after the contract is signed is the random realization of the manager’s disutility from the effort . For example, the manager may come to find himself well suited to the tasks required at the firm, in which case high effort has a relatively low disutility associated with it, or the opposite may be true. However, only the manager comes to know which case obtain. For example the manager of the firm know more about the potential profitability of various actions than does the owner . Mas-collel CH 14 priciple agent problem

HIDDEN INFORMATION and (monopolistic screening)
To formulate the problem ; effort level ; Gross profit excluding any wage pattern to the manager = π(e) : Π(0)=0 , π’(e) >0 , π”(e)<0 , all e . The manager is expected utility maximize; his utility function is u=u(w ,e, θ ) = v(w-g(e, θ)). θ is state of nature which is realized after the contract is signed and that only the manager observe it . g(e, θ) , measures the disutility of efforts in monetary units . In which g(0, θ)=0 for all θ and ; ge(e, θ)>0 , if e>0 and g e(e, θ)=0 if e=0 gee (e , θ)>0 for all e and gθ(e , θ)<0 for all e geθ (e , θ)<0 for all e>0 and geθ (e , θ) = 0 for all e=0 Thus the manager is averse to increase in effort (ge(e, θ)>0 ) level and this aversion is larger the greater the current level of effort (gee (e , θ)>0 ). Higher values of θ are more productive states in the sense that both the manager’s total disutility from effort at any current effort level , g(e , θ) and his marginal disutility from effort at an current effort level , ge (e , θ) , are lower when θ is greater ( since gθ(e , θ)<0 and geθ (e , θ)<0 ). Mas-collel CH 14 priciple agent problem

HIDDEN INFORMATION and (monopolistic (screening
The manager is strictly risk-averse v”(.) <0 . Manager’s reservation utility level = u0 . θ : ( θH , θL ) , and prob (θH ) =λ € (0,1). A contract must try to accomplish two objectives ; First ; insure the manager against the fluctuations in his income. Second ; maximizes the surplus available from the contract in terms of marginal managerial disutility of effort in each nature and owner’s profit level . Case 1 ; The state of θ is observable by owner and manager A complete information contract consist of two wage pairs ( wH , eH ) R R+ for θH and ( wL , eL ) R R+ for θL . The owner optimality is to choose the pairs of w and e in such a way to solve ; Max λ[π(eH ) – wH ] + (1-λ)[π(eL ) – wL ] over ( wH , eH) and (wL ,eL) all greater than or equal to zero . (C.1) s.t. λv(wH - g(eH , θH )) + (1-λ)v(wL - g(eL , θL )) ≥ U0 . Mas-collel CH 14 priciple agent problem

In any solution (e*H , w*H , e*L , w*L ), first order condition reveals that ; -λ + γλv’(w*H - g(e*H , θH )) = 0 (C.2) -(1-λ) + γ(1-λ)v’ (w*L - g(e*L , θL )) = 0 (C.3) λπ’(e*H ) - γλv’(w*H - g(e*H , θH )) ge(e*H , θH ) =0 , e*H >0 (C.4) λπ’(e*H ) - γλv’(w*H - g(e*H , θH )) ge(e*H , θH ) ≤0 , e*H =0 (1-λ)π’(e*L ) - γ(1-λ)v’ (w*L - g(e*L , θL )) ge (e*L , θL ) =0 , e*L >0 (C.5) (1-λ)π’(e*L ) - γ(1-λ)v’ (w*L - g(e*L , θL )) ge (e*L , θL ) ≤0 , e*L =0 These first order conditions show that how 1- the manager will be insured and 2- how to make efforts sensitive to states . From (C.2) and (C.3) we will get ; v’(w*H - g(e*H , θH )) = v’ (w*L - g(e*L , θL )) (C.6) The manager marginal utility of income is equalized in two state . This is the condition for a risk-neutral party optimality insuring a risk-averse person . (C.6) implies; w*H - g(e*H , θH ) = w*L - g(e*L , θL ) which implies that v(w*H - g(e*H , θH )) = v (w*L - g(e*L , θL )). This means that the utility of manager in each state should be the same and given the assumption (C.1) , utility in each state should be equal to u0 . Mas-collel CH 14 priciple agent problem

combining C.2 with C.4 and C.3 with C.5 we will get the following equality from the F.O.C. relations ; π’(e*i ) = ge (e*i , θi ) for i= L , H (C.7) the optimum level of effort in state θi equates the marginal benefit of effort in terms of increased profit with its marginal disutility cost . The optimum point could be shown in the following figure in the next page . Because the manager receives utility level u0 in state θi the owner seeks to find the most profitable point on the manager’s state θi indifference curve with utility level u0 . This is a point of tangency between the manager indifference curve and one of the owner’s iso-profit curves. At this point , the marginal benefit to additional effort in terms of increased profit is exactly equal to the marginal cost born by the manager . Mas-collel CH 14 priciple agent problem

{(w,e) : v(w – g(e , θi ))= u0 V -1 (u0 ) =w – g(e , θi ) V -1 (u0 ) – g(e , θi ) = w Manager’s better off {(w,e) : π(e) – w = π*i g(e , θi ) = 0 , w=v-1 (u0 ) = reservation wage v(w – g(e , θi ))= u0 Owner’s better off W*i Profit of owner in state θi = π* i = -w0 e*i Since π(e=0)=0 , if the wage payment at this point on the vertical axis is W0 <0 , the owner’s profit at (w*i , e*i ) is exactly equal to -w0 Mas-collel CH 14 priciple agent problem

From condition π’(e*i ) = ge (e*I , θi ) for i= L , H (C.7) we see that : when geθ ( e, θ) <0 and π”(e) <0 ,and gee (e , θ)>0 imply that e*H > e*L . Figure in the next page depict the optimal contract , {(w*H , e*H ) , (w*L , e*L )}, these observations are summarized in the proposition C.1 . Preposition C.1 ; In the principal agent model with an observable state variable θ , the optimal contract involves an effort level e*i in state θi such that π’(e*i )=ge (e, θi ) and fully insures the manager , setting his wage in each state θi at the level w*i such that v(w*i - g(e*i , θi ) = u0 . Thus with a strictly risk-averse manager , the first best contract is characterized by two basic features , first , the owner fully insures the manager against risk ; second , he requires the manager to work to the point at which the marginal benefit of effort exactly equals its marginal cost . Because the marginal cost of effort is lower in state θH than in state θL , the contract calls for more effort in state θH . Mas-collel CH 14 priciple agent problem

HIDDEN INFORMATION and (monopolistic screeing
v(w – g(e , θL ))= u0 v(w – g(e , θH ))= u0 In each effort level for reaching u0 higher wages should be paid in state L than state H W*H π(e) – w = π*L g(e , θi ) = 0 , w=v-1 (u0 ) =reservation wage v(w – g(e , θi ))= u0 W*L π(e) – w = π*H e*L e*H π*L In each wage level higher effort leads to higher profit in order to obtain the same reservation utility level U0 π*H 17 Mas-collel CH 14 Mas-collel CH 14 1440/03/11 priciple agent problem

Case II : The state θ is observed only by the manager Suppose that the owner offers a risk-averse manager the contract shown in page 17 and relies on the manager to reveal the state voluntarily . If so the owner will run into problem . as it is evident from the figure , in state θH , the manager prefers (W*L , e*L ) to point (W*H , e*H ) . Consequently , in state θH he will lie to the owner claiming that it is actually state θL . As it is evident from the figure this misrepresentation will lower the owner’s profit . What is the optimal contract ? The owner might offer a 1-compensation function w(π) that pays the manager as a function realized profit and that leaves the effort choice in each state to the manager’s discretion . 2- Alternatively the owner could offer a compensation schedule w(π) but restrict the possible effort choices by the manager to some degree. 3- A more complicated case is that the manager might be required to make an announcement about what the state is and then be free to choose his effort level while facing a compensation function that depends on his announcement of . Mas-collel CH 14 priciple agent problem

An important result known as the revelation principle greatly simplifies the analyses of these type of contacting problem . Preposition C.2 : The Revelation Principle Denote the set of possible states by In searching for an optimum contract , the owner can without loss restrict himself to contracts of the following form : After the state θ is realized , the manager is required to announce which state has occurred . (ii) The contract specifies an outcome an outcome for each possible announcement In every state , the manager finds it optimal to report the state truthfully . A contract that asks the manager to announce the state and associate outcomes with the various possible announcement is known as a revelation principle . Revelation mechanism with this truthfulness property are known as incentive compatible revelation principle . Mas-collel CH 14 priciple agent problem

For example imagine that the owner if offering a contract with a compensation schedule w(π) that leaves the choice of effort up to the manager . Let the resulting level of effort in states θL , and θH be eL and eH . We can show that there exist a truthful revelation mechanism that generates exactly the same outcome as this contract . In particular suppose that the owner uses a revelation mechanism that assigns outcome [w(π(eL )) , eL ] if the manager announces that the state is θL and outcome [w(π(eH )) , eH ] if the manager announces that the state is θH . Consider the manager’s incentive for truth telling when facing his revelation mechanism . Suppose first that the state is θL . Under the initial contract with compensation schedule w(π) , the manager could have achieved outcome [w(π(eH )) , eH ] in state θL by choosing effort level eH . Since he instead chose eL , it muse be that in state θL outcome [w(π(eL )) , eL ] is at least as good for the manager as outcome [w(π(eH )) , eH ] . Mas-collel CH 14 priciple agent problem

Thus , under the proposed revelation mechanism , the manager will find telling the truth to be an optimal response when the state is θL . A similar argument holds for state θH . We therefore see that this revelation mechanism results in truthful announcement s by the manager yields exactly the same outcome as the initial contract . To simplify the problem suppose that the manager is infinite risk-averse. In other words for the manager to accept the owner’s offer , it must be that the manager receives a utility of at least u0 in each state . Under these assumptions the revelation principle allows us to write the owner’s problem as follows : Max λ[π(eH ) – wH ] + (1- λ) [π(eL ) – wL ] over (wH ,eH) , (wL ,eL) s.t. (i) wL - g(eL , θL ) ≥ v-1 (u0) reservation utility constraint (ii) wH - g(eH , θH ) ≥ v-1 (u0) (iii) wH - g(eH , θH ) ≥ wL - g(eL , θH ) incentive compatibility , or (iv) wL - g(eL , θL ) ≥ wH - g(eH , θL ) truth telling constraints If he is going to accept the contract , he must be guaranteed a utility level of at least u0 in each state . So v(wi - g(ei , θi )) ≥ u0 for i= L , H or equivalently wi - g(ei , θi ) ≥ v-1 (u0 ) for i= L , H . Mas-collel CH 14 priciple agent problem

Consider constraint (iii) , the manager’s utility in state θH is v(w*H - g(e*H , θH )) , if he tells the truth , but instead it is v(w*L - g(e*L , θH )) if he instead claims that it is state θL . Thus , he will tell the truth if constraint (iii) holds , that is ; wH - g(eH , θH ) ≥ wL - g(eL , θH ) . The same analysis can hold for constraint (iv) Lemma C.1 ; Constraint (ii) can be ignored : taking into account constraint (i) and (iii) and knowing that state H is less harder than state L and do have less disutility or , g(eL , θH ) < g(eL , θL ) ; wH - g(eH , θH ) ≥ wL - g(eL , θH ) ≥ wL - g(eL , θL ) ≥ v-1 (u0) , so constraint (ii) is also satisfied . lemma C.1 can be seen in the following figure ; Mas-collel CH 14 priciple agent problem

V(w - g(e , θL ))=u0 different combination of w and e instate θ L gives utility level u0 w V(w - g(e , θ H ))= u0 different combination of w and e instate θ H gives utility level u0 Constraint 1 V(wL - g(eL , θ H )) > u0 W=V-1 (u0 ) a (wL ,eL) must lie in pink area by Constraint I e (WH , eH ) must lie on or above this indifference curve by constraint III so it is automatically greater than u0 ( utility at point a ) Mas-collel CH 14 priciple agent problem

Lemma C.2 ; An optimal contract in the above optimization ( p. 21) must have wL - g(eL , θL ) = v-1 (u0) . This is obvious from the point that the if wL - g(eL , θL ) > v-1 (u0) the owner could choose a wage level like w’ which is less than the w by a very small amount ( ∆) and get profit and constraint I could still satisfied if ( ∆) was very small enough . Now if this contract is optimal so the original contract could not be optimal . If the original contract is optimal this could not happen . Lemma c.3 ; In any optimal contract : eL ≤ e*L ; that is , the manager effort level in state θL (eL ) is no more than the level that would arise if θ were observable (e*L ) . eH = e*H ; that is , the manager’s effort level in state θH (eH ) is exactly equal to the level that would arise if θ were observable (e*H ) Mas-collel CH 14 priciple agent problem

b V(wH - g(eH , θH )) V(w - g(e , θL ))=u0 W V(w H - g(eH , θL )) V(wL - g(eL , θ H )) > u0 c V(w - g(e , θ H )) = u0 (w’L , e’L ) should lie on this line by lemma C.2 V-1 (u0 ) (w’L ,e’L) e The outcome for state θH : (wH , eH ) , will lie in this area (abc) because of constraints III and IV (truth telling constraints ) . Mas-collel CH 14 priciple agent problem

Part (i) e’L ≤ e*L V(w’L - g(e’L , θ H ))= uH > u0 V(w - g(e , θL ))=u0 ( wH , eH ) W Iso-profit curves any effort level greater than e*L like (e’L ) can not exist , because the owner can always move to higher level of profit and reach to e*L effort level . W*L V-1 (u0 ) (w’L ,e’L) e e*L e’L All the constraints are still satisfied at this point Mas-collel CH 14 priciple agent problem

HIDDEN INFORMATION part II ; eH = e*H W
V(w - g(e , θ H ))= v(w’L - g(e’L ,θH) part II ; eH = e*H b c W Πe (e) – w = ΠH V(w - g(e , θL ))=u0 (W*H , e*H ) W*H (w’L ,e’L) The owner problem is to find the location for wH , eH in the abc region that maximizes his profit in state H . The solution occurs at a point of tangency between the manager ‘s state θH indifference curve through point (w’ L ,e’L) and an iso-profit curve for the owner this tangency occurs at (W*H , e*H ) and necessarily involves effort level e*H . a V-1 (u0 ) e*L e e’L e*H Mas-collel CH 14 priciple agent problem

HIDDEN INFORMATION Lemma C.4 ; In any optimal contract , eL < e*L ; that is , the effort level in state θL is necessarily strictly below the level that would arise in state θL if θ were observable . W (W*L , e*L ) V(w - g(e , θL ))=u0 a V(w - g(e , θ H ))= uH > u0 b Iso-profit curves (W*H , e*H ) V-1 (u0 ) e*L e*H e State θL profit Starting from points a and b which is compatible with lemma 2 and lemma c.3 State θH profit > State θL profit The owner’s overall expected profit is the weighted average of these two profit ( weights = probability of the happening of each state . Mas-collel CH 14 priciple agent problem

HIDDEN INFORMATION A change in the state level θL outcome that lowers this state’s effort level to one slightly below e*L necessarily raises the owner’s expected profit . Iso-profit curves W (W*L , e*L ) V(w - g(e , θL ))=u0 V(w - g(e , θ H ))= uH > u0 a (W’L , e’L ) Since this curve have shifted to the right ( point b changes to point d b d (W*H , e*H ) V-1 (u0 ) e’L e*L e*H e Moving from point b to point d will lower the profit in state L . This will cause relaxing the incentive constraint in state H and enable the owner to lower the wage in state H (which lies on this line) . 29 Mas-collel CH 14 Mas-collel CH 14 priciple agent problem priciple agent problem

HIDDEN INFORMATION A change in the state level θL outcome that lowers this state’s effort level to one slightly below e*L necessarily raises the owner’s expected profit . W (W*L , e*L ) V(w - g(e , θL ))=u0 a V(w - g(e , θ H ))= uH > u0 (W’L , e’L ) b c Iso-profit curves (W*” H , e*H ) d V-1 (u0 ) W*0H , e*H e*L e*H e e’L relaxing the incentive constraint in state H enables the owner to lower the wage in state H and increasing the profit level in this state (moving from point a to point c ). It could be shown that increase in the profit level in state H outweighs decrease in state L (since we have started from point b which is the tangency point for state θL) and overall expected profit will increase. The lower is eL the higher is expected profit . How far should the owner go in lowering eL 30 30 Mas-collel CH 14 Mas-collel CH 14 Mas-collel CH 14 priciple agent problem priciple agent problem priciple agent problem

How far should the owner go in lowering e .The owner must weight the marginal loss in state θL against the marginal gain in state θH . In particular , the greater the likelihood of state θH , the more the owner is willing to distort the state θL outcome to increase profit in state θH . In the extreme case in which the probability of state θL get close to zero , the owner must set eL = 0 and hire the manager to work only in state θH . It could be shown that the optimum level of eL satisfies the following F.O.C. condition ; The first term of this expression is zero at eL = e*L (page 16 ) and is strictly positive at eL < e*L ; the second term is always strictly negative . Thus we must have eL < e*L to satisfy the condition . These findings are summarized in preposition C.3 : Mas-collel CH 14 priciple agent problem

preposition C.3 ; In the hidden information principle –agent model with an infinitely risk-averse manager the optimal contract sets the level of effort in state θH at its first best level e*H (full observability ). The effort level in state θL is distorted downward from its first best level e*L . In addition, the manager is inefficiently insured . Receiving a utility greater than u0 in state θH ( page 23 ) and a utility equal to u0 in state θL . The owner's expected payoff is strictly lower than the expected payoff he receives when θ is observable , while the infinitely risk-averse manager ‘s expected utility is the same when θ is observable. because of higher wage payment that the owner makes because the manager has a utility in state θH in excess of u0 . Mas-collel CH 14 priciple agent problem

THE MONOPOLISTIC SCREENING MODEL U= w – g(t , θ) where t=task level which the worker faces , w= wage level , u0 = reservation level of utility of the worker , θH = high productivity workers , θL = low productivity workers Fraction of θH = λ ; (0,1). Firm’s profit can not be observed publicly ; πH (t)= for type θH and πL (t) = for type θL worker . For example we could have πi (t) = θi (1-μt) , in which μ>0 . The firm can restrict its attention to offering a menu of wage-task pairs [ (wH , tH ) , (wL , tL ) ] to solve the following optimization ; Max λ[πH (tH ) – wH ] + (1 – λ)[πL (tL ) – wL ] (wH , tH) ≥0 , (wL , tL) ≥0 s.t. (i) wL - g( tL , θL ) ≥ u0 (ii) wH - g( tH , θH ) ≥ u0 (iii) wH - g( tH , θH ) ≥ wL - g( tL , θH ) (iiii) wL - g( tL , θL ) ≥ wH - g( tH , θL ) Mas-collel CH 14 priciple agent problem

Other applications ; 1- consumer of type θ has utility function of the type ; u(x,θ) – T , buying x from the monopoly and paying him a total payment of T . The reservation level of utility for the consumer is zero when x=0 . The monopolist has a constant unit cost of c and seeks to offer a menu of (xi ,Ti )pairs to maximize its profit . The monopoly problem takes the form of above optimization when ti = xi , wi = -Ti , u0 = 0 , g(ti , θi ) =- u(xi ,θi ) , πi (ti ) = -cxi . HIDDEN ACTION AND HIDDEN INFORMATION In these models both the state θ and also the effort level e are unobservable . Now if the profits be an stochastic function of effort , described by the conditional utility function . In essence , what we now have is a hidden action model , but one in which the owner also does not know something about the disutility of the manager (which is captured in the state variable θ ). The owner can now restrict attention to the following form ; Mas-collel CH 14 priciple agent problem

(i) after the state θ is realized , the manager announces which state has occurred . (ii) the contract specifies for each possible announcement , the effort level e( ) that the manager should take and a compensation scheme (iii) in every state θ , the manager is willing to be both truthful in stage (i) and obedient following stage (ii) . The contract is such a way that it is optimal for the manager to choose the effort level e(θ) in state θ . Suppose that effort is unobservable but the relationship between effort and profit is deterministic, given by the function π(e) . In that case for any particular announcement θ* , it is possible to induce any wage –effort pair that is desired , say ( w* , e* ) , by use of a simple forcing compensation scheme : reward the manager with a wage payment of w* if profits are π(e* ) and give him a wage payment of zero otherwise . Thus the combination of the observability of П and the one-to-one relation between П and e effectively allows the contract to specify e . This is like the optimization problem in page 21. Mas-collel CH 14 priciple agent problem

Hidden Information and Monopolistic Conpetition
Mas-collel CH 14 priciple agent problem

HIDDEN ACTIONS (MORAL HAZARD )

Similar presentations

Presentation on theme: "HIDDEN ACTIONS (MORAL HAZARD )"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

HIDDEN ACTIONS (MORAL HAZARD )

Similar presentations

Presentation on theme: "HIDDEN ACTIONS (MORAL HAZARD )"— Presentation transcript:

Similar presentations

About project

Feedback