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Solutions Manual to Accompany Contract Theory Contents Preface 1 Introduction 2 Hidden Information, Screening 2.1 Question 1 ........................................................................................... 2.2 Question 2 ........................................................................................... 2.3 Question 3 ........................................................................................... 2.3.1 Characterization of First-Best Solution .................................... 2.3.2 Two Types ..................................................................................... 2.3.3 Continuum of Types .................................................................. 2.4 Question 4 ........................................................................................... 2.5 Question 5 ........................................................................................... 2.5.1 Entrepreneur's Utility ............................................................... 2.5.2 First-Best Solution ................................................................... 2.5.3 Second-Best Solution ............................................................... 2.5.4 Binding Constraints ................................................................ 2.5.5 Low-Type Allocation ...................................................................... 2.5.6 Full Screening Problem ............................................................. 2.5.7 Discussion ............................................................................... xi 1 3 3 3 4 4 5 5 7 7 8 8 9 10 11 11 12 2.5.8 Competition ............................................................................... 12 3 Hidden Information, Signaling 15 3.1 Question 6 ........................................................................................... 15 3.2 Question 7............................................................................................ 15 3.3 Question 8 ........................................................................................... 16 3.3.1 Both Types Invest ...................................................................... 16 3.3.2 Only Bad Firms Invest .............................................................. 17 3.3.3 Wasteful Advertising .................................................................. 17 3.4 Question 9 ........................................................................................... 18 3.4.1 No Costs of Financial Distress .................................................. 18 3.4.2 Costs of Financial Distress ....................................................... 20 4 Hidden Action, Moral Hazard 4.1.1 Randomizing Scheme Cannot Be Optimal ............................... Question 11 ........................................................................................ Question 12 ........................................................................................ Question 13 ........................................................................................ 4.4.1 CEO Compensation ................................................................... 4.4.2 Comparison .............................................................................. Question 14 ........................................................................................ Question 15 ........................................................................................ 4.6.1 Self-Financing ........................................................................... 4.6.2 Debt-Financing ......................................................................... 4.6.3 Equity-Financing ...................................................................... Question 16 ........................................................................................ 4.7.1 Posttakeover Value .................................................................... 4.7.2 Bid Price ..................................................................................... 4.7.3 Second Best Contract ............................................................... 4.7.4 First Best Contract ................................................................... 23 23 24 24 25 25 26 27 27 28 28 30 31 31 32 32 33 4.1 Question 10 ........................................................................................ 23 4.2 4.3 4.4 4.5 4.6 4.7 5 Disclosure of Private Information 35 5.1 Question 17 ........................................................................................ 35 5.2 Question 18 ........................................................................................ 35 5.2.1 Ex-Post Payoffs ............................................................................ 36 5.2.2 Comparison of Disclosure Regimes ........................................... 5.2.3 Voluntary Disclosure ................................................................. 5.3 Question 19 ........................................................................................ 5.3.1 Unique Optimal Contract ......................................................... 5.3.2 Optimal Random Verification .................................................... 5.3.3 Optimal Contract with Risk Averse Entrepreneur.................... 5.4 Question 20 ........................................................................................ 37 38 38 38 40 41 41 6 Multidimensional Incentive Problems 43 6.1 Question 21 ........................................................................................ 43 6.2 Question 22 ........................................................................................ 6.2.1 First-Best Outcome .................................................................. 6.2.2 Linear Contracts ...................................................................... 6.3 Question 23 ........................................................................................ 6.3.1 First-Best Solution ................................................................... 6.3.2 Evidence-Based Rewards ........................................................... 6.3.3 Decision-Based Rewards ........................................................... 6.3.4 Information Disclosure .............................................................. 6.4 Question 24 ........................................................................................ 44 45 45 47 48 53 54 56 57 7 Bilateral Trading and Auctions 59 7.1 Question 25 ....................................................................................... 59 7.2 Question 26 ....................................................................................... 60 7.2.1 IC and IR Constraints .............................................................. 60 7.2.2 Efficient Trade ............................................................................ 61 7.2.3 Comparison with Myerson-Satterthwaite Theorem . . . ........... 62 7.3 Question 27 ....................................................................................... 63 7.4 Question 28 ....................................................................................... 63 7.5 Question 29 ....................................................................................... 63 7.5.1 Expected Payoff ........................................................................... 64 7.5.2 Standard Auctions .................................................................. 65 7.5.3 Optimal Auction ....................................................................... 66 7.5.4 Uniform Distribution................................................................. 66 8 Multiagent Moral Hazard and Collusion 69 8.1 Question 30 ....................................................................................... 69 8.1.1 Attaining the First Best Under Risk Neutrality ....................... 70 8.1.2 Risk Aversion ............................................................................. 71 8.2 Question 31 ....................................................................................... 72 8.3 Question 32 ....................................................................................... 73 8.3.1 Optimal Side Contract ............................................................. 74 8.3.2 Restriction to Collusion-Proof Contracts ................................. 75 8.3.3 Optimal Collusion-Proof Contract ............................................. 75 8.3.4 Collusion Impossible ................................................................ 77 8.4 Question 33 ....................................................................................... 79 9 Dynamic Adverse Selection 81 9.1 Question 34 ....................................................................................... 81 9.2 Question 35 ....................................................................................... 82 9.2.1 Full Commitment...................................................................... 82 9.2.2 No Commitment ........................................................................ 84 9.3 Question 36 ....................................................................................... 84 9.3.1 Pure Adverse Selection............................................................... 85 9.3.2 Adverse Selection and Moral Hazard ............................................ 86 9.4 Question 37 ....................................................................................... 87 10 Dynamic Moral Hazard 89 10.1 Question 38 ..................................................................................... 89 10.2 Question 39 ..................................................................................... 89 10.2.1 Debt Equals Cash Flow .......................................................... 91 10.2.2 Relaxing the Constraint ......................................................... 91 10.2.3 Optimal Values of Debt ........................................................... 91 10.2.4 Random First-Period Cash Flow ............................................ 92 10.2.5 Known New Investment Return .............................................. 92 10.2.6 Need for Short-Term Risky Debt ............................................. 93 10.3 Question 40 ..................................................................................... 93 10.3.1 Characterization of Rational-Expectations Equilibrium ..... 94 10.3.2 First-Period Allocation ........................................................... 95 10.3.3 Positive Return of Firm-Specific Project ............................... 95 11 Incomplete Contracts 99 11.1 Question 41 ..................................................................................... 99 11.2 Question 42 ................................................................................... 100 11.2.1 First-Best Allocation of Assets and Investment Levels . .... 101 11.2.2 Optimal Asset Ownership ................................................... 101 11.2.3 Comparison ....................................................................... 103 11.2.4 Ex Post Bargaining with an Outside Option ...................... 103 11.3 Question 43 ................................................................................... 104 11.4 Question 44 ................................................................................... 105 11.4.1 Feasibility Constraints ....................................................... 106 11.4.2 Optimal Control Structures ............................................... 110 11.4.3 Comparison with Aghion and Bolton (1992) .......................... 112 12 Unverifiable Information Contracting 113 12.1 Question 45 ................................................................................... 113 12.2 Question 46 ................................................................................... 114 12.3 Question 47 ................................................................................... 114 12.4 Question 48 ................................................................................... 115 12.5 Question 49 ................................................................................... 115 12.5.1 First-Best Solution ............................................................ 116 12.5.2 No Initial Contract .............................................................. 116 12.5.3 Single-Pair contract ............................................................ 117 12.5.4 At-Will-Contracting Provision .............................................. 118 12.5.5 No Direct Externalities ........................................................ 120 12.6 Question 50 ................................................................................... 121 12.6.1 First-Best Outcome ............................................................ 122 12.6.2 Null Contract with Renegotiation ....................................... 122 12.6.3 No Renegotiation .................................................................. 123 12.6.4 Contracting with Renegotiation .......................................... 123 12.6.5 Discussion ......................................................................... 125 12.7 Question 51 ................................................................................. 125 12.7.1 Aghion-Tirole with Quadratic Effort Costs .......................... 125 12.7.2 Strong Conflict of Interest .................................................. 127 12.7.3 Random Choice of Project .................................................... 128 13 Markets and Contracts 13.1 Question 52 ................................................................................. 13.1.1 Observable and Contractible Action ................................... 13.1.2 Unobservable or Non-Contractible Action .......................... 13.1.3 Common Agency ................................................................... 13.2 Question 53 ................................................................................. 13.3 Question 54 ................................................................................. 131 131 131 132 133 134 134 13.3.1 First-Best Solution .............................................................. 13.3.2 Joint Contract .................................................................... 13.3.3 Common Agency ..................................................................... 13.3.4 Comparison and Discussion ................................................ Bibliography 135 135 136 137 139