Lecture 8: Incomplete Contracts

Transcription

1 Lecture 8: Incomplete Contracts Cheng Chen School of Economics and Finance The University of Hong Kong (Cheng Chen (HKU)) Econ 6006 / 23

2 Introduction Motivation Development of microeconomics theory: General equilibrium theory (Arrow, Debreu, Scarf, Mas-Colell...) 2 Economics of uncertainly (Von Neumann, Morgenstein...) (Cheng Chen (HKU)) Econ / 23

3 Introduction Motivation Development of microeconomics theory: 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, Laont...) (Cheng Chen (HKU)) Econ / 23

4 Introduction Motivation Development of microeconomics theory: 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, Laont...) 5 Incomplete contract (Grossman, Hart, Moore, Bolton...) (Cheng Chen (HKU)) Econ / 23

5 Introduction Several Concepts Transaction-cost economics and boundary of rm: Coase (937), Williamson (975, 985). Hold-up problem: Klein, Crawford and Alchian (978). (Cheng Chen (HKU)) Econ / 23

6 Introduction Several Concepts Transaction-cost economics and boundary of rm: Coase (937), Williamson (975, 985). Hold-up problem: Klein, Crawford and Alchian (978). Ex post haggling (Simon) and ex ante ineciency (property-rights theory). (Cheng Chen (HKU)) Econ / 23

7 Introduction Several Concepts Transaction-cost economics and boundary of rm: Coase (937), Williamson (975, 985). Hold-up problem: Klein, Crawford and Alchian (978). Ex post haggling (Simon) and ex ante ineciency (property-rights theory). Property-rights theory (Grossman and Hart, 986; Hart and Moore, 990): Asset owner is residual claimant of ownership, not prot. Observability and Veriability (ex ante investment). (Cheng Chen (HKU)) Econ / 23

8 Introduction Several Concepts Transaction-cost economics and boundary of rm: Coase (937), Williamson (975, 985). Hold-up problem: Klein, Crawford and Alchian (978). Ex post haggling (Simon) and ex ante ineciency (property-rights theory). Property-rights theory (Grossman and Hart, 986; Hart and Moore, 990): Asset owner is residual claimant of ownership, not prot. Observability and Veriability (ex ante investment). Unforseen contingencies and cost of writing a contract. Cost and benet of integration and threat point. (Cheng Chen (HKU)) Econ / 23

9 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach A General Framework A printer (agent ) and a publisher (agent 2). Two assets: {a, a 2 }: Both are essential for production. (Cheng Chen (HKU)) Econ / 23

10 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach A General Framework A printer (agent ) and a publisher (agent 2). Two assets: {a, a 2 }: Both are essential for production. Investment to increase value of payo: x. Cost of investment: ψ i (x i ). (Cheng Chen (HKU)) Econ / 23

11 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach A General Framework A printer (agent ) and a publisher (agent 2). Two assets: {a, a 2 }: Both are essential for production. Investment to increase value of payo: x. Cost of investment: ψ i (x i ). Payos: V (x, x 2 ) V ({, 2}; {a, a 2 } x, x 2 ): total payo if two agents work together and two assets are used for production. (Cheng Chen (HKU)) Econ / 23

12 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach A General Framework A printer (agent ) and a publisher (agent 2). Two assets: {a, a 2 }: Both are essential for production. Investment to increase value of payo: x. Cost of investment: ψ i (x i ). Payos: V (x, x 2 ) V ({, 2}; {a, a 2 } x, x 2 ): total payo if two agents work together and two assets are used for production. Φ (x, x 2 ) V ({}; {a, a 2 } x, x 2 ): payo to agent if he owns both assets. (Cheng Chen (HKU)) Econ / 23

13 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach A General Framework A printer (agent ) and a publisher (agent 2). Two assets: {a, a 2 }: Both are essential for production. Investment to increase value of payo: x. Cost of investment: ψ i (x i ). Payos: V (x, x 2 ) V ({, 2}; {a, a 2 } x, x 2 ): total payo if two agents work together and two assets are used for production. Φ (x, x 2 ) V ({}; {a, a 2 } x, x 2 ): payo to agent if he owns both assets. Φ 2 (x, x 2 ) V ({2}; {a, a 2 } x, x 2 ): payo to agent 2 if he owns both assets. (Cheng Chen (HKU)) Econ / 23

14 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach A General Framework A printer (agent ) and a publisher (agent 2). Two assets: {a, a 2 }: Both are essential for production. Investment to increase value of payo: x. Cost of investment: ψ i (x i ). Payos: V (x, x 2 ) V ({, 2}; {a, a 2 } x, x 2 ): total payo if two agents work together and two assets are used for production. Φ (x, x 2 ) V ({}; {a, a 2 } x, x 2 ): payo to agent if he owns both assets. Φ 2 (x, x 2 ) V ({2}; {a, a 2 } x, x 2 ): payo to agent 2 if he owns both assets. V ({}; { } x, x 2 ): payo to agent if he does not own any asset. (Cheng Chen (HKU)) Econ / 23

15 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Insights Suppose investment x is made ex ante. Ex post bargaining on realized payo V ({, 2}; {a, a 2 } x, x 2 ) is ecient. I.e., negotiation does not break up, and max. payo is distributed to both agents. (Cheng Chen (HKU)) Econ / 23

16 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Insights Suppose investment x is made ex ante. Ex post bargaining on realized payo V ({, 2}; {a, a 2 } x, x 2 ) is ecient. I.e., negotiation does not break up, and max. payo is distributed to both agents. Assume Nash bargaining rule for ex post bargaining. (Cheng Chen (HKU)) Econ / 23

17 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Insights Suppose investment x is made ex ante. Ex post bargaining on realized payo V ({, 2}; {a, a 2 } x, x 2 ) is ecient. I.e., negotiation does not break up, and max. payo is distributed to both agents. Assume Nash bargaining rule for ex post bargaining. Key: dierence in threat points under dierent ownership structures. (Cheng Chen (HKU)) Econ / 23

18 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Insights Suppose investment x is made ex ante. Ex post bargaining on realized payo V ({, 2}; {a, a 2 } x, x 2 ) is ecient. I.e., negotiation does not break up, and max. payo is distributed to both agents. Assume Nash bargaining rule for ex post bargaining. Key: dierence in threat points under dierent ownership structures. No ex post ineciency. However, ex ante ineciency is key. (Cheng Chen (HKU)) Econ / 23

19 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Non-Integration Agent owns asset one; agent 2 owns asset two. If ex post negotiation breaks up, payo is zero to both agents. (Cheng Chen (HKU)) Econ / 23

20 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Non-Integration Agent owns asset one; agent 2 owns asset two. If ex post negotiation breaks up, payo is zero to both agents. Suppose bargaining power is /2 for each agent. Agent 's incentive to invest ex ante: max x 2 [V (x, x 2 ) 0] + 0 ψ (x ). (Cheng Chen (HKU)) Econ / 23

21 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Non-Integration Agent owns asset one; agent 2 owns asset two. If ex post negotiation breaks up, payo is zero to both agents. Suppose bargaining power is /2 for each agent. Agent 's incentive to invest ex ante: max x 2 [V (x, x 2 ) 0] + 0 ψ (x ). Agent 2's incentive to invest ex ante: max x 2 2 [V (x, x 2 ) 0] + 0 ψ 2 (x 2 ). (Cheng Chen (HKU)) Econ / 23

22 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Printer-Integration Assume Φ i (x i, x j )/ x j = 0: the other agent's investment does not aect my own outside option. See Che and Hausch (999) on this point. (Cheng Chen (HKU)) Econ / 23

23 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Printer-Integration Assume Φ i (x i, x j )/ x j = 0: the other agent's investment does not aect my own outside option. See Che and Hausch (999) on this point. If printer owns all assets (printer-integration) Agent 's incentive to invest ex ante: max x 2 [V (x, x 2 ) Φ (x )] + Φ (x ) ψ (x ). (Cheng Chen (HKU)) Econ / 23

24 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Printer-Integration Assume Φ i (x i, x j )/ x j = 0: the other agent's investment does not aect my own outside option. See Che and Hausch (999) on this point. If printer owns all assets (printer-integration) Agent 's incentive to invest ex ante: max x 2 [V (x, x 2 ) Φ (x )] + Φ (x ) ψ (x ). Agent 2's incentive to invest ex ante: max x 2 2 [V (x, x 2 ) Φ (x )] + 0 ψ 2 (x 2 ). (Cheng Chen (HKU)) Econ / 23

25 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Publisher-Integration If publisher owns all assets (publisher-integration) Agent 's incentive to invest ex ante: max x 2 [V (x, x 2 ) Φ 2 (x 2 )] + 0 ψ (x ). (Cheng Chen (HKU)) Econ / 23

26 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Publisher-Integration If publisher owns all assets (publisher-integration) Agent 's incentive to invest ex ante: max x 2 [V (x, x 2 ) Φ 2 (x 2 )] + 0 ψ (x ). Agent 2's incentive to invest ex ante: max x 2 2 [V (x, x 2 ) Φ 2 (x 2 )] + Φ 2 (x 2 ) ψ 2 (x 2 ). (Cheng Chen (HKU)) Econ / 23

27 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Publisher-Integration If publisher owns all assets (publisher-integration) Agent 's incentive to invest ex ante: max x 2 [V (x, x 2 ) Φ 2 (x 2 )] + 0 ψ (x ). Agent 2's incentive to invest ex ante: max x 2 2 [V (x, x 2 ) Φ 2 (x 2 )] + Φ 2 (x 2 ) ψ 2 (x 2 ). We assume that ex ante is relationship-specic. I.e. V (x, x 2 ) x > Φ (x ) for all x 2 and V (x, x 2 ) x 2 > Φ 2(x 2 ) for all x. (Cheng Chen (HKU)) Econ / 23

28 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Incentives to Invest For non-integration: 2 V (x NI, x NI ) 2 = ψ x (x NI ); 2 V (x NI, x NI ) 2 = ψ x 2(x NI 2 ) 2 (Cheng Chen (HKU)) Econ / 23

29 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Incentives to Invest For non-integration: 2 V (x NI, x NI ) 2 = ψ x (x NI ); 2 V (x NI, x NI ) 2 = ψ x 2(x NI 2 ) 2 For printer-integration: [ V (x PI, x PI ) ] 2 + Φ 2 x (x PI ) = ψ (x PI ); 2 V (x PI, x PI ) 2 = ψ x 2(x PI 2 ) 2 (Cheng Chen (HKU)) Econ / 23

30 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Incentives to Invest For non-integration: 2 V (x NI, x NI ) 2 = ψ x (x NI ); 2 V (x NI, x NI ) 2 = ψ x 2(x NI 2 ) 2 For printer-integration: [ V (x PI, x PI ) ] 2 + Φ 2 x (x PI ) = ψ (x PI ); 2 V (x PI, x PI ) 2 = ψ x 2(x PI 2 ) 2 For publisher-integration: V (x pi, x pi ) 2 = ψ 2 x (x pi ); [ V (x pi, x pi ) ] 2 + Φ 2 x 2(x pi ) 2 = ψ 2(x pi ) 2 2 (Cheng Chen (HKU)) Econ / 23

31 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Incentives to Invest For non-integration: 2 V (x NI, x NI ) 2 = ψ x (x NI ); 2 V (x NI, x NI ) 2 = ψ x 2(x NI 2 ) 2 For printer-integration: [ V (x PI, x PI ) ] 2 + Φ 2 x (x PI ) = ψ (x PI ); 2 V (x PI, x PI ) 2 = ψ x 2(x PI 2 ) 2 For publisher-integration: V (x pi, x pi ) 2 = ψ 2 x (x pi ); [ V (x pi, x pi ) ] 2 + Φ 2 x 2(x pi ) 2 = ψ 2(x pi ) 2 2 All investment level is below FB level: V (x FB, x FB 2 ) = ψ x (x FB V (x FB );, x FB 2 ) = ψ x 2(x FB 2 ). 2 (Cheng Chen (HKU)) Econ / 23

32 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Equilibrium Ownership Structure Firm chooses ownership structure maximize ex post payo: V (x, x 2 ) ψ (x ) ψ 2 (x 2 ). (Cheng Chen (HKU)) Econ / 23

33 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Equilibrium Ownership Structure Firm chooses ownership structure maximize ex post payo: V (x, x 2 ) ψ (x ) ψ 2 (x 2 ). If Φ (x ) > 0, non-integration is never optimal. (Cheng Chen (HKU)) Econ / 23

34 Ownership and Property-Rights theory of the Firm (Section.2.) Grossman-Hart-Moore Approach Equilibrium Ownership Structure Firm chooses ownership structure maximize ex post payo: V (x, x 2 ) ψ (x ) ψ 2 (x 2 ). If Φ (x ) > 0, non-integration is never optimal. If printer's investment matters more for nal payo, I.e. V (x, x 2 ) x >> V (x, x 2 ) x 2, then printer-integration is optimal and vice versa. It is possible that Φ (x ) < 0. Thus, non-integration might be optimal. Cost and benet of integration. Not just transaction costs (i.e., costs associated with market transactions)! (Cheng Chen (HKU)) Econ / 23

35 The Holdup Problem (Section 2.3.) Setup References: Goldberg (976), Klein, Crawford, Alchian (978), and Williamson (975, 985). (Cheng Chen (HKU)) Econ 6006 / 23

36 The Holdup Problem (Section 2.3.) Setup References: Goldberg (976), Klein, Crawford, Alchian (978), and Williamson (975, 985). A buyer and a seller. Quantity of trading: q [0, ]. Value: v {v L, v H }, v L < v H and Prob(v H ) = j. Cost: c {c L, c H }, c L < c H and Prob(c L ) = i. (Cheng Chen (HKU)) Econ 6006 / 23

37 The Holdup Problem (Section 2.3.) Setup References: Goldberg (976), Klein, Crawford, Alchian (978), and Williamson (975, 985). A buyer and a seller. Quantity of trading: q [0, ]. Value: v {v L, v H }, v L < v H and Prob(v H ) = j. Cost: c {c L, c H }, c L < c H and Prob(c L ) = i. Ex post payos: vq P ψ(j) and P cq φ(i). (Cheng Chen (HKU)) Econ 6006 / 23

38 The Holdup Problem (Section 2.3.) Setup References: Goldberg (976), Klein, Crawford, Alchian (978), and Williamson (975, 985). A buyer and a seller. Quantity of trading: q [0, ]. Value: v {v L, v H }, v L < v H and Prob(v H ) = j. Cost: c {c L, c H }, c L < c H and Prob(c L ) = i. Ex post payos: vq P ψ(j) and P cq φ(i). c H > v H > c L > v L Ex post ecient level of trade is q = if θ = (v H, c L ) and 0 otherwise. (Cheng Chen (HKU)) Econ 6006 / 23

39 The Holdup Problem (Section 2.3.) FB and the Holdup Problem FB is Solution: and max{ij(v H c L ) ψ(j) φ(i)} i,j i (v H c L ) = ψ (j ) j (v H c L ) = φ (i ). (Cheng Chen (HKU)) Econ / 23

40 The Holdup Problem (Section 2.3.) FB and the Holdup Problem FB is Solution: and max{ij(v H c L ) ψ(j) φ(i)} i,j i (v H c L ) = ψ (j ) j (v H c L ) = 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 and 2 i SB (v H c L ) = ψ (j SB ) 2 j SB (v H c L ) = φ (i SB ). (Cheng Chen (HKU)) Econ / 23

41 The Holdup Problem (Section 2.3.) FB and the Holdup Problem FB is Solution: and max{ij(v H c L ) ψ(j) φ(i)} i,j i (v H c L ) = ψ (j ) j (v H c L ) = 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 and 2 i SB (v H c L ) = ψ (j SB ) 2 j SB (v H c L ) = φ (i SB ). (Cheng Chen (HKU)) Econ / 23

42 Real and Formal Authority (Section 2.4.2) Setup Reference: Aghion and Tirole (997). Formal authority = real authority. (Cheng Chen (HKU)) Econ / 23

43 Real and Formal Authority (Section 2.4.2) Setup Reference: Aghion and Tirole (997). Formal authority = real authority. P: Principal. A: Agent. N potential projects k {, 2,..., N}. (Cheng Chen (HKU)) Econ / 23

44 Real and Formal Authority (Section 2.4.2) Setup Reference: Aghion and Tirole (997). Formal authority = real authority. P: Principal. A: Agent. N potential projects k {, 2,..., N}. P has one most preferred project with payo H and βh to P and A respectively. (Cheng Chen (HKU)) Econ / 23

45 Real and Formal Authority (Section 2.4.2) Setup Reference: Aghion and Tirole (997). Formal authority = real authority. P: Principal. A: Agent. N potential projects k {, 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. (Cheng Chen (HKU)) Econ / 23

46 Real and Formal Authority (Section 2.4.2) Setup Reference: Aghion and Tirole (997). Formal authority = real authority. P: Principal. A: Agent. N potential projects k {, 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 (conict of interests): α, β. (Cheng Chen (HKU)) Econ / 23

47 Real and Formal Authority (Section 2.4.2) Setup (cont.) P knows which project she prefers most with Prob E, if she exerts eort at cost ψ P (E ). A knows which project she prefers most with Prob e, if she exerts eort at cost ψ A (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 / 23

48 Real and Formal Authority (Section 2.4.2) P-Control Assume P has formal authority. With Prob. E : P has both formal and real authority. With Prob. ( E )e: P has formal authority, while A has real authority. (Cheng Chen (HKU)) Econ / 23

49 Real and Formal Authority (Section 2.4.2) P-Control Assume P has formal authority. With Prob. E : P has both formal and real authority. With Prob. ( E )e: P has formal authority, while A has real authority. Payos: U P = EH + ( E )eαh ψ P (E ) and U A = E βh + ( E )eh ψ A (e). (Cheng Chen (HKU)) Econ / 23

50 Real and Formal Authority (Section 2.4.2) P-Control (cont.) FOC: and ( αe)h = ψ P(E ) ( E )h = ψ A(e) Key parameters: α and β. Key economic force: crowding-out eect. (Cheng Chen (HKU)) Econ / 23

51 Real and Formal Authority (Section 2.4.2) P-Control (cont.) FOC: and ( αe)h = ψ P(E ) ( E )h = ψ A(e) Key parameters: α and β. Key economic force: crowding-out eect. Substitutability between e and E. Eect of α and β on A's eort choice. (Cheng Chen (HKU)) Econ / 23

52 Real and Formal Authority (Section 2.4.2) E-Control Assume A has formal authority. With Prob. e: A has both formal and real authority. With Prob. ( e)e : A has formal authority, while P has real authority. (Cheng Chen (HKU)) Econ / 23

53 Real and Formal Authority (Section 2.4.2) E-Control Assume A has formal authority. With Prob. e: A has both formal and real authority. With Prob. ( e)e : A has formal authority, while P has real authority. Payos: U P = eαh + ( e)eh ψ P (E ) and U A = eh + ( e)e βh ψ A (e). (Cheng Chen (HKU)) Econ / 23

54 Real and Formal Authority (Section 2.4.2) E-Control (cont.) FOC: and ( e)h = ψ P(E ) ( βe )h = ψ A(e) Key parameters: α and β. Key economic force: crowding-out eect. (Cheng Chen (HKU)) Econ / 23

55 Real and Formal Authority (Section 2.4.2) E-Control (cont.) FOC: and ( e)h = ψ P(E ) ( βe )h = ψ A(e) Key parameters: α and β. Key economic force: crowding-out eect. Substitutability between e and E. Eect of α and β on A's eort choice. (Cheng Chen (HKU)) Econ / 23

56 Real and Formal Authority (Section 2.4.2) E-Control (cont.) FOC: and ( e)h = ψ P(E ) ( βe )h = ψ A(e) Key parameters: α and β. Key economic force: crowding-out eect. Substitutability between e and E. Eect of α and β on A's eort choice. When α, β : A-control is better? (Cheng Chen (HKU)) Econ / 23

57 Incomplete Contract and Entry Barriers (Section 3.2) Setup Reference: Aghion and Bolton (987). 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 eciency) (Cheng Chen (HKU)) Econ / 23

58 Incomplete Contract and Entry Barriers (Section 3.2) Setup Reference: Aghion and Bolton (987). 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 eciency) Two periods with discounting (t = 0, ). Incumbent sells one good to consumer in both periods. (Cheng Chen (HKU)) Econ / 23

59 Incomplete Contract and Entry Barriers (Section 3.2) Setup Reference: Aghion and Bolton (987). 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 eciency) Two periods with discounting (t = 0, ). Incumbent sells one good to consumer in both periods. Valuation of consumer: v =. Cost of incumbent: c I 2 (deterministic) (Cheng Chen (HKU)) Econ / 23

60 Incomplete Contract and Entry Barriers (Section 3.2) Setup Reference: Aghion and Bolton (987). 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 eciency) Two periods with discounting (t = 0, ). Incumbent sells one good to consumer in both periods. Valuation of consumer: v =. Cost of incumbent: c I 2 (deterministic) Entrant may enter when t =, and its cost realization c E U[0, ]. (Cheng Chen (HKU)) Econ / 23

61 Incomplete Contract and Entry Barriers (Section 3.2) Spot Contract When only spot contract is available. Price p 0 = and p = when realized cost c E < c I. (entry decision is made before pricing decision) (Cheng Chen (HKU)) Econ / 23

62 Incomplete Contract and Entry Barriers (Section 3.2) Spot Contract When only spot contract is available. Price p 0 = and p = when realized cost c E < c I. (entry decision is made before pricing decision) Consumer's payo: ( c I )c I. Incumbent's payo: c I + ( c I ) 2. (Cheng Chen (HKU)) Econ / 23

63 Incomplete Contract and Entry Barriers (Section 3.2) Long-Term Contract Suppose incumbent and consumer can make a long-term contract (p 0, p ). Punishment d for breaking contract. Now we assume that entry decision is made after p is announced. (Cheng Chen (HKU)) Econ / 23

64 Incomplete Contract and Entry Barriers (Section 3.2) Long-Term Contract Suppose incumbent and consumer can make a long-term contract (p 0, p ). Punishment d for breaking contract. Now we assume that entry decision is made after p is announced. Contract is broken, if Entry happens with Prob. p d. p E p + d. (Cheng Chen (HKU)) Econ / 23

65 Incomplete Contract and Entry Barriers (Section 3.2) Long-Term Contract (Cont.) Incumbent's ex ante payo and objective function: max p 0 c I + (p c I )( p + d) + d(p d). p 0,p,d s.t. PC for consumer: ( p 0 ) + ( p ) ( c I )c I (PC ). (Cheng Chen (HKU)) Econ / 23

66 Incomplete Contract and Entry Barriers (Section 3.2) Long-Term Contract (Cont.) Incumbent's ex ante payo and objective function: max p 0 c I + (p c I )( p + d) + d(p d). p 0,p,d s.t. PC for consumer: ( p 0 ) + ( p ) ( c I )c I (PC ). We can set p 0 = (maybe sub-optimal). Express p in terms of c I using (PC ). Solutions: and d = + ( c I )( 2c I ) 2 Prob(entry) = p d = c I 2. (Cheng Chen (HKU)) Econ / 23

67 Incomplete Contract and Entry Barriers (Section 3.2) Discussion Long-term contract always dominates spot contract (binding PC + (d = 0) + (P 0 = ) + same timing assumption). Entry is deterred, since Prob(entry) = c I 2. (Cheng Chen (HKU)) Econ / 23

68 Incomplete Contract and Entry Barriers (Section 3.2) Discussion Long-term contract always dominates spot contract (binding PC + (d = 0) + (P 0 = ) + same timing assumption). Entry is deterred, since Prob(entry) = c I 2. Obviously, not socially ecient. No way to improve, since contract is fully enforceable. (Cheng Chen (HKU)) Econ / 23

69 Incomplete Contract and Entry Barriers (Section 3.2) Discussion Long-term contract always dominates spot contract (binding PC + (d = 0) + (P 0 = ) + same timing assumption). Entry is deterred, since Prob(entry) = c I 2. Obviously, not socially ecient. No way to improve, since contract is fully enforceable. If entrant could promise something when t = 0, what would happen? (Cheng Chen (HKU)) Econ / 23