EC516 Contracts and Organisations for Research Students: Lecture 3 - PowerPoint PPT Presentation

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli LSE, D6 5 March 2009

Filling the Gaps EC516 Contracts and Organisations In all models we have seen so far courts of law are for Research Students: assigned the role of passive enforcers of what the Lecture 3 contracting parties write in their contract. Leonardo Felli Filling the Gaps Indeed, with “perfect” (complete) contracts, Courts have A Model of little to do ⇒ Enforce all that parties write. Insurance Disclosure Precedents Model With complete contracts, the Court’s behaviour is First Best Passive Court extremely simple: Any breach is punished very severely . Active Court Ambiguous Courts Menu Contracts We need “imperfect” (incomplete) contracts to identify a realistic role for a Court (Grossman, Hart and Moore).

EC516 Contracts and Organisations In reality, courts regularly intervene in contracts at the for Research behest of one of the contracting parties to void, or Students: Lecture 3 otherwise modify, an agreement the parties have agreed to. Leonardo Felli Filling the We now consider a Court that insures the parties against Gaps A Model of unforeseen changes in the environment between the time Insurance Disclosure when the agreement was reached and the time when it is Precedents to be consummated. Model First Best Passive Court Active Court Ambiguous Clearly renegotiation is an alternative way to achieve the Courts Menu Contracts same objective, but does not protect the parties from the fluctuations in utility (insurance).

EC516 Contracts and We consider now a contracting model in which the court is Organisations for Research an active player. Students: Lecture 3 Leonardo Felli We characterize the decision rule for an optimally designed court. Filling the Gaps A Model of Insurance We are going to focus on the classic tradeoff between Disclosure insurance and incentives. Precedents Model First Best Passive Court We assume a simple court that can only uphold or void a Active Court Ambiguous contracts (detail-free court). Courts Menu Contracts The key risk is going to be the possibility of unforeseen contingencies.

The Setup: EC516 Contracts and One risk neutral buyer and one risk averse seller, V ( · ), Organisations for Research they trade one widget. Students: Lecture 3 Leonardo Felli Valuations: Filling the Gaps ∆ = v H − c H = v N − c N = v L − c L . A Model of Insurance Disclosure where Precedents Model c H ≥ c N ≥ c L . First Best Passive Court Active Court Ambiguous Courts The buyer may undertake a non-contractible investment Menu Contracts e ∈ [0 , 1] that increases value of the widget by ( e R ) and costs ψ ( e ) .

The structure of Uncertainty: EC516 Contracts and Organisations State space is unit circle Ω. Element ω . for Research Students: Lecture 3 Leonardo Felli Unforeseen contingency Θ is an interval in Ω with center x and width θ : Filling the Gaps A Model of ω Insurance Ω q Disclosure Precedents Model First Best ❵ Passive Court q Active Court Ambiguous Courts Θ Menu Contracts q

EC516 Contracts and If ω �∈ Θ then cost is c N and v N = c N + ∆. Organisations for Research Students: If ω ∈ Θ then cost is: Lecture 3 Leonardo Felli c H and v H = c H + ∆ Filling the ✸ ✑ Gaps ✑✑✑✑ q H A Model of Insurance Disclosure κ ❍❍❍❍ r Precedents Model 1 − q H ❍ ❥ First Best c L and v L = c L + ∆ Passive Court Active Court Ambiguous Courts Menu Contracts x and ω are uniformly distributed on unit circle. θ is uniformly distributed on [0 , 1 / 2]. (¯ θ = 1 / 4.)

EC516 Size of change in cost and value does depend on θ . Contracts and Organisations for Research c H ( θ ) , c L ( θ ) Students: Lecture 3 Leonardo Felli for given θ the expected cost is c N : Filling the q H c H ( θ ) + (1 − q H ) c L ( θ ) = c N Gaps A Model of Insurance Disclosure Precedents if θ = 1 / 2 no risk: Model First Best Passive Court Active Court c H (1 / 2) = c L (1 / 2) = c N , Ambiguous Courts Menu Contracts if θ = 0 infinite risk: θ → 0 c H ( θ ) = − lim lim θ → 0 c L ( θ ) = + ∞

Timing: EC516 Contracts and Organisations for Research The court publicly announces the decision rule she will Students: Lecture 3 follow to settle a possible dispute (precedents). Leonardo Felli Filling the Negotiation between the contracting parties occurs. Gaps A Model of Insurance Disclosure Precedents The buyer chooses e . Model First Best Passive Court Active Court Ambiguous ω is realized and observed by both parties, if ω ∈ Θ they Courts Menu Contracts also observe κ = c i , i ∈ { L , H } .

EC516 Contracts and Organisations for Research The court observes: θ and whether ω ∈ Θ. Students: Lecture 3 Leonardo Felli Each party can bring the other party to court. Filling the Gaps A Model of Insurance Disclosure The court rules on the dispute. Precedents Model First Best Passive Court Active Court The parties renegotiate (if the court voids) and then trade Ambiguous Courts occurs. Menu Contracts

EC516 Contracts and Ex-ante buyer has all bargaining power. Organisations for Research Students: Lecture 3 Ex-post seller has all bargaining power. (We only need the Leonardo Felli opposite not to be true.) Filling the Gaps A Model of Contracts cannot be contingent on the values and costs v i Insurance Disclosure and c i and the unforeseen contingencies Θ. Precedents Model First Best Passive Court The court ex-post can condition her ruling on θ and Active Court Ambiguous whether ω ∈ Θ. Courts Menu Contracts The parties ex-post observe the realization of all uncertainty c i and v i .

Tradeoff: EC516 Contracts and Organisations Ex-post negotiation is enough to insure the seller against for Research Students: the fluctuations in payoffs (full insurance). Lecture 3 Leonardo Felli Ex-ante commitment is the only way to induce the buyer Filling the to exert any effort (incentive problem). Gaps A Model of Insurance An ex-ante contingent contract may achieve first best: full Disclosure Precedents insurance and full incentives, ruled out by incompleteness. Model First Best Passive Court Active Court The seller ex-post appropriates all the gains from trade. Ambiguous Courts Menu Contracts The continuation payoff to the buyer is 0 in every state of nature.

The Optimal Ex-Ante Contract EC516 Contracts and Organisations Contract is: ( p , t ), where p the trading price and t is ex-ante for Research Students: transfer. Lecture 3 Leonardo Felli Take court’s decision rule as given: Filling the Gaps A Model of Insurance Disclosure enforce if ω ∈ Θ and θ ∈ E ⊂ [0 , 1 / 2], Precedents Model First Best Passive Court Active Court enforce if ω �∈ Θ and θ ∈ N ⊂ [0 , 1 / 2], Ambiguous Courts Menu Contracts void otherwise.

EC516 Contracts and In the event of no ex-ante contract: Organisations for Research Students: Lecture 3 Leonardo Felli the effort choice is ˆ e = 0 Filling the Gaps A Model of the seller’s payoff is V (∆) Insurance Disclosure Precedents the buyer’s payoff is 0. Model First Best Passive Court Active Court Ambiguous Courts Let Menu Contracts � � ¯ ¯ (1 − θ ) 2 d θ, θ N = θ E = θ 2 d θ N E

EC516 The parties’ optimal ex-ante contract solves: Contracts and Organisations for Research � ¯ θ N + ¯ B ∗ ( p , t ) = � eR + ∆ + c N − p ] − t − ψ (ˆ max θ E [ˆ e ) Students: Lecture 3 p , t Leonardo Felli V ∗ ( p , t ) ≥ V (∆) s . t . Filling the Gaps e ) = (¯ θ N + ¯ ψ ′ (ˆ θ E ) R A Model of Insurance Disclosure Precedents where Model First Best Passive Court V ∗ ( p , t ) = Active Court Ambiguous Courts � Menu Contracts = θ [ q H V ( p + t − c H ) + (1 − q H ) V ( p + t − c L )] 2 d θ E + ¯ θ N V ( p + t − c N ) + (1 − ¯ θ N − ¯ θ E ) V (ˆ eR + ∆ + t )

EC516 Contracts and Proposition Organisations for Research Students: The optimal ex-ante contract ( p ∗ , t ∗ ) provides the parties with Lecture 3 partial insurance: Leonardo Felli θ N V ′ ( p ∗ + t ∗ − c N ) + Filling the ¯ Gaps A Model of � q H V ′ ( p ∗ + t ∗ − c H ) + (1 − q H ) V ′ ( p ∗ + t ∗ − c L ) Insurance � � + θ 2 d θ Disclosure E Precedents = (¯ θ N + ¯ θ E ) V ′ (ˆ eR + ∆ + t ∗ ) Model First Best Passive Court and hence p ∗ − c N ≥ ˆ Active Court e R + ∆ while the transfer t ∗ is such that Ambiguous Courts Menu Contracts V ∗ ( p ∗ , t ∗ ) = V (∆)

The Optimal Decision Rule for the Court EC516 Given the characterization of ex-ante contract above we move Contracts and Organisations back to the optimal court decision. for Research Students: Lecture 3 Lemma Leonardo Felli It is optimal for the court to always enforce the contract if Filling the Gaps ω �∈ Θ . In other words: A Model of Insurance Disclosure N = [0 , 1 / 2] Precedents Model First Best Passive Court Active Court Ambiguous Intuition: Voiding the contract provides the parties with Courts Menu Contracts insurance but for ω �∈ Θ no insurance is needed. Therefore, the buyer’s incentives are enhanced by upholding the contract.