EC537 Microeconomic Theory for Research Students, Part II: Lecture 4 - PowerPoint PPT Presentation

EC537 Microeconomic Theory for Research Students, Part II: Lecture 4 Leonardo Felli CLM.G.4 29 November, 2011

Transaction Costs We now return to the Coase Theorem and consider how the result is affected by the presence of transaction costs. Theorem (Strong version of the Coase Theorem) The Coase theorem guarantees efficiency: 1 regardless of the way in which property rights are assigned, and 2 whenever the mutual gains from trade exceed the necessary transaction costs. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 2 / 66

We are going to show that this is not necessarily the case. The reason is the strategic role of transaction costs. Key factor: some transaction costs have to be paid ex-ante , before the negotiation starts. These ex-ante transaction costs generate an inefficiency known as a hold-up problem . The hold-up problem yield an outcome that is constrained inefficient . Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 3 / 66

Numerical Example Potential Surplus = 100, Ex-ante cost to each negotiating party = 20, Distribution of bargaining power = (10%, 90%), Ex-ante Payoff to party A = (10% 100 − 20) = − 10, Ex-ante Payoff to party B = (90% 100 − 20) = 70, Social surplus = 60. Coasian negotiation opportunity is left unexploited. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 4 / 66

Natural question: whether it is possible to find a Coasian solution to this inefficiency. In other words we are asking whether the parties can agree ex-ante on a transfer contingent on each party entering a future negotiation. We are going to show that under plausible conditions a Coasian solution of this form may not be available. The reason is that any new negotiation may itself be associated with (possibly small) ex-ante transaction costs. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 5 / 66

In the Numerical Example above Party B makes a transfer to party A contingent on the cost of 20 being paid by A . Assume that B makes a take-it-or-leave-it offer to A , Ex-ante costs to each party associated with this ‘agreement contingent on future negotiation’ = 1, A accepts this transfer if: 10% 100 − 20 + x ≥ 0 , or x ≥ 10. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 6 / 66

There always exists an equilibrium in which x = 10. Ex-ante payoff to party A π A = 10% 100 − 20 + 10 − 1 = − 1 No negotiation (contingent or not) will take place. A Coasian solution is not available. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 7 / 66

What are the transaction costs? Ex-ante transaction costs: time to arrange and/or participate in a meeting, time and effort to conceive and agree upon a suitable negotiation language, time and effort to collect information about the legal environment in which the agreement is enforced, time to collect and analyze background information for the negotiation, time and effort to think about the negotiation at hand. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 8 / 66

These costs can be monetized through the hiring of an outside party: typically a lawyer. The problem does not disappear if the lawyer needs to be paid independently of the success of the negotiation: no contingent fees. Indeed, monetizing the costs may increase the magnitude of the inefficiency: moral hazard. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 9 / 66

Simple Coasian Negotiation: Consider the following simple coasian negotiation: two agents, i ∈ { A , B } ; share a surplus, size of the surplus normalized to one, parties’ payoffs in case of disagreement to zero. Each party faces ex-ante costs: ( c A , c B ). Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 10 / 66

Assume that ( c A , c B ) are: complements: each party i has to pay c i for the negotiation to be feasible; affordable: party i ’s endowment covers c i ; efficient: c A + c B < 1. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 11 / 66

Timing: Simult. Decisions on ( c A , c B ) Contract enforced Contract Negotiated ✲ ✲ s s s t = 0 t = 1 t = 2 Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 12 / 66

We solve the model backward. We start with a simple bargaining rule: Let λ be the bargaining power of A . The division of surplus at t = 1 is then ( λ, 1 − λ ). Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 13 / 66

Result For any given λ there exists a pair ( c A , c B ) of affordable and efficient ex-ante costs such that the unique SPE is ( not pay c A , not pay c B ) Result For any pair ( c A , c B ) of affordable and efficient ex-ante costs there exists a value of λ such that the unique SPE is ( not pay c A , not pay c B ) Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 14 / 66

Proof: The ‘reduced form’ of the two stage game is: pay c B not pay c B pay c A λ − c A , 1 − λ − c B − c A , 0 not pay c A 0 , − c B 0 , 0 A pays c A iff λ ≥ c A and B pays c B , A does not pay c A if B does not pay c B , B pays c B iff 1 − λ ≥ c B and A pays c A , B does not pay c B if A does not pay c A . Therefore the result holds when λ < c A or 1 − λ < c B . Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 15 / 66

Assume now that ( c A , c B ) are: substitutes: either party has to pay c i ; affordable: party i ’s endowment covers c i ; efficient: min { c A , c B } < 1 . Result Both results above hold. In the second result only one type of inefficiency may occur. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 16 / 66

Proof: The reduced form game is now: pay c B not pay c B pay c A λ − c A , 1 − λ − c B λ − c A , 1 − λ not pay c A λ, 1 − λ − c B 0 , 0 A pays c A iff λ ≥ c A and B does not pay c B , A does not pay c A if B pays c B , B pays c B iff 1 − λ ≥ c B and A does not pay c A , B does not pay c B if A pays c A . Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 17 / 66

We then have two types of inefficiencies: an inefficiency that leads to a unique SPE with no agreement: λ < c A , and (1 − λ ) < c B an inefficiency that leads to an agreement obtained paying too high a cost: if c A < c B , λ < c A , and (1 − λ ) > c B Results 1 and 2 also generalize to the case in which ( c A , c B ) are substitutes and strategic complements. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 18 / 66

The Impossibility of a Coasian Solution Is there a Coasian solution to this hold-up problem? Consider the following simple contingent agreement: A transfer σ B ≥ 0 ( σ A ≥ 0 ) payable contingent on whether the other party decides to pay c A , (c B ). Key assumption: this new negotiation is associated with a fresh set of ex-ante costs ( c 1 A , c 1 B ); the two sets of ex-ante costs are assumed to be complements, affordable and efficient. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 19 / 66

Assume: λ < c A Simult. Decision Simult. Decision on ( c 1 A , c 1 B ) on ( c A , c B ) Contract A Accepts/Rejects enforced B makes offer Tranfers to A Negotiation ✻ A / B does ✇ ✲ ✲ ✲ not pay s s s s s s s − 2 − 1 0 1 2 Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 20 / 66

Result There always exists a SPE of this game in which both agents pay neither the second tier, ( c 1 A , c 1 B ) , nor the first tier, ( c A , c B ) , of ex-ante costs. Proof: At each stage the two agents decide simultaneously and independently whether to pay their ex-ante costs. An agreement is achieved only if both agents pay ( c 1 A , c 1 B ) and ( c A , c B ). Either agent will never pay if he expects the other not to pay his ex-ante cost. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 21 / 66

Result There always exists a SPE of this game in which both agents pay the second tier, ( c 1 A , c 1 B ) , and the first tier, ( c A , c B ) , of ex-ante costs and an agreement is successfully negotiated . Proof: Assume that: both parties have paid the ex-ante costs ( c 1 A , c 1 B ) at t = − 2 and party A has accepted the transfer σ B ≥ 0. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 22 / 66

The parties’ continuation game is then: pay c B not pay c B pay c A λ − c A + σ B , 1 − λ − c B − σ B − c A , 0 not pay c A 0 , − c B 0 , 0 It follows: A pays c A if B pays c B and λ + σ B > c A and B pays c B if A pays c A and 1 − λ − σ B > c B . Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 23 / 66

Therefore if 1 − λ − c B > σ B > c A − λ the subgame has two Pareto-ranked equilibria: one in which an agreement is successfully negotiated, an other one in which an agreement does not arise. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 24 / 66

We can then construct a SPE of the model such that at t = 0 if λ + σ B ≥ c A + c 1 A the (constrained) efficient equilibrium is played. if λ + σ B < c A + c 1 A the no-agreement equilibrium is played. Leonardo Felli (LSE) EC537 Advanced Microeconomics 29 November, 2011 25 / 66