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Lecture 8: Incomplete Contracts
Cheng Chen
School of Economics and Finance
The University of Hong Kong
(Cheng Chen (HKU)) Econ 6006 1 / 23
Introduction
Motivation
Development of microeconomics theory:1 General equilibrium theory (Arrow, Debreu, Scarf, Mas-Colell...)2 Economics of uncertainly (Von Neumann, Morgenstein...)
3 Complete contract and incentive theory (Mirrlees, Akerlof, Stiglitz,Spence, Myerson, Maskin, Holmstrom, Milgrom)
4 Dynamic contract and renegotiation (Tirole, Tirole, La�ont...)5 Incomplete contract (Grossman, Hart, Moore, Bolton...)
(Cheng Chen (HKU)) Econ 6006 2 / 23
Introduction
Motivation
Development of microeconomics theory:1 General equilibrium theory (Arrow, Debreu, Scarf, Mas-Colell...)2 Economics of uncertainly (Von Neumann, Morgenstein...)3 Complete contract and incentive theory (Mirrlees, Akerlof, Stiglitz,
Spence, Myerson, Maskin, Holmstrom, Milgrom)4 Dynamic contract and renegotiation (Tirole, Tirole, La�ont...)
5 Incomplete contract (Grossman, Hart, Moore, Bolton...)
(Cheng Chen (HKU)) Econ 6006 2 / 23
Introduction
Motivation
Development of microeconomics theory:1 General equilibrium theory (Arrow, Debreu, Scarf, Mas-Colell...)2 Economics of uncertainly (Von Neumann, Morgenstein...)3 Complete contract and incentive theory (Mirrlees, Akerlof, Stiglitz,
Spence, Myerson, Maskin, Holmstrom, Milgrom)4 Dynamic contract and renegotiation (Tirole, Tirole, La�ont...)5 Incomplete contract (Grossman, Hart, Moore, Bolton...)
(Cheng Chen (HKU)) Econ 6006 2 / 23
Introduction
Several Concepts
Transaction-cost economics and boundary of �rm: Coase (1937),
Williamson (1975, 1985).
Hold-up problem: Klein, Crawford and Alchian (1978).
Ex post haggling (Simon) and ex ante ine�ciency (property-rights
theory).
Property-rights theory (Grossman and Hart, 1986; Hart and Moore,1990):
I Asset owner is residual claimant of ownership, not pro�t.I Observability and Veri�ability (ex ante investment).I Unforseen contingencies and cost of writing a contract.I Cost and bene�t of integration and threat point.
(Cheng Chen (HKU)) Econ 6006 3 / 23
Introduction
Several Concepts
Transaction-cost economics and boundary of �rm: Coase (1937),
Williamson (1975, 1985).
Hold-up problem: Klein, Crawford and Alchian (1978).
Ex post haggling (Simon) and ex ante ine�ciency (property-rights
theory).
Property-rights theory (Grossman and Hart, 1986; Hart and Moore,1990):
I Asset owner is residual claimant of ownership, not pro�t.I Observability and Veri�ability (ex ante investment).I Unforseen contingencies and cost of writing a contract.I Cost and bene�t of integration and threat point.
(Cheng Chen (HKU)) Econ 6006 3 / 23
Introduction
Several Concepts
Transaction-cost economics and boundary of �rm: Coase (1937),
Williamson (1975, 1985).
Hold-up problem: Klein, Crawford and Alchian (1978).
Ex post haggling (Simon) and ex ante ine�ciency (property-rights
theory).
Property-rights theory (Grossman and Hart, 1986; Hart and Moore,1990):
I Asset owner is residual claimant of ownership, not pro�t.I Observability and Veri�ability (ex ante investment).
I Unforseen contingencies and cost of writing a contract.I Cost and bene�t of integration and threat point.
(Cheng Chen (HKU)) Econ 6006 3 / 23
Introduction
Several Concepts
Transaction-cost economics and boundary of �rm: Coase (1937),
Williamson (1975, 1985).
Hold-up problem: Klein, Crawford and Alchian (1978).
Ex post haggling (Simon) and ex ante ine�ciency (property-rights
theory).
Property-rights theory (Grossman and Hart, 1986; Hart and Moore,1990):
I Asset owner is residual claimant of ownership, not pro�t.I Observability and Veri�ability (ex ante investment).I Unforseen contingencies and cost of writing a contract.I Cost and bene�t of integration and threat point.
(Cheng Chen (HKU)) Econ 6006 3 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
A General Framework
A printer (agent 1) and a publisher (agent 2).
Two assets: {a1, a2}: Both are essential for production.
Investment to increase value of payo�: x .
Cost of investment: ψi (xi ).
Payo�s:I V (x1, x2) ≡ V ({1, 2}; {a1, a2}
∣∣x1, x2): total payo� if two agents worktogether and two assets are used for production.
I Φ1(x1, x2) ≡ V ({1}; {a1, a2}∣∣x1, x2): payo� to agent 1 if he owns
both assets.I Φ2(x1, x2) ≡ V ({2}; {a1, a2}
∣∣x1, x2): payo� to agent 2 if he ownsboth assets.
I V ({1}; {∅}∣∣x1, x2): payo� to agent 1 if he does not own any asset.
(Cheng Chen (HKU)) Econ 6006 4 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
A General Framework
A printer (agent 1) and a publisher (agent 2).
Two assets: {a1, a2}: Both are essential for production.
Investment to increase value of payo�: x .
Cost of investment: ψi (xi ).
Payo�s:I V (x1, x2) ≡ V ({1, 2}; {a1, a2}
∣∣x1, x2): total payo� if two agents worktogether and two assets are used for production.
I Φ1(x1, x2) ≡ V ({1}; {a1, a2}∣∣x1, x2): payo� to agent 1 if he owns
both assets.I Φ2(x1, x2) ≡ V ({2}; {a1, a2}
∣∣x1, x2): payo� to agent 2 if he ownsboth assets.
I V ({1}; {∅}∣∣x1, x2): payo� to agent 1 if he does not own any asset.
(Cheng Chen (HKU)) Econ 6006 4 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
A General Framework
A printer (agent 1) and a publisher (agent 2).
Two assets: {a1, a2}: Both are essential for production.
Investment to increase value of payo�: x .
Cost of investment: ψi (xi ).
Payo�s:I V (x1, x2) ≡ V ({1, 2}; {a1, a2}
∣∣x1, x2): total payo� if two agents worktogether and two assets are used for production.
I Φ1(x1, x2) ≡ V ({1}; {a1, a2}∣∣x1, x2): payo� to agent 1 if he owns
both assets.I Φ2(x1, x2) ≡ V ({2}; {a1, a2}
∣∣x1, x2): payo� to agent 2 if he ownsboth assets.
I V ({1}; {∅}∣∣x1, x2): payo� to agent 1 if he does not own any asset.
(Cheng Chen (HKU)) Econ 6006 4 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
A General Framework
A printer (agent 1) and a publisher (agent 2).
Two assets: {a1, a2}: Both are essential for production.
Investment to increase value of payo�: x .
Cost of investment: ψi (xi ).
Payo�s:I V (x1, x2) ≡ V ({1, 2}; {a1, a2}
∣∣x1, x2): total payo� if two agents worktogether and two assets are used for production.
I Φ1(x1, x2) ≡ V ({1}; {a1, a2}∣∣x1, x2): payo� to agent 1 if he owns
both assets.
I Φ2(x1, x2) ≡ V ({2}; {a1, a2}∣∣x1, x2): payo� to agent 2 if he owns
both assets.I V ({1}; {∅}
∣∣x1, x2): payo� to agent 1 if he does not own any asset.
(Cheng Chen (HKU)) Econ 6006 4 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
A General Framework
A printer (agent 1) and a publisher (agent 2).
Two assets: {a1, a2}: Both are essential for production.
Investment to increase value of payo�: x .
Cost of investment: ψi (xi ).
Payo�s:I V (x1, x2) ≡ V ({1, 2}; {a1, a2}
∣∣x1, x2): total payo� if two agents worktogether and two assets are used for production.
I Φ1(x1, x2) ≡ V ({1}; {a1, a2}∣∣x1, x2): payo� to agent 1 if he owns
both assets.I Φ2(x1, x2) ≡ V ({2}; {a1, a2}
∣∣x1, x2): payo� to agent 2 if he ownsboth assets.
I V ({1}; {∅}∣∣x1, x2): payo� to agent 1 if he does not own any asset.
(Cheng Chen (HKU)) Econ 6006 4 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
A General Framework
A printer (agent 1) and a publisher (agent 2).
Two assets: {a1, a2}: Both are essential for production.
Investment to increase value of payo�: x .
Cost of investment: ψi (xi ).
Payo�s:I V (x1, x2) ≡ V ({1, 2}; {a1, a2}
∣∣x1, x2): total payo� if two agents worktogether and two assets are used for production.
I Φ1(x1, x2) ≡ V ({1}; {a1, a2}∣∣x1, x2): payo� to agent 1 if he owns
both assets.I Φ2(x1, x2) ≡ V ({2}; {a1, a2}
∣∣x1, x2): payo� to agent 2 if he ownsboth assets.
I V ({1}; {∅}∣∣x1, x2): payo� to agent 1 if he does not own any asset.
(Cheng Chen (HKU)) Econ 6006 4 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Insights
Suppose investment x is made ex ante.
Ex post bargaining on realized payo� V ({1, 2}; {a1, a2}∣∣x1, x2) is
e�cient. I.e., negotiation does not break up, and max. payo� is
distributed to both agents.
Assume Nash bargaining rule for ex post bargaining.
Key: di�erence in threat points under di�erent ownership structures.
No ex post ine�ciency. However, ex ante ine�ciency is key.
(Cheng Chen (HKU)) Econ 6006 5 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Insights
Suppose investment x is made ex ante.
Ex post bargaining on realized payo� V ({1, 2}; {a1, a2}∣∣x1, x2) is
e�cient. I.e., negotiation does not break up, and max. payo� is
distributed to both agents.
Assume Nash bargaining rule for ex post bargaining.
Key: di�erence in threat points under di�erent ownership structures.
No ex post ine�ciency. However, ex ante ine�ciency is key.
(Cheng Chen (HKU)) Econ 6006 5 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Insights
Suppose investment x is made ex ante.
Ex post bargaining on realized payo� V ({1, 2}; {a1, a2}∣∣x1, x2) is
e�cient. I.e., negotiation does not break up, and max. payo� is
distributed to both agents.
Assume Nash bargaining rule for ex post bargaining.
Key: di�erence in threat points under di�erent ownership structures.
No ex post ine�ciency. However, ex ante ine�ciency is key.
(Cheng Chen (HKU)) Econ 6006 5 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Insights
Suppose investment x is made ex ante.
Ex post bargaining on realized payo� V ({1, 2}; {a1, a2}∣∣x1, x2) is
e�cient. I.e., negotiation does not break up, and max. payo� is
distributed to both agents.
Assume Nash bargaining rule for ex post bargaining.
Key: di�erence in threat points under di�erent ownership structures.
No ex post ine�ciency. However, ex ante ine�ciency is key.
(Cheng Chen (HKU)) Econ 6006 5 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Non-Integration
Agent 1 owns asset one; agent 2 owns asset two.
If ex post negotiation breaks up, payo� is zero to both agents.
Suppose bargaining power is 1/2 for each agent.
Agent 1's incentive to invest ex ante:
maxx1
1
2[V (x1, x2)− 0] + 0− ψ1(x1).
Agent 2's incentive to invest ex ante:
maxx2
1
2[V (x1, x2)− 0] + 0− ψ2(x2).
(Cheng Chen (HKU)) Econ 6006 6 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Non-Integration
Agent 1 owns asset one; agent 2 owns asset two.
If ex post negotiation breaks up, payo� is zero to both agents.
Suppose bargaining power is 1/2 for each agent.
Agent 1's incentive to invest ex ante:
maxx1
1
2[V (x1, x2)− 0] + 0− ψ1(x1).
Agent 2's incentive to invest ex ante:
maxx2
1
2[V (x1, x2)− 0] + 0− ψ2(x2).
(Cheng Chen (HKU)) Econ 6006 6 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Non-Integration
Agent 1 owns asset one; agent 2 owns asset two.
If ex post negotiation breaks up, payo� is zero to both agents.
Suppose bargaining power is 1/2 for each agent.
Agent 1's incentive to invest ex ante:
maxx1
1
2[V (x1, x2)− 0] + 0− ψ1(x1).
Agent 2's incentive to invest ex ante:
maxx2
1
2[V (x1, x2)− 0] + 0− ψ2(x2).
(Cheng Chen (HKU)) Econ 6006 6 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Printer-Integration
Assume ∂Φi (xi , xj )/∂xj = 0: the other agent's investment does not
a�ect my own outside option.
See Che and Hausch (1999) on this point.
If printer owns all assets (printer-integration)I Agent 1's incentive to invest ex ante:
maxx1
1
2[V (x1, x2)−Φ1(x1)] + Φ1(x1)− ψ1(x1).
I Agent 2's incentive to invest ex ante:
maxx2
1
2[V (x1, x2)−Φ1(x1)] + 0− ψ2(x2).
(Cheng Chen (HKU)) Econ 6006 7 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Printer-Integration
Assume ∂Φi (xi , xj )/∂xj = 0: the other agent's investment does not
a�ect my own outside option.
See Che and Hausch (1999) on this point.
If printer owns all assets (printer-integration)I Agent 1's incentive to invest ex ante:
maxx1
1
2[V (x1, x2)−Φ1(x1)] + Φ1(x1)− ψ1(x1).
I Agent 2's incentive to invest ex ante:
maxx2
1
2[V (x1, x2)−Φ1(x1)] + 0− ψ2(x2).
(Cheng Chen (HKU)) Econ 6006 7 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Printer-Integration
Assume ∂Φi (xi , xj )/∂xj = 0: the other agent's investment does not
a�ect my own outside option.
See Che and Hausch (1999) on this point.
If printer owns all assets (printer-integration)I Agent 1's incentive to invest ex ante:
maxx1
1
2[V (x1, x2)−Φ1(x1)] + Φ1(x1)− ψ1(x1).
I Agent 2's incentive to invest ex ante:
maxx2
1
2[V (x1, x2)−Φ1(x1)] + 0− ψ2(x2).
(Cheng Chen (HKU)) Econ 6006 7 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Publisher-Integration
If publisher owns all assets (publisher-integration)I Agent 1's incentive to invest ex ante:
maxx1
1
2[V (x1, x2)−Φ2(x2)] + 0− ψ1(x1).
I Agent 2's incentive to invest ex ante:
maxx2
1
2[V (x1, x2)−Φ2(x2)] + Φ2(x2)− ψ2(x2).
We assume that ex ante is relationship-speci�c. I.e.
∂V (x1, x2)
∂x1> Φ
′1(x1) for all x2
and∂V (x1, x2)
∂x2> Φ
′2(x2) for all x1.
(Cheng Chen (HKU)) Econ 6006 8 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Publisher-Integration
If publisher owns all assets (publisher-integration)I Agent 1's incentive to invest ex ante:
maxx1
1
2[V (x1, x2)−Φ2(x2)] + 0− ψ1(x1).
I Agent 2's incentive to invest ex ante:
maxx2
1
2[V (x1, x2)−Φ2(x2)] + Φ2(x2)− ψ2(x2).
We assume that ex ante is relationship-speci�c. I.e.
∂V (x1, x2)
∂x1> Φ
′1(x1) for all x2
and∂V (x1, x2)
∂x2> Φ
′2(x2) for all x1.
(Cheng Chen (HKU)) Econ 6006 8 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Publisher-Integration
If publisher owns all assets (publisher-integration)I Agent 1's incentive to invest ex ante:
maxx1
1
2[V (x1, x2)−Φ2(x2)] + 0− ψ1(x1).
I Agent 2's incentive to invest ex ante:
maxx2
1
2[V (x1, x2)−Φ2(x2)] + Φ2(x2)− ψ2(x2).
We assume that ex ante is relationship-speci�c. I.e.
∂V (x1, x2)
∂x1> Φ
′1(x1) for all x2
and∂V (x1, x2)
∂x2> Φ
′2(x2) for all x1.
(Cheng Chen (HKU)) Econ 6006 8 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Incentives to InvestFor non-integration:
1
2
∂V (xNI1 , xNI
2 )
∂x1= ψ
′1(x
NI1 );
1
2
∂V (xNI1 , xNI2 )
∂x2= ψ
′2(x
NI2 )
For printer-integration:
1
2
[∂V (xPI1 , xPI2 )
∂x1+ Φ
′1(x
PI1 )]= ψ
′1(x
PI1 );
1
2
∂V (xPI1 , xPI2 )
∂x2= ψ
′2(x
PI2 )
For publisher-integration:
1
2
∂V (xpI1 , xpI2 )
∂x1= ψ
′1(x
pI1 );
1
2
[∂V (xpI1 , xpI2 )
∂x2+ Φ
′2(x
pI2 )]= ψ
′2(x
pI2 )
All investment level is below FB level:
∂V (xFB1 , xFB2 )
∂x1= ψ
′1(x
FB1 );
∂V (xFB1 , xFB2 )
∂x2= ψ
′2(x
FB2 ).
(Cheng Chen (HKU)) Econ 6006 9 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Incentives to InvestFor non-integration:
1
2
∂V (xNI1 , xNI
2 )
∂x1= ψ
′1(x
NI1 );
1
2
∂V (xNI1 , xNI2 )
∂x2= ψ
′2(x
NI2 )
For printer-integration:
1
2
[∂V (xPI1 , xPI2 )
∂x1+ Φ
′1(x
PI1 )]= ψ
′1(x
PI1 );
1
2
∂V (xPI1 , xPI2 )
∂x2= ψ
′2(x
PI2 )
For publisher-integration:
1
2
∂V (xpI1 , xpI2 )
∂x1= ψ
′1(x
pI1 );
1
2
[∂V (xpI1 , xpI2 )
∂x2+ Φ
′2(x
pI2 )]= ψ
′2(x
pI2 )
All investment level is below FB level:
∂V (xFB1 , xFB2 )
∂x1= ψ
′1(x
FB1 );
∂V (xFB1 , xFB2 )
∂x2= ψ
′2(x
FB2 ).
(Cheng Chen (HKU)) Econ 6006 9 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Incentives to InvestFor non-integration:
1
2
∂V (xNI1 , xNI
2 )
∂x1= ψ
′1(x
NI1 );
1
2
∂V (xNI1 , xNI2 )
∂x2= ψ
′2(x
NI2 )
For printer-integration:
1
2
[∂V (xPI1 , xPI2 )
∂x1+ Φ
′1(x
PI1 )]= ψ
′1(x
PI1 );
1
2
∂V (xPI1 , xPI2 )
∂x2= ψ
′2(x
PI2 )
For publisher-integration:
1
2
∂V (xpI1 , xpI2 )
∂x1= ψ
′1(x
pI1 );
1
2
[∂V (xpI1 , xpI2 )
∂x2+ Φ
′2(x
pI2 )]= ψ
′2(x
pI2 )
All investment level is below FB level:
∂V (xFB1 , xFB2 )
∂x1= ψ
′1(x
FB1 );
∂V (xFB1 , xFB2 )
∂x2= ψ
′2(x
FB2 ).
(Cheng Chen (HKU)) Econ 6006 9 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Incentives to InvestFor non-integration:
1
2
∂V (xNI1 , xNI
2 )
∂x1= ψ
′1(x
NI1 );
1
2
∂V (xNI1 , xNI2 )
∂x2= ψ
′2(x
NI2 )
For printer-integration:
1
2
[∂V (xPI1 , xPI2 )
∂x1+ Φ
′1(x
PI1 )]= ψ
′1(x
PI1 );
1
2
∂V (xPI1 , xPI2 )
∂x2= ψ
′2(x
PI2 )
For publisher-integration:
1
2
∂V (xpI1 , xpI2 )
∂x1= ψ
′1(x
pI1 );
1
2
[∂V (xpI1 , xpI2 )
∂x2+ Φ
′2(x
pI2 )]= ψ
′2(x
pI2 )
All investment level is below FB level:
∂V (xFB1 , xFB2 )
∂x1= ψ
′1(x
FB1 );
∂V (xFB1 , xFB2 )
∂x2= ψ
′2(x
FB2 ).
(Cheng Chen (HKU)) Econ 6006 9 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Equilibrium Ownership Structure
Firm chooses ownership structure maximize ex post payo�:
V (x1, x2)− ψ1(x1)− ψ2(x2).
If Φ′1(x1) > 0, non-integration is never optimal.
If printer's investment matters more for �nal payo�, I.e.
∂V (x1, x2)
∂x1>>
∂V (x1, x2)
∂x2,
then printer-integration is optimal and vice versa.
It is possible that Φ′1(x1) < 0. Thus, non-integration might be
optimal.
Cost and bene�t of integration. Not just transaction costs (i.e., costs
associated with market transactions)!
(Cheng Chen (HKU)) Econ 6006 10 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Equilibrium Ownership Structure
Firm chooses ownership structure maximize ex post payo�:
V (x1, x2)− ψ1(x1)− ψ2(x2).
If Φ′1(x1) > 0, non-integration is never optimal.
If printer's investment matters more for �nal payo�, I.e.
∂V (x1, x2)
∂x1>>
∂V (x1, x2)
∂x2,
then printer-integration is optimal and vice versa.
It is possible that Φ′1(x1) < 0. Thus, non-integration might be
optimal.
Cost and bene�t of integration. Not just transaction costs (i.e., costs
associated with market transactions)!
(Cheng Chen (HKU)) Econ 6006 10 / 23
Ownership and Property-Rights theory of the Firm (Section11.2.1) Grossman-Hart-Moore Approach
Equilibrium Ownership Structure
Firm chooses ownership structure maximize ex post payo�:
V (x1, x2)− ψ1(x1)− ψ2(x2).
If Φ′1(x1) > 0, non-integration is never optimal.
If printer's investment matters more for �nal payo�, I.e.
∂V (x1, x2)
∂x1>>
∂V (x1, x2)
∂x2,
then printer-integration is optimal and vice versa.
It is possible that Φ′1(x1) < 0. Thus, non-integration might be
optimal.
Cost and bene�t of integration. Not just transaction costs (i.e., costs
associated with market transactions)!
(Cheng Chen (HKU)) Econ 6006 10 / 23
The Holdup Problem (Section 12.3.1)
Setup
References: Goldberg (1976), Klein, Crawford, Alchian (1978), and
Williamson (1975, 1985).
A buyer and a seller.
Quantity of trading: q ∈ [0, 1].
Value: v ∈ {vL, vH}, vL < vH and Prob(vH) = j .
Cost: c ∈ {cL, cH}, cL < cH and Prob(cL) = i .
Ex post payo�s:
vq − P − ψ(j)
and
P − cq − φ(i).
cH > vH > cL > vL
Ex post e�cient level of trade is q = 1 if θ = (vH , cL) and 0 otherwise.
(Cheng Chen (HKU)) Econ 6006 11 / 23
The Holdup Problem (Section 12.3.1)
Setup
References: Goldberg (1976), Klein, Crawford, Alchian (1978), and
Williamson (1975, 1985).
A buyer and a seller.
Quantity of trading: q ∈ [0, 1].
Value: v ∈ {vL, vH}, vL < vH and Prob(vH) = j .
Cost: c ∈ {cL, cH}, cL < cH and Prob(cL) = i .
Ex post payo�s:
vq − P − ψ(j)
and
P − cq − φ(i).
cH > vH > cL > vL
Ex post e�cient level of trade is q = 1 if θ = (vH , cL) and 0 otherwise.
(Cheng Chen (HKU)) Econ 6006 11 / 23
The Holdup Problem (Section 12.3.1)
Setup
References: Goldberg (1976), Klein, Crawford, Alchian (1978), and
Williamson (1975, 1985).
A buyer and a seller.
Quantity of trading: q ∈ [0, 1].
Value: v ∈ {vL, vH}, vL < vH and Prob(vH) = j .
Cost: c ∈ {cL, cH}, cL < cH and Prob(cL) = i .
Ex post payo�s:
vq − P − ψ(j)
and
P − cq − φ(i).
cH > vH > cL > vL
Ex post e�cient level of trade is q = 1 if θ = (vH , cL) and 0 otherwise.
(Cheng Chen (HKU)) Econ 6006 11 / 23
The Holdup Problem (Section 12.3.1)
Setup
References: Goldberg (1976), Klein, Crawford, Alchian (1978), and
Williamson (1975, 1985).
A buyer and a seller.
Quantity of trading: q ∈ [0, 1].
Value: v ∈ {vL, vH}, vL < vH and Prob(vH) = j .
Cost: c ∈ {cL, cH}, cL < cH and Prob(cL) = i .
Ex post payo�s:
vq − P − ψ(j)
and
P − cq − φ(i).
cH > vH > cL > vL
Ex post e�cient level of trade is q = 1 if θ = (vH , cL) and 0 otherwise.
(Cheng Chen (HKU)) Econ 6006 11 / 23
The Holdup Problem (Section 12.3.1)
FB and the Holdup ProblemFB is
maxi ,j{ij(vH − cL)− ψ(j)− φ(i)}
Solution:
i∗(vH − cL) = ψ′(j∗)
and
j∗(vH − cL) = φ′(i∗).
However, assume investment happens ex ante, and both agents
bargain over generated payo� through using a Nash bargaining rule.
Assume they have equal bargaining power. Investment level is
1
2iSB(vH − cL) = ψ
′(jSB)
and1
2jSB(vH − cL) = φ
′(iSB).
Follow-up research: Di�erent assumptions on the extent to which level
of trade is contractable. E�cient ex post renegotiation.
(Cheng Chen (HKU)) Econ 6006 12 / 23
The Holdup Problem (Section 12.3.1)
FB and the Holdup ProblemFB is
maxi ,j{ij(vH − cL)− ψ(j)− φ(i)}
Solution:
i∗(vH − cL) = ψ′(j∗)
and
j∗(vH − cL) = φ′(i∗).
However, assume investment happens ex ante, and both agents
bargain over generated payo� through using a Nash bargaining rule.
Assume they have equal bargaining power. Investment level is
1
2iSB(vH − cL) = ψ
′(jSB)
and1
2jSB(vH − cL) = φ
′(iSB).
Follow-up research: Di�erent assumptions on the extent to which level
of trade is contractable. E�cient ex post renegotiation.
(Cheng Chen (HKU)) Econ 6006 12 / 23
The Holdup Problem (Section 12.3.1)
FB and the Holdup ProblemFB is
maxi ,j{ij(vH − cL)− ψ(j)− φ(i)}
Solution:
i∗(vH − cL) = ψ′(j∗)
and
j∗(vH − cL) = φ′(i∗).
However, assume investment happens ex ante, and both agents
bargain over generated payo� through using a Nash bargaining rule.
Assume they have equal bargaining power. Investment level is
1
2iSB(vH − cL) = ψ
′(jSB)
and1
2jSB(vH − cL) = φ
′(iSB).
Follow-up research: Di�erent assumptions on the extent to which level
of trade is contractable. E�cient ex post renegotiation.
(Cheng Chen (HKU)) Econ 6006 12 / 23
Real and Formal Authority (Section 12.4.2)
Setup
Reference: Aghion and Tirole (1997).
Formal authority 6= real authority.
P: Principal. A: Agent.
N potential projects k ∈ {1, 2, ...,N}.P has one most preferred project with payo� H and βh to P and A
respectively.
A has one most preferred project with payo� αH and h to P and A
respectively.
Congruence parameters (con�ict of interests): α, β.
(Cheng Chen (HKU)) Econ 6006 13 / 23
Real and Formal Authority (Section 12.4.2)
Setup
Reference: Aghion and Tirole (1997).
Formal authority 6= real authority.
P: Principal. A: Agent.
N potential projects k ∈ {1, 2, ...,N}.
P has one most preferred project with payo� H and βh to P and A
respectively.
A has one most preferred project with payo� αH and h to P and A
respectively.
Congruence parameters (con�ict of interests): α, β.
(Cheng Chen (HKU)) Econ 6006 13 / 23
Real and Formal Authority (Section 12.4.2)
Setup
Reference: Aghion and Tirole (1997).
Formal authority 6= real authority.
P: Principal. A: Agent.
N potential projects k ∈ {1, 2, ...,N}.P has one most preferred project with payo� H and βh to P and A
respectively.
A has one most preferred project with payo� αH and h to P and A
respectively.
Congruence parameters (con�ict of interests): α, β.
(Cheng Chen (HKU)) Econ 6006 13 / 23
Real and Formal Authority (Section 12.4.2)
Setup
Reference: Aghion and Tirole (1997).
Formal authority 6= real authority.
P: Principal. A: Agent.
N potential projects k ∈ {1, 2, ...,N}.P has one most preferred project with payo� H and βh to P and A
respectively.
A has one most preferred project with payo� αH and h to P and A
respectively.
Congruence parameters (con�ict of interests): α, β.
(Cheng Chen (HKU)) Econ 6006 13 / 23
Real and Formal Authority (Section 12.4.2)
Setup
Reference: Aghion and Tirole (1997).
Formal authority 6= real authority.
P: Principal. A: Agent.
N potential projects k ∈ {1, 2, ...,N}.P has one most preferred project with payo� H and βh to P and A
respectively.
A has one most preferred project with payo� αH and h to P and A
respectively.
Congruence parameters (con�ict of interests): α, β.
(Cheng Chen (HKU)) Econ 6006 13 / 23
Real and Formal Authority (Section 12.4.2)
Setup (cont.)
P knows which project she prefers most with Prob E , if she exerts
e�ort at cost ψP(E ).
A knows which project she prefers most with Prob e, if she exerts
e�ort at cost ψA(e).
∃ One bad project generating extremely negative payo� to both P and
A → Don't choose any project, if both P and A don't know state.
(Cheng Chen (HKU)) Econ 6006 14 / 23
Real and Formal Authority (Section 12.4.2)
P-Control
Assume P has formal authority.
With Prob. E : P has both formal and real authority.
With Prob. (1− E )e: P has formal authority, while A has real
authority.
Payo�s:
UP = EH + (1− E )eαH − ψP(E )
and
UA = Eβh+ (1− E )eh− ψA(e).
(Cheng Chen (HKU)) Econ 6006 15 / 23
Real and Formal Authority (Section 12.4.2)
P-Control
Assume P has formal authority.
With Prob. E : P has both formal and real authority.
With Prob. (1− E )e: P has formal authority, while A has real
authority.
Payo�s:
UP = EH + (1− E )eαH − ψP(E )
and
UA = Eβh+ (1− E )eh− ψA(e).
(Cheng Chen (HKU)) Econ 6006 15 / 23
Real and Formal Authority (Section 12.4.2)
P-Control (cont.)
FOC:
(1− αe)H = ψ′P(E )
and
(1− E )h = ψ′A(e)
Key parameters: α and β.
Key economic force: crowding-out e�ect.
Substitutability between e and E .
E�ect of α and β on A's e�ort choice.
(Cheng Chen (HKU)) Econ 6006 16 / 23
Real and Formal Authority (Section 12.4.2)
P-Control (cont.)
FOC:
(1− αe)H = ψ′P(E )
and
(1− E )h = ψ′A(e)
Key parameters: α and β.
Key economic force: crowding-out e�ect.
Substitutability between e and E .
E�ect of α and β on A's e�ort choice.
(Cheng Chen (HKU)) Econ 6006 16 / 23
Real and Formal Authority (Section 12.4.2)
E-Control
Assume A has formal authority.
With Prob. e: A has both formal and real authority.
With Prob. (1− e)E : A has formal authority, while P has real
authority.
Payo�s:
UP = eαH + (1− e)EH − ψP(E )
and
UA = eh+ (1− e)Eβh− ψA(e).
(Cheng Chen (HKU)) Econ 6006 17 / 23
Real and Formal Authority (Section 12.4.2)
E-Control
Assume A has formal authority.
With Prob. e: A has both formal and real authority.
With Prob. (1− e)E : A has formal authority, while P has real
authority.
Payo�s:
UP = eαH + (1− e)EH − ψP(E )
and
UA = eh+ (1− e)Eβh− ψA(e).
(Cheng Chen (HKU)) Econ 6006 17 / 23
Real and Formal Authority (Section 12.4.2)
E-Control (cont.)
FOC:
(1− e)H = ψ′P(E )
and
(1− βE )h = ψ′A(e)
Key parameters: α and β.
Key economic force: crowding-out e�ect.
Substitutability between e and E .
E�ect of α and β on A's e�ort choice.
When α, β→ 1: A-control is better?
(Cheng Chen (HKU)) Econ 6006 18 / 23
Real and Formal Authority (Section 12.4.2)
E-Control (cont.)
FOC:
(1− e)H = ψ′P(E )
and
(1− βE )h = ψ′A(e)
Key parameters: α and β.
Key economic force: crowding-out e�ect.
Substitutability between e and E .
E�ect of α and β on A's e�ort choice.
When α, β→ 1: A-control is better?
(Cheng Chen (HKU)) Econ 6006 18 / 23
Real and Formal Authority (Section 12.4.2)
E-Control (cont.)
FOC:
(1− e)H = ψ′P(E )
and
(1− βE )h = ψ′A(e)
Key parameters: α and β.
Key economic force: crowding-out e�ect.
Substitutability between e and E .
E�ect of α and β on A's e�ort choice.
When α, β→ 1: A-control is better?
(Cheng Chen (HKU)) Econ 6006 18 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Setup
Reference: Aghion and Bolton (1987).
Key insight: In a dynamic model, incumbent �rm and consumer can
sign a long-term contract to prevent entry of new �rm (tradeo�
between rent and allocative e�ciency)
Two periods with discounting (t = 0, 1).
Incumbent sells one good to consumer in both periods.
Valuation of consumer: v = 1.
Cost of incumbent: cI ≤ 12 (deterministic)
Entrant may enter when t = 1, and its cost realization cE ∼ U [0, 1].
(Cheng Chen (HKU)) Econ 6006 19 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Setup
Reference: Aghion and Bolton (1987).
Key insight: In a dynamic model, incumbent �rm and consumer can
sign a long-term contract to prevent entry of new �rm (tradeo�
between rent and allocative e�ciency)
Two periods with discounting (t = 0, 1).
Incumbent sells one good to consumer in both periods.
Valuation of consumer: v = 1.
Cost of incumbent: cI ≤ 12 (deterministic)
Entrant may enter when t = 1, and its cost realization cE ∼ U [0, 1].
(Cheng Chen (HKU)) Econ 6006 19 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Setup
Reference: Aghion and Bolton (1987).
Key insight: In a dynamic model, incumbent �rm and consumer can
sign a long-term contract to prevent entry of new �rm (tradeo�
between rent and allocative e�ciency)
Two periods with discounting (t = 0, 1).
Incumbent sells one good to consumer in both periods.
Valuation of consumer: v = 1.
Cost of incumbent: cI ≤ 12 (deterministic)
Entrant may enter when t = 1, and its cost realization cE ∼ U [0, 1].
(Cheng Chen (HKU)) Econ 6006 19 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Setup
Reference: Aghion and Bolton (1987).
Key insight: In a dynamic model, incumbent �rm and consumer can
sign a long-term contract to prevent entry of new �rm (tradeo�
between rent and allocative e�ciency)
Two periods with discounting (t = 0, 1).
Incumbent sells one good to consumer in both periods.
Valuation of consumer: v = 1.
Cost of incumbent: cI ≤ 12 (deterministic)
Entrant may enter when t = 1, and its cost realization cE ∼ U [0, 1].
(Cheng Chen (HKU)) Econ 6006 19 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Spot Contract
When only spot contract is available.
Price p0 = 1 and p1 = 1 when realized cost cE < cI . (entry decision
is made before pricing decision)
Consumer's payo�: (1− cI )cI .
Incumbent's payo�: 1− cI + (1− cI )2.
(Cheng Chen (HKU)) Econ 6006 20 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Spot Contract
When only spot contract is available.
Price p0 = 1 and p1 = 1 when realized cost cE < cI . (entry decision
is made before pricing decision)
Consumer's payo�: (1− cI )cI .
Incumbent's payo�: 1− cI + (1− cI )2.
(Cheng Chen (HKU)) Econ 6006 20 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Long-Term Contract
Suppose incumbent and consumer can make a long-term contract (p0,p1). Punishment d for breaking contract.
Now we assume that entry decision is made after p1 is announced.
Contract is broken, if
1− pE ≥ 1− p1 + d .
Entry happens with Prob. p1 − d .
(Cheng Chen (HKU)) Econ 6006 21 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Long-Term Contract
Suppose incumbent and consumer can make a long-term contract (p0,p1). Punishment d for breaking contract.
Now we assume that entry decision is made after p1 is announced.
Contract is broken, if
1− pE ≥ 1− p1 + d .
Entry happens with Prob. p1 − d .
(Cheng Chen (HKU)) Econ 6006 21 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Long-Term Contract (Cont.)
Incumbent's ex ante payo� and objective function:
maxp0,p1,d
p0 − cI + (p1 − cI )(1− p1 + d) + d(p1 − d).
s.t. PC for consumer:
(1− p0) + (1− p1) ≥ (1− cI )cI (PC ).
We can set p0 = 1 (maybe sub-optimal). Express p1 in terms of cIusing (PC ).
Solutions:
d∗ =1+ (1− cI )(1− 2cI )
2
and
Prob(entry) = p1 − d∗ =cI2.
(Cheng Chen (HKU)) Econ 6006 22 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Long-Term Contract (Cont.)
Incumbent's ex ante payo� and objective function:
maxp0,p1,d
p0 − cI + (p1 − cI )(1− p1 + d) + d(p1 − d).
s.t. PC for consumer:
(1− p0) + (1− p1) ≥ (1− cI )cI (PC ).
We can set p0 = 1 (maybe sub-optimal). Express p1 in terms of cIusing (PC ).
Solutions:
d∗ =1+ (1− cI )(1− 2cI )
2
and
Prob(entry) = p1 − d∗ =cI2.
(Cheng Chen (HKU)) Econ 6006 22 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Discussion
Long-term contract always dominates spot contract (binding PC +(d = 0) + (P0 = 1) + same timing assumption).
Entry is deterred, since Prob(entry) = cI2 .
Obviously, not socially e�cient.
No way to improve, since contract is fully enforceable.
If entrant could promise something when t = 0, what would happen?
(Cheng Chen (HKU)) Econ 6006 23 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Discussion
Long-term contract always dominates spot contract (binding PC +(d = 0) + (P0 = 1) + same timing assumption).
Entry is deterred, since Prob(entry) = cI2 .
Obviously, not socially e�cient.
No way to improve, since contract is fully enforceable.
If entrant could promise something when t = 0, what would happen?
(Cheng Chen (HKU)) Econ 6006 23 / 23
Incomplete Contract and Entry Barriers (Section 13.2)
Discussion
Long-term contract always dominates spot contract (binding PC +(d = 0) + (P0 = 1) + same timing assumption).
Entry is deterred, since Prob(entry) = cI2 .
Obviously, not socially e�cient.
No way to improve, since contract is fully enforceable.
If entrant could promise something when t = 0, what would happen?
(Cheng Chen (HKU)) Econ 6006 23 / 23