Teoria das organizações e contratos

Transcription

1 Teoria das organizações e contratos Chapter 5: The Moral Hazard Problem: Applications Mestrado Profissional em Economia 3 o trimestre 2015 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

2 Outline 1 Incentives for managers 2 Fishing contracts between countries 3 Rationing in the credit market 4 Outside Financing: Private benefit and moral hazard 5 Moral hazard in teams EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

3 Outline 1 Incentives for managers 2 Fishing contracts between countries 3 Rationing in the credit market 4 Outside Financing: Private benefit and moral hazard 5 Moral hazard in teams EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

4 Shareholders contracting a manager Consider a firm owned by shareholders Their objective is to obtain the greatest possible profit This depends on how the firm is managed Shareholders are not qualified to run the firm They need to hire a manager EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

5 The manager s effort is not contractible We consider a situation where the manager s effort is not verifiable We have a moral hazard situation Shareholders are assumed to be risk-neutral and the manager is risk-averse The efficient risk-sharing is to pay a fixed amount to the manager This may not be compatible with incentives to exert the optimal effort level EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

6 Agent s preferences The manager s utility function is of the form U(w, e) = u(w) v(e) The payment is w The effort level is e 0 Analysis of market conditions Search for the best conditions from suppliers Strategy of the firm (investment, marketing) Assumption u > 0, u > 0, v > 0, v > 0, v(0) = 0 and v (0) = 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

7 Verifiable variables The shareholders may need to provide incentives One way is to include the result of the manager s effort in his payment It could be the firm s profits or sales We assume that sales are verifiable Usually the profits (or the value of the firm) are difficult to control and verify EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

8 Shareholders profits Take the form B(x, w) = px cx w There is a competitive market for the firm s product The firm takes the price p of the product as given Sales are represented by x X (an interval) The marginal cost is c (assumed to be constant) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

9 Sales Sales depend on the agent s effort and a random variable We assume that the distribution of sales is represented by a density function f(x, e) z Prob ({x z} e) = f(x, e)dx 0 In particular, we have E[g(x) e] = g(x)f(x, e)dx for any (measurable and bounded) function g( ) X EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

10 Symmetric information: optimal wage Assume that the shareholders can contract on the effort level Fix an effort e chosen by shareholders The problem of the optimal wage scheme is [px cx w(x)]f(x, e)dx subject to max w( ) X participation constraint u(w(x))f(x, e)dx U + v(e) X EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

11 Symmetric information: optimal wage The problem is convex There is a Lagrange multiplier λ 0 such that w ( ) is a solution to the problem of the shareholders if and only if 1 w ( ) solves the problem max [px cx w(x) + λu(w(x))] f(x, e)dx w( ) X (L) 2 We have [ ] λ u(w (x))f(x, e)dx v(e) U = 0 X EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

12 Symmetric information: optimal wage w solves (L) if and only if x X, w (x) argmax{ w + λu(w) : w R} A necessary and sufficient condition is x X, λu (w (x)) = 1 Implying that w ( ) must be constant w(e), w ( ) = w(e) The value w(e) is given by the binding participation constraint (observe that λ > 0) u(w(e)) = U + v(e) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

13 Symmetric information: optimal effort Shareholders incorporate in their maximization problem that the optimal wage scheme is given by w(e) They solve the following problem max [px cx]f(x, e)dx u 1 (U + v(e)) e X The optimal effort e satisfies the necessary condition [px cx]f e(x, e v (e ) )dx = u (u 1 (U + v(e )) X where f e(x, e) := f (x, e) e EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

14 Moral hazard When the manager s effort is not verifiable Shareholders need to add the incentive compatibility constraint u(w(x))f(x, e)dx v(e) u(w(x))f(x, e )dx v(e ) (IC) X for every effort e We assume the first order approach is valid and replace (IC) by u(w(x))f e(x, e)dx v (e) = 0 (FO) X X EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

15 Moral hazard Denote by λ and µ the Kuhn-Tucker multipliers of (IC) and (FO) respectively Fix an arbitrary effort level e A necessary condition for an optimal wage contract w ( ) is f(x, e) + λu (w (x))f(x, e) + µu (w (x))f e(x, e) = 0 Or, equivalently, for any sales level x 1 u (w (x)) = λ + e(x, e) µf f(x, e) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

16 Moral Hazard If µ > 0 then 1 manager s wage must depend on sales If the function x f e(x, e) f(x, e) is increasing in x then the wage is also increasing in x This property means that greater sales in general signals greater effort In that case, the manager receives a bonus (possibly variable) according to sales This is the case if x = e + ε where ε N (0, σ) { f(x, e) = 1 σ 2π exp 1 ( ) } x e 2 2 σ 1 If the FO approach is valid, we necessarily have µ > 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

17 Outline 1 Incentives for managers 2 Fishing contracts between countries 3 Rationing in the credit market 4 Outside Financing: Private benefit and moral hazard 5 Moral hazard in teams EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

18 Coastal and Fishing States The coastal state (CS) has the legal property right to exploit exclusive territorial waters with large resources However, the CS does not have the appropriate technology (fleet) The fishing state (FS) has the appropriate technology but has no resources in its exclusive territorial There are gains to trade: the CS can allow the FS to exploit its territorial waters in exchange of an amount to be paid by the FS EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

19 Verifiable and unverifiable variables The CS cannot directly observe the effort e exerted in the activity Effort is an indication of the labour and capital used in the activity capacity of the boat, size of the nets, number of trips made Effort is not observable but the catch x is The fish must be unloaded and weighted at some particular predetermined port The set of possible efforts is E = {e 1,..., e m } The set of possible catches is X = {x 1,..., x n } Effort influences the level of catch but environmental conditions too (climate, location of the stock) p j (e) := Prob({x j } e) and p(x e) := Prob({x} e) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

20 Preferences of the CS The stock is renewable subject to its own particular laws of growth (reproduction) The decrease in the stock generated by fishing is a loss to the CS The monetary equivalent of the loss due to a catch x is represented by β(x) Denote by T ( ) the revenue obtained from the contract: the function T ( ) can depend on the catch x The principal is the CS who is assumed to be risk-neutral The objective function is then represented by E[T (x) β(x) e] := x X p(x e)[t (x) β(x)] = n p j (e)[t (x j ) β(x j )] j=1 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

21 Preferences of the FS The FS is the agent The costs in utility terms of exerting effort e is v(e) Risk-aversion is represented by a concave Bernoulli function u The objective function is U(x, e) := u(px T (x)) v(e) The exogenous market price of one unit of catch is p The reservation utility U indicates the possibility of not fishing, or fishing in other waters Assumption u > 0, u < 0, v > 0, v 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

22 Moral Hazard The FS is not worried about preserving the stock level Given that effort is not verifiable, there is a tendency to fish too much The CS will attempt, via the contract, to limit the damage done to the stock EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

23 Optimal contract under symmetric information Denote by e the effort the CS would like the FS to exert The CS should then solve the following maximization problem p(x e )[T (x) β(x)] subject to max T ( ) x X the participation constraint p(x e )u(px T (x)) v(e ) U x X (PC) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

24 Optimal contract under symmetric information There exists a Lagrange multiplier λ 0 such that 1 u (px T (x)) = λ This implies that the participation constraint is binding (λ > 0) There exists k > 0 such that T (x) = px k The CS makes a constant payment k to the FS, and receives the outcome EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

25 Optimal contract under moral hazard Denote by e the effort the CS would like the FS to exert The CS should then solve the following maximization problem p(x e )[T (x) β(x)] subject to max T ( ) x X the participation constraint p(x e )u(px T (x)) v(e ) U x X the incentive compatibility constraint x X p(x e )u(px T (x)) v(e ) x X for every e i E (PC) p(x e i )u(px T (x)) v(e i ) (IC) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

26 Optimal contract under moral hazard There exists λ 0 and µ e 0 for each effort e such that 1 u (px T (x)) = λ + e E µ e p(x e ) p(x e i ) p(x e ) The participation constraint is binding (λ > 0) Assume that µ e = 0 for every lower effort e < e (?) We then have 1 u (px T (x)) = λ + µ e p(x e ) p(x e) p(x e ) e>e EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

27 Optimal contract under moral hazard Restrict attention to X = {x l, x h } with x l < x h We assume that the greater is the effort, the easier it is to get a large catch e > e, p(x h e ) p(x h e) < 0 This implies that T (x h ) T (x l ) > px h px l The increase in the payment due is greater than the increase in revenue EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

28 Optimal contract under moral hazard If the FS gets too many fish, it would prefer to throw the excess back into the sea instead of taking it to the port This is because it would lead to an increase in the tax that is greater than the market worth of the excess Therefore, the CS cannot observe the true result It only observes what the FS brings to the port, which could be less than what was really caught EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

29 Outline 1 Incentives for managers 2 Fishing contracts between countries 3 Rationing in the credit market 4 Outside Financing: Private benefit and moral hazard 5 Moral hazard in teams EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

30 Credit rationing We say that a firm s credit is rationed if it cannot obtain all the money it wants even though it is prepared to pay more than the current market rate of interest Why the banking sector does not raise interest rates? Moral hazard is a possible explanation EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

31 Investment projects Consider an entrepreneur who can choose between two investment projects, a and b Both projects require an investment of I to be carried out For each project i {a, b}, the random result is represented by a random variable X i that can take two values X i {0, X i } with Prob{ X i = X i } = p i EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

32 Investment projects Project a is less risky 1 > p a > p b > 0 Project b s payoff is greater when successful X b > X a > 0 In expectations, project a is more profitable E[ X a ] > E[ X b ] i.e., p a X a > p b X b EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

33 The terms of the contract The entrepreneur must borrow to invest the amount I The (gross) interest payment, denoted by R, will be paid only if the project is successful The bank (lending to the entrepreneur) cannot get payments out of a bankrupt firm EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

34 Expected payoffs All participants are risk-neutral The expected payoff of the entrepreneur when project i is started: U(R, i) = p i (X i R) The bank s expected profits is Π(R, i) = p i R I There is a single bank that is a monopolist The bank is the principal and the entrepreneur is the agent EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

35 Symmetric information Assume the bank not only chooses the interest rate R but also the project i The outside option of the entrepreneur is normalized to 0 The optimal contract of the bank is to choose project a to charge the interest R = Xa The bank extracts all the surplus and gets the profits p a X a I The entrepreneur gets its reservation utility EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

36 Moral hazard: entrepreneur s optimal choice The entrepreneur s choice of project is not verifiable The debt contract cannot be made contingent on the project chosen Once the interest payment R has been fixed, the entrepreneur chooses the project to maximize his payoff Project a is chosen if, and only if, p a (X a R) p b (X b R) i.e., R ˆR := p ax a p b X b p a p b Observe that ˆR < X a EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

37 Moral hazard: optimal contract The bank s profits are then p a R I if 0 R ˆR Π (R) = p b R I if ˆR < R Xb The participation constraint prevents the entrepreneur to accept any contract involving interest R > X b EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

38 Moral hazard: optimal contract EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

39 Moral hazard: optimal contract The bank chooses R to maximizes its expected profits The function Π ( ) has two local maxima Comparing this local maxima, we get ˆR if p a ˆR > pb X b R = X b if p a ˆR < pb X b EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

40 Moral hazard: credit rationing Assume that the total amount of money L the bank can lend is fixed Assume that I L < NI where N is the number of entrepreneurs (all identical) The bank cannot lend to everyone If the optimal interest is R = X b, then the entrepreneurs getting loans and the others have the same expected utility In that case, there is no real credit rationing: entrepreneurs are indifferent between asking for a loan or not EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

41 Moral hazard: credit rationing Assume now that primitives are such that the optimal interest is R = ˆR The payoff of an entrepreneur that obtains a loan is U( ˆR, a) = p a (X a ˆR) > 0 All entrepreneurs will ask for a loan The demand for loanable funds is NI The offer is L < NI Some entrepreneurs are denied access to credit, although they are ready to pay more than the market rate ˆR Banks voluntary decide not to increase interest rates EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

42 Limited commitment We have inefficiencies under moral hazard The market interest rate is either higher (R = X b ) or lower (R = ˆR) than the efficient level X a These inefficiencies occur although both the agent and the principal are risk-neutral The standard efficient contract (franchise-type) cannot be implemented due to the limited commitment condition The bank cannot require the entrepreneur to make a payment in case of failure (bankruptcy) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

43 Outline 1 Incentives for managers 2 Fishing contracts between countries 3 Rationing in the credit market 4 Outside Financing: Private benefit and moral hazard 5 Moral hazard in teams EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

44 The fixed-investment model: the entrepreneur An entrepreneur (the borrower or insider) has a project which requires a fixed investment I The entrepreneur has assets (cash in hand) A < I that can be invested or consumed To implement the project, the entrepreneur needs to borrow at least I A from lenders EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

45 The fixed-investment model: the project If undertaken, the project may succeed and yield verifiable income R fail and yield no income The entrepreneur can behave or misbehave behave: work, exert effort, take no private benefit misbehave: shirk, take private benefit Behaving yields probability p h of success and no private benefit to the entrepreneur Misbehaving yields a probability p l < p h of success and private benefit B > 0 to the entrepreneur. The private benefit can be interpreted as a disutility of effort saved by the entrepreneur by shirking We let p = p h p l EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

46 Private benefit Another possible interpretation of private benefit is as follows: the entrepreneur chooses between a project with a high probability of success and another project which he prefers because it is easier to implement is more fun benefits a friend delivers perks is more glamorous EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

47 The fixed-investment model: preferences Implicitly there are two time periods t {0, 1} At t = 0 the investment occurs (and agents consume) At t = 1 the project yields income (and agents consume) Both type of agents, investors and entrepreneurs have no time preference and are risk neutral, i.e., U(c 0, c 1, Q) = c 0 + E Q [c 1 ] where Q is the objective probability on exogenous uncertainty (success or failure) that may depend on the entrepreneur s action (behave or not) { ph if the entrepreneur behaves Q(sucess) = if the entrepreneur does not behave p l EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

48 The fixed-investment model: lenders Several (perfect competition) prospective lenders compete for issuing a loan to the borrower If there is a loan offer, it must maximize the entrepreneur s payoff under the participation constraints Otherwise the borrower could turn to an alternative lender The entrepreneur makes a take it or leave it offer to some lender The rate of return expected by investors is 0 (they are indifferent between consuming today or tomorrow): An investor is willing to lend 1 at t = 0 in exchange of a random stream w = (w s, w s ) satisfying E Q [w] = 1 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

49 The fixed-investment model: sharing income There is limited liability for the borrower: both sides receive 0 in case of failure In case of success, the two parties share benefits Rb 0 goes to the borrower R l 0 goes to the lender Nothing is lost: R = R b + R l There is an incentive scheme for the entrepreneur: R b in case of success, 0 in case of failure EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

50 The fixed-investment model: the timing 1 Loan agreement (sharing rule) 2 Investment 3 Moral hazard: entrepreneur s behavior 4 Outcome and benefit sharing EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

51 The fixed-investment model: net present value We assume that the project is viable only in the absence of moral hazard, i.e., we assume that the project has positive NPV if the entrepreneur behaves, p h R I > 0 the project has negative NPV if the entrepreneur does not behave, even including private benefit, p l R I + B < 0 As a consequence, the entrepreneur and the lender cannot agree on a loan that gives an incentive to the borrower to misbehave since for any sharing rule (R b, R l ) [p l R l (I A)] + [p }{{} l R b + B A] < 0 }{{} lender s NPV borrower s NPV EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

52 The lender s credit analysis The loan contract should provide incentives to the entrepreneur for behaving Assume that agents agree on a loan contract (R b, R l ), the borrower faces the following tradeoff misbehaving to get the private benefit B but this reduces the probability of success: the expected return is p l R b + B behaving, in that case the expected return is p h R b EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

53 Incentive compatible constraint The loan contract (R b, R l ) is granted only if the following incentive compatible constraint is satisfied: p h R b p l R b + B or ( p)r b B The entrepreneur stake in the firm s income should be large enough The highest income that can be pledged to the lenders without jeopardizing the borrower s incentive is then R B p and the expected pledgeable income is then ( P = p h R B ) p EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

54 Individual rationality constraint In order to be willing to finance the project, the following individual rationality constraint should be satisfied ( P p h R B ) I A p This constraint is also called breakeven constraint or participation constraint EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

55 Necessary condition A necessary condition for the financing to be arranged is We will assume that A A = p h B p (p hr I) A > 0 p h R I < p h B p the NPV if the borrower behaves is smaller than the minimum expected rent that must be left to the borrower to provide him with an incentive to behave The borrower must have enough assets in order to be granted a loan EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

56 Credit rationing: assume A < A The project may have positive NPV and yet it cannot be financed With insufficient assets, the entrepreneur must borrow a large amount and therefore pledge a large fraction of the return in case of success The entrepreneur then keeps a small fraction of the income and is demotivated The two parties cannot find a loan agreement that both induces effort allows lenders to recoup investment There is credit rationing, the borrower may be willing to give a high fraction of the return to the lenders, i.e., pay a high interest rate but the lenders do not want to grant such a loan EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

57 Optimal contract Assume that the borrower has enough assets, i.e., A > A then the entrepreneur can secure financing The entrepreneur offers claim R l to competitive investors so as not to leave them with a surplus: The entrepreneur stake is then p h R l = I A R b = R R l = R I A p h and induces him to behave One only lends to the rich R I A p h = B p EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

58 Agency rent Recall that A = p h B p (p hr I) B The term p h p is the minimum expected monetary payoff to be left to the borrower to preserve incentives. This is called the agency rent The term p h R I is the expected monetary profit of the project The borrower should make a sufficiently high initial contribution A to reduce the agency rent p h B p below the expected monetary profit (p h R I) + A EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

59 Expected net payoff If we define Π b the expected net payoff (of the borrower) by subtracting the consumption utility A to the expected payoff, then we get { 0 if A < A Π b = p h R b A = p h R I if A A By the competition hypothesis, lenders have zero profits and the borrowers perceive the entire social surplus or NPV if the project is funded EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

60 Full investment of entrepreneurial assets Consider that the borrower consumes c A and invests only A c If the project is still funded, the borrower still obtains the entire NPV, i.e., p h R I However, it becomes more difficult to obtain a loan since A should now exceed A + c Therefore, the entrepreneur cannot gain by not investing her entire wealth in the project But the project may not be funded if c is such that A c < A EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

61 Dilution and overborrowing: deepening investment Assume that the project is funded through a loan contract (R b, R l ) where the borrower s stake satisfies the incentive-compatibility constraint R b B/ p Suppose there is an opportunity for deepening investment the new investment costs an extra J it increases the probability of success by τ Assume that this deepening investment is inefficient in the sense that its net cost C 1 is positive, i.e., C 1 J τr > 0 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

62 Covenants Usually, the debt contract with the initial lenders includes covenants prohibiting the dilution of creditor s through the issue of new securities. There are two reasons Lenders don t want the borrower to issue claims that have a higher seniority as theirs, as this reduces the amount they can collect More subtle, the issue of new securities may alter managerial incentives and then the probability of success EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

63 Dilution and overborrowing: timing 1 Borrower has wealth A and borrows I A from initial lenders. The loan contract allocates the return R (in the case of success) between borrower R b and lenders R l 2 Borrower can contract with new lenders to finance deepening investment J. If so, the new loan contract allocates the stake R b between the borrower R b and new lenders R l 3 Moral hazard: the borrower behaves (p = p h and no private benefit) or misbehaves (p = p l and private benefit) 4 Outcome: success with probability p + τ or failure with probability 1 p τ EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

64 Overborrowing and managerial incentives The new investment reduces the total value by C 1. Someone must loose in the process. The borrower cannot still behave. If he behaves, the expected value of initial investors claim is increased to (p h + τ)r l Either the new lenders loose or the borrower looses. It cannot be the new lenders, otherwise the new loan would not be funded The borrower misbehaves and there is another cost C 2 = ( p)r B EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

65 Gains from overborrowing In case of success, the borrower s stake R b is diluted into R b + R l Assuming that the entrepreneur makes a take it or leave it offer to the the new lenders, then (p l + τ) R l = J The entrepreneur gains from overborrowing if or equivalently (p l + τ) R b + B > p h R b [(p l + τ)r b J] + B > p h R b or [p h (p l + τ)] R l > C 1 + C 2 EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

66 Interpretation The term C 1 + C 2 is the total cost of refinancing: direct cost plus incentive cost The term [p h (p l + τ)] R l is the (negative) externality on the initial investors Recall that R b = R (I A)/p h If the borrower s balance sheet measured by A improves, R b increases and R l decreases The sufficient condition for reinvestment is less likely to be satisfied In the absence of negative covenants, overborrowing is more likely to happen with weak borrowers EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

67 Outline 1 Incentives for managers 2 Fishing contracts between countries 3 Rationing in the credit market 4 Outside Financing: Private benefit and moral hazard 5 Moral hazard in teams EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

68 Moral hazard in teams Holmstrom, B. Moral hazard in teams Bell Journal of Economics (1982) Find a scheme to compensate team members When individuals cannot observe the effort level of others They can observe only the total output of the team EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

69 Moral hazard in teams: technology A finite set I of agents Each agent i chooses an action or effort e i R + The team s monetary reward x depends on the effort of each agent x : e = (e i ) i I x(e) R + We assume that x is continuous, strictly increasing, concave, and differentiable EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

70 Moral hazard in teams: taste Quasi-linear utility U i (t i, e i ) = t i v i (e i ) t i is the compensation received by team member i v i (e) is the minimum compensation needed to induced agent i to exert effort level e i We assume that v i is continuous, strictly increasing, convex, and differentiable EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

71 Moral hazard in teams: allocations An allocation is a pair (t, e) with t = (t i ) i I and e = (e i ) i I such that t i x(e) i I Compensation must be derived from the team s output Definition An allocation (t, e) is efficient (Pareto optimal) if there does not exist another allocation (t, e ) which Pareto dominates (t, e), i.e., U i (t i, e i) U i (t i, e i ) for each i, with a strict inequality for at least one team member EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

72 Moral hazard in teams: efficient allocations Proposition An allocation (t, e ) is efficient if and only if e maximizes total surplus S(e) = x(e) v i (e i ) i I and total reward is fully distributed t i = x(e ) i I Assumption A total surplus maximizer e R I ++ exists and the surplus is positive x(e ) v i (e i ) > 0 i I EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

73 Moral hazard in teams: incentives Only output is observable: compensation can depend only on the total output A sharing rule is a function s : R + R I satisfying s i (x) x i I It is exact when we have an equality s i (x) is agent i s compensation when the total output is x EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

74 Moral hazard in teams: implementation A sharing rule s defines a non-cooperative game Strategies are effort levels Payoffs are given by π i (e i, e i ) = s i (x(e i, e i )) v i (e i ) Definition A sharing rule s implements effort vector ē when ē is a Nash-equilibrium, i.e., ē i argmax{s i (x(e i, ē i )) v i (e i ) : e i 0} EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

75 Moral hazard in teams: incentives vs. efficiency Theorem If e R I ++ maximizes surplus then there is no sharing rule satisfying exact budget balance which implements e EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76

76 Moral hazard in teams: breaking the budget If we are willing to throw away money, there are many sharing rules that implement e Choose b i satisfying i I, b i > v i (e i ) and b i < x(e ) i I Define s i (x) = { bi if x x(e ) 0 if x < x(e ) EESP (FGV) Teoria das organizações e contratos 3 o trimestre / 76