Optimal Contract Design with Unilateral Market Option

Transcription

1 Optimal Contract Design with Unilateral Market Option Antonio Nicita University of Siena, Dept. of Economics, Italy Simone M. Sepe University of Arizona, J. E. Rogers College of Law

2 Summary We extend the uncertainty framework in standard incomplete contracts in so as to include the party's market opportunity. Investment efficiency is enhanced when authority is assigned to the party having market opportunity (in some sense to the least specific party). A neglected rationale for vertical integration against hold-up?

3 Motivation Puzzle on the role of ex-post decision rights: Incomplete Contracts vs. Optimal Mechanism Design In many real world business cases the degree of specificity may vary over time due to contractmarket interactions (Spulber, 2002) No clear theory to govern these Intermediate cases

4 Hold-Up and Competition Literature: Edlin and Hermalin, 1998; de Meza and Lockwood, 1998; Felli and Roberts, 2002; Chatterjee and Chiu, 2007; Ishiguro, 2009; Nicita and Sepe, Silicon Graphics and asset specificity in ICT Asset Specificity and Standards in network industries Freeland (2000) on Fisher Body/General Motors: in mid-1919, when Fisher obtained its largest order for closed bodies ever from Ford. Fearing that Ford was experimenting with closed bodies on the inexpensive Model T, GM management worried that they were about to fall further behind their primary competitors in an important strategic area

5

6 Our argument We focus on the case where a unilateral market option exists under the implementation mechanism of Chung, 1991; ADR, when the fixed claimant has a market option, the residual claimant may face a hold-up problem: the implementation mechanism brakes down (Second) best solution: authority should be assigned to the party having a market option

7 A sketch of the model two agents B, S U B (Γ, i, θ 1 )=v(q, θ 1,i) tq h B (i) U S (Γ, j, θ 1 )=tq c(q, θ 1,j) h S (j) v qi > 0 c qj < 0 specific self-investments contractual uncertainty contractual scheme i I R + j J R + θ 1 Θ 1 R n r =(Γ, RG) F (θ 1 ) Γ [0,q max ] [ R +] default option Γ(q, t) p ro t e c t e d by s p e c i fi c performance bargaining game with outside options and alternate offers. One party is is residual claimant and the other it fixed claimant on Γ(q, t)

8 r =(Γ, RG) RS(q, θ 1, i, j) =v(q, θ 1,i) c(q, θ 1,j) [v(q, θ 1,i) c(q, θ 1,j)] U B (Γ, θ 1,i)=v(q, θ 1,i) tq + αrs(q, θ 1, i, j) h B (i) α =1

9 Buyer/Seller problem Max Γ [v(q, θ 1,i) tq h B (i)] = v(q,! 1,i) tq + " RS(q,! 1, i, j) h B (i) α =1 s.t. tq c(q,! 1,j) h S (j) tq c(q,! 1,j) h S (j) =U S Proposition 1 (Chung-ADR): the contract r assures first best investment levels, whatever is the assignment of ex-post decision rights.

10 Unilateral Market Option Market Uncertainty: seller s (fixed claimant) market option X(θ with θ 2 Θ 2 R m 2 ), F (θ 2 ), Cov(θ 1, θ 2 )=0 X S generates a random contract Γ(θ 1, θ 2 ) Lemma 1: market option raises a net extra utility for the seller: X S = Max {0; [t(θ 2 )[q(θ 2 ) q] [c(q(θ 2 ), θ 1,j] c(q,θ 1,j)]} Lemma 2: α = Max { 0, X S affects the buyer bargaining power α [RS(q, θ 1, i, j) X ] } S /RS(q, θ 1, i, j)

11 Buyer/Seller problem U B (Γ, θ 1, θ 2,i)=v(q, θ 1,i) tq + αrs(q, θ 1, i, j) h B (i) U S (Γ, θ 1, θ 2,j)=tq c(q, θ 1,j)+X S (q, θ 1, θ 2,j) h S (j) where: α = Max { 0, [RS(q, θ 1, i, j) X S ] } /RS(q, θ 1, i, j)

12 Main Result Proposition 2: Under any r =(Γ, RG) claimant has a market option X(θ 2 ): when the fixed 1. the fixed claimant will over-invest relative to the contract, j>j*; 2. the residual claimant will under-invest relative to the contract, i>i*; 3. the pair of efficient investments (i*,j*) will never be a Nash equilibrium.

13 Authority matters Proposition 3: Under any r =(Γ, RG) when the fixed claimant has a market option X(θ 2 ) the assignment of authority to the party having the market option enhances efficiency. In particular: 1. the fixed claimant party will invest optimally; 2. the residual claimant (with market option) will over-invest, relative to the contract; 3. the residual claimant's over-investment will be less severe than in the alternative allocation of ex-post decision rights.

14 Implications/1 1. Comparing the two cases: when a market option exists, hold up may occur under Chung-ADR: bilateral efficient investments and irrelevance of authority assignment do not hold anymore 2. Authority matters when there is a market option: the party less specific should have it, then specific performance solves hold-up (direction) - applicable to both cases (increased or decreased specificity) 3. otherwise, authority is not enough and specific performance provides too much protection

15 Implications/2 4. In intermediate cases, contract-matket interactions affect the hold-up problem (Ishiguro, 2009) 5. Optimal contracts design is not independent of market options 6. another rationale for (quasi)vertical integration? controlling counterpart s market option 7. Freeland (2009): FB/GM a case of hold-up through merger, as the less specific party was the fixed claimant