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

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Filling the Gaps

In all models we have seen so far courts of law are assigned the role of passive enforcers of what the contracting parties write in their contract. Indeed, with “perfect” (complete) contracts, Courts have little to do ⇒ Enforce all that parties write. With complete contracts, the Court’s behaviour is extremely simple: Any breach is punished very severely. We need “imperfect” (incomplete) contracts to identify a realistic role for a Court (Grossman, Hart and Moore).

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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In reality, courts regularly intervene in contracts at the behest of one of the contracting parties to void, or

• therwise modify, an agreement the parties have agreed to.

We now consider a Court that insures the parties against unforeseen changes in the environment between the time when the agreement was reached and the time when it is to be consummated. Clearly renegotiation is an alternative way to achieve the same objective, but does not protect the parties from the fluctuations in utility (insurance).

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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We consider now a contracting model in which the court is an active player. We characterize the decision rule for an optimally designed court. We are going to focus on the classic tradeoff between insurance and incentives. We assume a simple court that can only uphold or void a contracts (detail-free court). The key risk is going to be the possibility of unforeseen contingencies.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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The Setup:

One risk neutral buyer and one risk averse seller, V (·), they trade one widget. Valuations: ∆ = vH − cH = vN − cN = vL − cL. where cH ≥ cN ≥ cL. The buyer may undertake a non-contractible investment e ∈ [0, 1] that increases value of the widget by (e R) and costs ψ(e).

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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The structure of Uncertainty:

State space is unit circle Ω. Element ω. Unforeseen contingency Θ is an interval in Ω with center x and width θ:

❵ q q q

Ω ω Θ

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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If ω ∈ Θ then cost is cN and vN = cN + ∆. If ω ∈ Θ then cost is:

✑✑✑✑ ✑ ✸ ❍❍❍❍ ❍ ❥

κ cH and vH = cH + ∆ cL and vL = cL + ∆

qH 1 − qH

r

x and ω are uniformly distributed on unit circle. θ is uniformly distributed on [0, 1/2]. (¯ θ = 1/4.)

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Size of change in cost and value does depend on θ. cH(θ), cL(θ) for given θ the expected cost is cN: qH cH(θ) + (1 − qH) cL(θ) = cN if θ = 1/2 no risk: cH(1/2) = cL(1/2) = cN, if θ = 0 infinite risk: lim

θ→0 cH(θ) = − lim θ→0 cL(θ) = +∞

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Timing:

The court publicly announces the decision rule she will follow to settle a possible dispute (precedents). Negotiation between the contracting parties occurs. The buyer chooses e. ω is realized and observed by both parties, if ω ∈ Θ they also observe κ = ci, i ∈ {L, H}.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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The court observes: θ and whether ω ∈ Θ. Each party can bring the other party to court. The court rules on the dispute. The parties renegotiate (if the court voids) and then trade

• ccurs.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Ex-ante buyer has all bargaining power. Ex-post seller has all bargaining power. (We only need the

• pposite not to be true.)

Contracts cannot be contingent on the values and costs vi and ci and the unforeseen contingencies Θ. The court ex-post can condition her ruling on θ and whether ω ∈ Θ. The parties ex-post observe the realization of all uncertainty ci and vi.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Tradeoff:

Ex-post negotiation is enough to insure the seller against the fluctuations in payoffs (full insurance). Ex-ante commitment is the only way to induce the buyer to exert any effort (incentive problem). An ex-ante contingent contract may achieve first best: full insurance and full incentives, ruled out by incompleteness. The seller ex-post appropriates all the gains from trade. The continuation payoff to the buyer is 0 in every state of nature.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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The Optimal Ex-Ante Contract

Contract is: (p, t), where p the trading price and t is ex-ante transfer. Take court’s decision rule as given: enforce if ω ∈ Θ and θ ∈ E ⊂ [0, 1/2], enforce if ω ∈ Θ and θ ∈ N ⊂ [0, 1/2], void otherwise.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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In the event of no ex-ante contract: the effort choice is ˆ e = 0 the seller’s payoff is V (∆) the buyer’s payoff is 0. Let ¯ θN =

• N

(1 − θ) 2 dθ, ¯ θE =

• E

θ 2 dθ

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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The parties’ optimal ex-ante contract solves: max

p,t

B∗(p, t) = ¯ θN + ¯ θE

• [ˆ

eR + ∆ + cN − p] − t − ψ(ˆ e) s.t. V ∗(p, t) ≥ V (∆) ψ′(ˆ e) = (¯ θN + ¯ θE) R where V ∗(p, t) = =

• E

θ [qHV (p + t − cH) + (1 − qH)V (p + t − cL)] 2 dθ + ¯ θN V (p + t − cN) + (1 − ¯ θN − ¯ θE) V (ˆ eR + ∆ + t)

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Proposition The optimal ex-ante contract (p∗, t∗) provides the parties with partial insurance: ¯ θN V ′(p∗ + t∗ − cN) + +

• E

θ

• qHV ′(p∗ + t∗ − cH) + (1 − qH)V ′(p∗ + t∗ − cL)
• 2 dθ

= (¯ θN + ¯ θE) V ′(ˆ eR + ∆ + t∗) and hence p∗ − cN ≥ ˆ e R + ∆ while the transfer t∗ is such that V ∗(p∗, t∗) = V (∆)

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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The Optimal Decision Rule for the Court

Given the characterization of ex-ante contract above we move back to the optimal court decision. Lemma It is optimal for the court to always enforce the contract if ω ∈ Θ. In other words: N = [0, 1/2] Intuition: Voiding the contract provides the parties with insurance but for ω ∈ Θ no insurance is needed. Therefore, the buyer’s incentives are enhanced by upholding the contract.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Lemma The optimal decision rule for the court is such that there exists a θ∗ ∈ (0, 1/2) such that the court will: enforce the ex-ante contract if ω ∈ Θ and θ ≥ θ∗ void the ex-ante contract it if ω ∈ Θ and θ < θ∗ Intuition: The loss in incentives only depend on the expected probability with which the contract is voided ¯ θN + ¯ θE

• .

The gains from insurance are greater the smaller is θ. In other words: E = [θ∗, 1/2].

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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We still need to show that 0 < θ∗ < 1/2. If θ∗ → 1/2 gains from insurance vanishing, while loss in incentives is strictly positive. If θ∗ → 0 the gains from insurance are increasing unboundedly, while the loss in incentives does not exceed R. We have now all the elements to characterise the Court’s

• ptimal decision rule.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Proposition The optimal decision rule for the court exists and it is unique. The court upholds the ex-ante contract if a contingency ω ∈ Θ occurs. If an unforeseen contingency arises, ω ∈ Θ, the court voids the contract if θ < θ∗ and upholds the contract if θ ≥ θ∗. Moreover θ∗ ∈ (0, 1/2)

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Notice that θ at the same time measures: how exceptional the unforeseen contingency is and how devastating in terms of parties utility is the unforeseen contingency. Of course this does not need to be the case. However, the qualitative characterization of the Court’s optimal decision rule still holds true in the general case.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Court’s Role in Providing Insurance

The optimal decision rule of the court consists in: determining whether an unforeseen contingency, Θ, has

• ccurred,

evaluating the impact and probability of the unforeseen contingency (negatively correlated in our model), trading off the incentive effect of enforcing the contract against the insurance effects of voiding it.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Promoting Disclosure

Question: should a court always enforce what the contracting parties write?. Suppose contracting parties are sophisticated — (fully rational) no behavioural problems. (Big firms, lots of experts, lawyers etc.) Even in the presence of incomplete contracts it is not

• bvious that there exist a role for active courts (beyond

enforcement) (Schwartz and Scott 2003). We argue that this is not the case: mandatory rules can promote the appropriate disclosure of information.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Suppose that a Court cannot condition its decision on any variable that cannot be contracted upon by the parties themselves. Is it then the case that an active Court can enhance the parties’s welfare? Yes it is.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Key Ingredient:

Inefficiency generated by the presence of asymmetric information among the contracting parties. The institutional role of the Court: to maximize the parties’ ex-ante welfare. The Court is the commitment device through which the founding fathers guaranteed that the parties maximize their welfare under a veil of ignorance.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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We study a buyer-seller model with asymmetric information and ex-ante investments, in which some contingencies cannot be contracted on. Some parties hide their private information by mimicking

• ther types the result is an inefficiency that takes the form
• f a transaction that yields negative surplus.

An active Court that voids a contract that the contracting parties would like to see enforced induces the different types to disclose their private information.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Precedents

Parties need to be able to anticipate the Court’s future decision, this is accomplished by precedents. Precedents are modeled assuming that the Court announces its decision rule in the beginning. We further assume that precedents are binding (stare decisis).

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Very Simple Example

A Buyer (Home Owner) and a Seller (Contractor) face a potentially profitable trade. There exists three distinct trade opportunities labelled: wi, i ∈ {1, 2, 3}. Opportunities w1 and w2 correspond, for example, to some structural work that need to be done in the house, this work can be done with all relevant permits w1 or without all relevant permits w2.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Both w1 and w2 require an ex-ante investment by the buyer I = 1/3 to be profitable, moreover w1 and w2 are mutually exclusive. There exists two equally likely potential types of buyer: buyer α (careless HO) and buyer β (careful HO). Denote vi

j and ci j the value (net of I = 1/3) and costs,

associated with the trade of wi, i ∈ {1, 2} between the buyer of type j ∈ {α, β} and the seller.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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We take these values (net of the ex-ante investment I = 1/3) and costs to be: w1 w2 Careless HO (α) v1

α = 21

c1

α = 1

v2

α = 25

c2

α = 1

Careful HO (β) v1

β = −1

c1

β = 1

v2

β = 3

c2

β = 1

The relevant permits have a strictly positive opportunity cost (equal to 4) and the value of the structural work is higher if the HO has been careless.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Opportunity w3 is, for example, drying the basement and requires no ex-ante investment. However, the value and cost depend on the type of HO. We take the values and costs of w3 to be: w3 Careless HO (α) v3

α = 76

c3

α = 100

Careful HO (β) v3

β = 65

c3

β = 3

Independently on whether the opportunities w1 or w2 are taken w3 can also be taken (in a spot fashion).

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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First Best:

All trade opportunities are summarized as follows: w1 w2 w3 Careless HO (α) v1

α = 21

c1

α = 1

v2

α = 25

c2

α = 1

v3

α = 76

c3

α = 100

Careful HO (β) v1

β = −1

c1

β = 1

v2

β = 3

c2

β = 1

v3

β = 65

c3

β = 3

Notice that efficiency implies that it is optimal for the Careless HO to invest and take the opportunity w2,

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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for the Careful HO to invest and take the opportunity w2, to take the trade opportunity w3 when the HO is of type β and not to take this opportunity w3 when the HO is of type α. The first best expected surplus is: WFB = 44.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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The Buyer (HO) has all bargaining power ex-ante. The Seller (Contractor) has all bargaining power ex-post. The Court maximizes welfare under a veil of ignorance: it does not observe the parties’ types and hence “averages” across all possibilities. The Court can only void or uphold the ex-ante contract and condition only on w1, w2 or w3 specified in the contract not on values and costs. The Court always upholds spot contracts.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Timeline

The Court chooses a rule for voiding or upholding

• contracts. This is announced to all.

Draw by Nature that determines the HO’s type j ∈ {α, β} with probability 1/2. The HO observes his type j the Contractor does not. The HO (α or β) makes a take-it-or-leave-it offer of an ex-ante contract to trade w1 or w2 to the Contractor. Contractor accepts or rejects the offer.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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HO (α or β) decides whether to undertake I. Either party can decide to take contract to Court. Court decides wether to uphold or void the contract. Renegotiation: take-it-or-leave-it offer from the Contractor to the HO. Trade occurs. According to contract or according to a renegotiated agreement (for example if Court voids or no contract was agreed at an ex-ante stage).

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Passive Court:

Proposition (Equilibrium with a Passive Court) When the Court upholds all contracts there exists a unique equilibrium outcome such that: buyer α and β pool in investing and taking the w2 trading

• pportunity at the price p2 = c2

α = c2 β = 1, the contract is

accepted by the seller. If an offer to take the w1 trading opportunity is made the seller may hold any belief (CK: buyer α), the seller ex-post takes the w3 trading opportunity with both types of buyer at the price p3 = v3

β = 65.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Proof: In equilibrium the seller’s expected payoff is: 1 2

• p3 − c3

β + p3 − c3 α

• = 13.5

By deviating the only possibility the seller has is not to trade w3 for a payoff of zero. In equilibrium buyer α’s payoff is v2

α − p2 + v3 α − p3 = 35

By deviating and offering the trade w1 the lowest price the seller will accept is ˆ p1 = 1. If buyer α is believed to be α w3 is not traded and buyer α’s payoff is: v1

α − ˆ

p1 = 20. (If believed to be β payoff is 31).

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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In equilibrium buyer β’s payoff is v2

β − p2 + v3 β − p3 = 2

By deviating and offering the trade w1 at the lowest price the seller will accept ˆ p1 = 1 buyer β payoff is v1

β − ˆ

p1 = −2 independent of the seller’s beliefs. Intuition: Given that the two types of buyer pool on w2 the seller does not learn and hence trades w3 with both types of buyer.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Moreover, no other equilibrium outcome exists. In particular the following Claim is the most interesting. Proposition When the Court upholds all contracts there does not exist an equilibrium where buyer α and β separate and buyer α invests and trades w1 at the price p1 = c1

α = 1,

the seller accepts the contract and w3 is not traded, buyer β invests and trades w2 at the price p2 = c2

β = 1,

the seller accepts the contract and w3 is traded at the price p3 = v3

β = 65.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Proof: w1 w2 w3 Careless HO (α) v1

α = 21

c1

α = 1

v2

α = 25

c2

α = 1

v3

α = 76

c3

α = 100

Careful HO (β) v1

β = −1

c1

β = 1

v2

β = 3

c2

β = 1

v3

β = 65

c3

β = 3

In equilibrium buyer α’s payoff is v1

α − p1 = 20

By deviating and offering the trade w2 buyer α is believed to be β hence the lowest price the seller will accept is ˆ p2 = c2

β = 1 and the opportunity w3 is traded, buyer α’s

payoff is then: v2

α − ˆ

p2 + v3

α − p3 = 35.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Observations:

By pooling on w2 buyer α gains for two separate reasons:

he obtains the highest payoff when choosing opportunity w2 (payoff of 24) instead of w1 (payoff of 20), he does not reveal his type and hence can trade widget 3 at the price p3 = v 3

β = 65 (payoff of 11).

In so doing buyer α exercises a negative externality on the seller (payoff of 13.5 instead of 31) and yields an ex-post inefficiency (the w3 trade when the buyer is of type α, loss

• f 24).

Given that information is soft or unverifiable unless the two types of buyer separate in the ex-ante contract for the trade opportunity w1 or w2 the seller cannot “serve” only buyer β in the trade opportunity w3.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Active Court:

Assume now that the Court voids any ex-ante contract on w2. Proposition (Equilibrium with an Active Court) When the Court voids any ex-ante contract for w2 the unique equilibrium is such that buyer α and β separate: buyer α invests and offers an ex-ante contract for w1 at the price p1 = c1

α = 1 and the contract is accepted by the

• seller. The opportunity w3 is not taken.

buyer β does not invest and offer any ex-ante contract and takes the opportunity w3 at the price p3 = v3

β = 65 at the

ex-post stage. clearly the trade of w2 does not occur.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Proof: w1 w2 w3 Careless HO (α) v1

α = 21

c1

α = 1

v2

α = 25

c2

α = 1

v3

α = 76

c3

α = 100

Careful HO (β) v1

β = −1

c1

β = 1

v2

β = 3

c2

β = 1

v3

β = 65

c3

β = 3

In equilibrium buyer α’s payoff is v1

α − p1 = 20

By deviating and not investing but just taking the w3

• pportunity (at the ex-post stage) at the price

ˆ p3 = v3

β = 65 buyer α is believed to be β and his payoff is

then: v3

α − ˆ

p3 = 11.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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In equilibrium buyer β’s payoff is v3

β − p3 = 0

By deviating and offering the trade w1 at the lowest price the seller will accept ˆ p1 = 1 buyer β is believed to be α and hence w3 is not traded, his payoff is then: v1

β − ˆ

p1 = −2. The Court eliminates the gain (24) buyer α gets by pooling with buyer β and taking the trade opportunity w2 and hence α wants to separate.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Interpretation:

The Court voids any contract to undertake structural work without permit this induces separation of the two types of HO:

the careless HO will only undertake structural work with permit w1 the careful HO will only undertake the drying of the basement w3.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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We can now characterize the optimal decision rule for the Court. Proposition (Optimality of Court’s Intervention) It is optimal for the Court to intervene and void any ex-ante contracts for the trade w2.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Proof: The expected surplus if the Court enforces all ex-ante contracts is: 1 2[v2

α − c2 α + v2 β − c2 β + v3 α − c3 α + v3 β − c3 β] = 32

The expected surplus if the Court voids the ex-ante contract for w2 is: 1 2[v1

α − c1 α + v3 β − c3 β] = 41

Clearly the Court’s intervention is optimal.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Ambiguous Courts:

Consider now an ambiguous Court: that voids the ex-ante contract for w2 with probability µ∗. We interpret ambiguous Courts as situations in which the state of the Law or of the body of precedents, or both, will be ambiguous, creating genuine uncertainty for the contracting parties as to what the Court ruling will be.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

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Proposition (Optimality of an Ambiguous Court) It is optimal for an ambiguous Court: to uphold any ex-ante contract for w2 with probability equal to (1 − µ∗) ∈ [1/7, 28/73]. buyer α and β separate. Buyer α invests and offers an ex-ante contract for w1 at the price p1 = c1

α = 1 and the opportunity w3 is not taken.

Buyer β invests and offers an ex-ante contract for w2 at the price p2 = c2

β = 1 and the opportunity w3 is taken

ex-post at the price p3 = v3

β = 65.

If the Court voids the contract for w2 the parties renegotiate the trade of w2 at the price p ′

2 = 10/3.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

Disclosure

Precedents Model First Best Passive Court Active Court Ambiguous Courts Menu Contracts

Proof: (intuition) Assume the Court voids the ex-ante contract for w2 with probability µ. Two constraints are key for the ambiguous Courts: The β buyer invests in the opportunity to trade w2: (1 − µ) (v2

β − p2) − µ I = (1 − µ) (v2 β − c2 β) − µ I ≥ 0

• r µ ≤ 6/7

The α buyer invests in the opportunity to trade w1 rather than w2: v1

α − c1 α ≥ (1 − µ) (v2 α − c2 α) − µ I + (v3 α − v3 β)

• r µ ≥ 45/73

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

Disclosure

Precedents Model First Best Passive Court Active Court Ambiguous Courts Menu Contracts

(Graph) W

✲

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pool on w2 α and β separate β invests in w2 β does not invest

45 73

α and β µ

✻ q ✻ ✻

1

q

................................................. 32 µ∗

6 7

q q

42 41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .................................

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

Disclosure

Precedents Model First Best Passive Court Active Court Ambiguous Courts Menu Contracts

Menu Contracts:

Assume that the parties can sign an ex-ante menu contract contingent on the buyer’s announcement of his type. This announcement takes place after the seller has committed to the menu (Maskin and Tirole 1990, 1992, Maskin 2005). The menu contract is such that: the first item lists the trade(s) and price(s) that will take place if the buyer announces type α, the second item lists the the trade(s) and price(s) that will take place if the buyer announces type β.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

Disclosure

Precedents Model First Best Passive Court Active Court Ambiguous Courts Menu Contracts

Proposition (Menu Contracts and Passive Court — Pooling) There exists an equilibrium of the model with menu contracts in which: The trading and investment outcome correspond to inefficient pooling as in Proposition 1. The menu contract in this equilibrium is degenerate in the sense that both types of buyer offer the same menu contract and both items of the menu are identical. Both types of buyer invest in and trade w2 and w3. The Court’s expected payoff is WMP = 32.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

Disclosure

Precedents Model First Best Passive Court Active Court Ambiguous Courts Menu Contracts

Proposition (Menu Contracts and Passive Court — Separation) There exists an equilibrium of the model with menu contracts in which: The trading and investment outcome correspond to separation as in Proposition 2. The menu contract in this equilibrium is non-degenerate in the sense that both types of buyer offer the same menu but the two items on the menu differ. The type α buyer invests in and trades w1, while the type β buyer does not invest in either w1 or w2, and trades w3. The Court’s expected payoff is WMS = 41.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

Disclosure

Precedents Model First Best Passive Court Active Court Ambiguous Courts Menu Contracts

Proposition (Maximal Equilibrium Payoff for the Court) There does not exist any equilibrium of the model with menu contracts in which the Courts’ expected payoff exceeds WMS = 41. Clearly, this results leaves ample scope for Court’s intervention. If we interpret the Court as a player then the Court will intervene only if it expects the parties to play the pooling equilibrium. Alternatively, if we interpret the Court as an institution

• utside the model then the Court by intervening insures

that the parties separate in the then unique equilibrium of the negotiation subgame.

EC516 Contracts and Organisations for Research Students: Lecture 3 Leonardo Felli Filling the Gaps

A Model of Insurance

Disclosure

Precedents Model First Best Passive Court Active Court Ambiguous Courts Menu Contracts

Conclusions

The model advocates the use of mandatory rules or alternatively legal or statutory rules in certain situations. The result can be viewed as identifying a kind of second best phenomenon in an incomplete contract world. We start with a model with contractual incompleteness. In this world it is in fact welfare-improving to impose further incompleteness by making some contracts effectively impossible in equilibrium. The Court needs to commit ex-ante to the future ruling. In

• ther words, the Court is affected by a potential time

inconsistency problem.