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Lecture Three: Adverse Selection
Cheng Chen
School of Economics and Finance
The University of Hong Kong
(Cheng Chen (HKU)) Econ 6006 1 / 14
Introduction
Motivation
Examples:I The lemon market (Akerlof, 1970).I The insurance market.
I Dropouts of classes after the exam.I Others?
Why do we care about it?I Information asymmetry is everywhere.I Neoclassical economics and frictions. (Pareto improvement and the
mechanism design).I Market e�ciency and welfare (e.g., market shutdown).
(Cheng Chen (HKU)) Econ 6006 2 / 14
Introduction
Motivation
Examples:I The lemon market (Akerlof, 1970).I The insurance market.I Dropouts of classes after the exam.I Others?
Why do we care about it?I Information asymmetry is everywhere.I Neoclassical economics and frictions. (Pareto improvement and the
mechanism design).I Market e�ciency and welfare (e.g., market shutdown).
(Cheng Chen (HKU)) Econ 6006 2 / 14
Introduction
Motivation
Examples:I The lemon market (Akerlof, 1970).I The insurance market.I Dropouts of classes after the exam.I Others?
Why do we care about it?I Information asymmetry is everywhere.
I Neoclassical economics and frictions. (Pareto improvement and themechanism design).
I Market e�ciency and welfare (e.g., market shutdown).
(Cheng Chen (HKU)) Econ 6006 2 / 14
Introduction
Motivation
Examples:I The lemon market (Akerlof, 1970).I The insurance market.I Dropouts of classes after the exam.I Others?
Why do we care about it?I Information asymmetry is everywhere.I Neoclassical economics and frictions. (Pareto improvement and the
mechanism design).I Market e�ciency and welfare (e.g., market shutdown).
(Cheng Chen (HKU)) Econ 6006 2 / 14
Introduction Preliminaries (Section 1.3.1)
An Example
Adverse selection: Hidden information.A bilateral contracting: an employer (the principal) and an employee(the agent).
I The employee has one unit of time.I Output equals θi (1− li ), where i ∈ H, L (θH > θL two types).I The employee knows his type, while the employer does not.
I The employer's utility is
U(αθi (1− li )− ti ),
and the employee's utility is
u(θi li + ti ) ≥ u(θi ).
Assume that ex post output is unobservable and α > 1.
No asymmetric information→ θi = ti and li = 0 for all i (First-Best orFB). (Derivation?)
Not incentive compatible: L type guy wants to mimic H type guy.
(Why?)
(Cheng Chen (HKU)) Econ 6006 3 / 14
Introduction Preliminaries (Section 1.3.1)
An Example
Adverse selection: Hidden information.A bilateral contracting: an employer (the principal) and an employee(the agent).
I The employee has one unit of time.I Output equals θi (1− li ), where i ∈ H, L (θH > θL two types).I The employee knows his type, while the employer does not.I The employer's utility is
U(αθi (1− li )− ti ),
and the employee's utility is
u(θi li + ti ) ≥ u(θi ).
Assume that ex post output is unobservable and α > 1.
No asymmetric information→ θi = ti and li = 0 for all i (First-Best orFB). (Derivation?)
Not incentive compatible: L type guy wants to mimic H type guy.
(Why?)
(Cheng Chen (HKU)) Econ 6006 3 / 14
Introduction Preliminaries (Section 1.3.1)
An Example
Adverse selection: Hidden information.A bilateral contracting: an employer (the principal) and an employee(the agent).
I The employee has one unit of time.I Output equals θi (1− li ), where i ∈ H, L (θH > θL two types).I The employee knows his type, while the employer does not.I The employer's utility is
U(αθi (1− li )− ti ),
and the employee's utility is
u(θi li + ti ) ≥ u(θi ).
Assume that ex post output is unobservable and α > 1.
No asymmetric information→ θi = ti and li = 0 for all i (First-Best orFB). (Derivation?)
Not incentive compatible: L type guy wants to mimic H type guy.
(Why?)
(Cheng Chen (HKU)) Econ 6006 3 / 14
Introduction Preliminaries (Section 1.3.1)
An Example
Adverse selection: Hidden information.A bilateral contracting: an employer (the principal) and an employee(the agent).
I The employee has one unit of time.I Output equals θi (1− li ), where i ∈ H, L (θH > θL two types).I The employee knows his type, while the employer does not.I The employer's utility is
U(αθi (1− li )− ti ),
and the employee's utility is
u(θi li + ti ) ≥ u(θi ).
Assume that ex post output is unobservable and α > 1.
No asymmetric information→ θi = ti and li = 0 for all i (First-Best orFB). (Derivation?)
Not incentive compatible: L type guy wants to mimic H type guy.
(Why?)
(Cheng Chen (HKU)) Econ 6006 3 / 14
Introduction Preliminaries (Section 1.3.1)
Mathematical Formulation
Maximize the principal's payo� under constraints:
maxlj ,tj
pLU(αθL(1− lL)− tL) + pHU(αθH(1− lH)− tH)
s.t. u(θLlL + tL) ≥ u(θL),
u(θH lH + tH) ≥ u(θH),
u(θH lH + tH) ≥ u(θH lL + tL),
u(θLlL + tL) ≥ u(θLlH + tH).
Revelation Principle.
First two inequalities: Individual Rationality (IR) or Participation
Constraints (PC).
Last two inequalities: Incentive Compatibility (IR) constraints.
(Cheng Chen (HKU)) Econ 6006 4 / 14
Introduction Preliminaries (Section 1.3.1)
Mathematical Formulation
Maximize the principal's payo� under constraints:
maxlj ,tj
pLU(αθL(1− lL)− tL) + pHU(αθH(1− lH)− tH)
s.t. u(θLlL + tL) ≥ u(θL),
u(θH lH + tH) ≥ u(θH),
u(θH lH + tH) ≥ u(θH lL + tL),
u(θLlL + tL) ≥ u(θLlH + tH).
Revelation Principle.
First two inequalities: Individual Rationality (IR) or Participation
Constraints (PC).
Last two inequalities: Incentive Compatibility (IR) constraints.
(Cheng Chen (HKU)) Econ 6006 4 / 14
Introduction Preliminaries (Section 1.3.1)
Basic Principles
One option: lH = lL = 0 and tH = tL = θH (a simple contract).I L type agent: information rents (monopoly power).I H type agent: no allocative distortion.
In general, the tradeo� between information rents and allocativee�ciency.
I The agent that has incentive to mimic (L type): information rents.I The agent that is mimicked (H type): allocative distortion.
How to solve the problem?I If the uninformed party makes the contract: screening. (i.e., Mirrlees
(1971), Myerson (1979), Stiglitz and Weiss (1981))I If the informed party makes the contract: signalling. (i.e., Spence
(1973, 1974))
(Cheng Chen (HKU)) Econ 6006 5 / 14
Introduction Preliminaries (Section 1.3.1)
Basic Principles
One option: lH = lL = 0 and tH = tL = θH (a simple contract).I L type agent: information rents (monopoly power).I H type agent: no allocative distortion.
In general, the tradeo� between information rents and allocativee�ciency.
I The agent that has incentive to mimic (L type): information rents.I The agent that is mimicked (H type): allocative distortion.
How to solve the problem?I If the uninformed party makes the contract: screening. (i.e., Mirrlees
(1971), Myerson (1979), Stiglitz and Weiss (1981))I If the informed party makes the contract: signalling. (i.e., Spence
(1973, 1974))
(Cheng Chen (HKU)) Econ 6006 5 / 14
Introduction Preliminaries (Section 1.3.1)
Basic Principles
One option: lH = lL = 0 and tH = tL = θH (a simple contract).I L type agent: information rents (monopoly power).I H type agent: no allocative distortion.
In general, the tradeo� between information rents and allocativee�ciency.
I The agent that has incentive to mimic (L type): information rents.I The agent that is mimicked (H type): allocative distortion.
How to solve the problem?I If the uninformed party makes the contract: screening. (i.e., Mirrlees
(1971), Myerson (1979), Stiglitz and Weiss (1981))I If the informed party makes the contract: signalling. (i.e., Spence
(1973, 1974))
(Cheng Chen (HKU)) Econ 6006 5 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Setup
Classical references: Mussa and Rosen (1978) and Maskin and Riley
(1984a)
A bilateral contracting: a seller (the principal) and a buyer (theagent).
I The seller's payo�: π = T − cq.I The buyer's payo�: u(θi , q,T ) = θiv(q)− T ≥ u where i ∈ {H, L}.I We have θH > θL.I Asymmetric information: seller does not know θi . Prob(θ = θL) = β.
FB (no information friction):
maxTi ,qi
Ti − cqi
s.t. θiv(qi )− Ti ≥ u.
Solution (type-speci�c two-part tari�s): θiv′(qi ) = c and
θiv(qi ) = Ti + u.
(Cheng Chen (HKU)) Econ 6006 6 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Setup
Classical references: Mussa and Rosen (1978) and Maskin and Riley
(1984a)
A bilateral contracting: a seller (the principal) and a buyer (theagent).
I The seller's payo�: π = T − cq.I The buyer's payo�: u(θi , q,T ) = θiv(q)− T ≥ u where i ∈ {H, L}.I We have θH > θL.I Asymmetric information: seller does not know θi . Prob(θ = θL) = β.
FB (no information friction):
maxTi ,qi
Ti − cqi
s.t. θiv(qi )− Ti ≥ u.
Solution (type-speci�c two-part tari�s): θiv′(qi ) = c and
θiv(qi ) = Ti + u.
(Cheng Chen (HKU)) Econ 6006 6 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Setup
Classical references: Mussa and Rosen (1978) and Maskin and Riley
(1984a)
A bilateral contracting: a seller (the principal) and a buyer (theagent).
I The seller's payo�: π = T − cq.I The buyer's payo�: u(θi , q,T ) = θiv(q)− T ≥ u where i ∈ {H, L}.I We have θH > θL.I Asymmetric information: seller does not know θi . Prob(θ = θL) = β.
FB (no information friction):
maxTi ,qi
Ti − cqi
s.t. θiv(qi )− Ti ≥ u.
Solution (type-speci�c two-part tari�s): θiv′(qi ) = c and
θiv(qi ) = Ti + u.
(Cheng Chen (HKU)) Econ 6006 6 / 14
Screening: Two Types (Section 2.1) Theory
Incentive CompatibilityHowever, this is not incentive-compatible for H type. I.e., H type
wants to mimic L type:
TL = θLv(qL)− u
If H type takes L type's contract, he receives
θHv(qL)− TL = (θH − θL)v(qL) + u > u.
On the other hand, payment to H type is
TH = θHv(qH)− u
Incentive compatible for L type. If L type takes H type's contract, he
receives
θLv(qH)− TH = (θL − θH)v(qH) + u < u.
Intuition: Transfer to employer is too much for H type, since its
willingness to pay is high.
(Cheng Chen (HKU)) Econ 6006 7 / 14
Screening: Two Types (Section 2.1) Theory
Incentive CompatibilityHowever, this is not incentive-compatible for H type. I.e., H type
wants to mimic L type:
TL = θLv(qL)− u
If H type takes L type's contract, he receives
θHv(qL)− TL = (θH − θL)v(qL) + u > u.
On the other hand, payment to H type is
TH = θHv(qH)− u
Incentive compatible for L type. If L type takes H type's contract, he
receives
θLv(qH)− TH = (θL − θH)v(qH) + u < u.
Intuition: Transfer to employer is too much for H type, since its
willingness to pay is high.
(Cheng Chen (HKU)) Econ 6006 7 / 14
Screening: Two Types (Section 2.1) Theory
Incentive CompatibilityHowever, this is not incentive-compatible for H type. I.e., H type
wants to mimic L type:
TL = θLv(qL)− u
If H type takes L type's contract, he receives
θHv(qL)− TL = (θH − θL)v(qL) + u > u.
On the other hand, payment to H type is
TH = θHv(qH)− u
Incentive compatible for L type. If L type takes H type's contract, he
receives
θLv(qH)− TH = (θL − θH)v(qH) + u < u.
Intuition: Transfer to employer is too much for H type, since its
willingness to pay is high.(Cheng Chen (HKU)) Econ 6006 7 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Linear Pricing
Normalize u = 0.
Suppose it is optimal to sell to both types of agents.
Linear pricing: (q, P) (one type of contract)
q: quantity; P : unit price.
From F.O.C. θiv′(q) = P , we derive demand function: qi = Di (P).
Buyer's payo�:
Si (P) = θiv [Di (q)]− PDi (P).
Let
D(P) = βDL(P) + (1− β)DH(P)
and
S(P) = βSL(P) + (1− β)SH(P).
(Cheng Chen (HKU)) Econ 6006 8 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Linear Pricing
Normalize u = 0.
Suppose it is optimal to sell to both types of agents.
Linear pricing: (q, P) (one type of contract)
q: quantity; P : unit price.
From F.O.C. θiv′(q) = P , we derive demand function: qi = Di (P).
Buyer's payo�:
Si (P) = θiv [Di (q)]− PDi (P).
Let
D(P) = βDL(P) + (1− β)DH(P)
and
S(P) = βSL(P) + (1− β)SH(P).
(Cheng Chen (HKU)) Econ 6006 8 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Linear Pricing
Normalize u = 0.
Suppose it is optimal to sell to both types of agents.
Linear pricing: (q, P) (one type of contract)
q: quantity; P : unit price.
From F.O.C. θiv′(q) = P , we derive demand function: qi = Di (P).
Buyer's payo�:
Si (P) = θiv [Di (q)]− PDi (P).
Let
D(P) = βDL(P) + (1− β)DH(P)
and
S(P) = βSL(P) + (1− β)SH(P).
(Cheng Chen (HKU)) Econ 6006 8 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Linear Pricing
Normalize u = 0.
Suppose it is optimal to sell to both types of agents.
Linear pricing: (q, P) (one type of contract)
q: quantity; P : unit price.
From F.O.C. θiv′(q) = P , we derive demand function: qi = Di (P).
Buyer's payo�:
Si (P) = θiv [Di (q)]− PDi (P).
Let
D(P) = βDL(P) + (1− β)DH(P)
and
S(P) = βSL(P) + (1− β)SH(P).
(Cheng Chen (HKU)) Econ 6006 8 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Linear Pricing
Normalize u = 0.
Suppose it is optimal to sell to both types of agents.
Linear pricing: (q, P) (one type of contract)
q: quantity; P : unit price.
From F.O.C. θiv′(q) = P , we derive demand function: qi = Di (P).
Buyer's payo�:
Si (P) = θiv [Di (q)]− PDi (P).
Let
D(P) = βDL(P) + (1− β)DH(P)
and
S(P) = βSL(P) + (1− β)SH(P).
(Cheng Chen (HKU)) Econ 6006 8 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Linear Pricing (Cont.)
Maximization problem for seller:
maxP
(P − c)D(P),
where θiv′(Di (P)) = P .
Solution:
Pm = c − D(P)
D ′(P).
Rents for both types of buyers:
SL(P) > 0; SH(P) > 0.
Ine�ciently low consumption:
θiv′(q) = P > c.
(Cheng Chen (HKU)) Econ 6006 9 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Linear Pricing (Cont.)
Maximization problem for seller:
maxP
(P − c)D(P),
where θiv′(Di (P)) = P .
Solution:
Pm = c − D(P)
D ′(P).
Rents for both types of buyers:
SL(P) > 0; SH(P) > 0.
Ine�ciently low consumption:
θiv′(q) = P > c.
(Cheng Chen (HKU)) Econ 6006 9 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Linear Pricing (Cont.)
Maximization problem for seller:
maxP
(P − c)D(P),
where θiv′(Di (P)) = P .
Solution:
Pm = c − D(P)
D ′(P).
Rents for both types of buyers:
SL(P) > 0; SH(P) > 0.
Ine�ciently low consumption:
θiv′(q) = P > c.
(Cheng Chen (HKU)) Econ 6006 9 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Single Two-Part Tari�
Single two-part tari�: (Z , P) (one type of contract)
Z : �xed fee. P : unit price.I H type always participates.
maxP
Z + (P − c)D(P),
where Z = SL(P) and SL(P) = θLv [DL(P)]− PDL(P): buyer's netsurplus.
I Solution:Pd = c − D(P)+S′L(P)
D′ (P)
and S′L(P) = −D
′L(P) > 0.
Extract all rents from L type and leave some rents to H type.
Single two-part tari� is better than linear pricing, and
Pm > Pd > Pc = c .
(Cheng Chen (HKU)) Econ 6006 10 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Single Two-Part Tari�
Single two-part tari�: (Z , P) (one type of contract)
Z : �xed fee. P : unit price.I H type always participates.
maxP
Z + (P − c)D(P),
where Z = SL(P) and SL(P) = θLv [DL(P)]− PDL(P): buyer's netsurplus.
I Solution:Pd = c − D(P)+S′L(P)
D′ (P)
and S′L(P) = −D
′L(P) > 0.
Extract all rents from L type and leave some rents to H type.
Single two-part tari� is better than linear pricing, and
Pm > Pd > Pc = c .
(Cheng Chen (HKU)) Econ 6006 10 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: Single Two-Part Tari�
Single two-part tari�: (Z , P) (one type of contract)
Z : �xed fee. P : unit price.I H type always participates.
maxP
Z + (P − c)D(P),
where Z = SL(P) and SL(P) = θLv [DL(P)]− PDL(P): buyer's netsurplus.
I Solution:Pd = c − D(P)+S′L(P)
D′ (P)
and S′L(P) = −D
′L(P) > 0.
Extract all rents from L type and leave some rents to H type.
Single two-part tari� is better than linear pricing, and
Pm > Pd > Pc = c .
(Cheng Chen (HKU)) Econ 6006 10 / 14
Screening: Two Types (Section 2.1) Theory
Graphical Representation
(Cheng Chen (HKU)) Econ 6006 11 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: IC Contracts
Second-Best outcome (SB) and nonlinear pricing (remember the
revelation principle):
maxTi ,qi
β[T (qL)− cqL] + (1− β)[T (qH)− cqH ]
s.t. θHv(qH)− TH ≥ θHv(qL)− TL, (ICH)
θLv(qL)− TL ≥ θLv(qH)− TH , (ICL)
θHv(qH)− TH ≥ 0, (IRH)
θLv(qL)− TL ≥ 0. (IRL)
First two inequalities: IRs.
Last two inequalities: ICs.
(Cheng Chen (HKU)) Econ 6006 12 / 14
Screening: Two Types (Section 2.1) Theory
Two Types: IC Contracts
Second-Best outcome (SB) and nonlinear pricing (remember the
revelation principle):
maxTi ,qi
β[T (qL)− cqL] + (1− β)[T (qH)− cqH ]
s.t. θHv(qH)− TH ≥ θHv(qL)− TL, (ICH)
θLv(qL)− TL ≥ θLv(qH)− TH , (ICL)
θHv(qH)− TH ≥ 0, (IRH)
θLv(qL)− TL ≥ 0. (IRL)
First two inequalities: IRs.
Last two inequalities: ICs.
(Cheng Chen (HKU)) Econ 6006 12 / 14
Screening: Two Types (Section 2.1) Theory
IC Contracts: Two Binding Constraints
IRH is redundant, because
θHv(qH)− TH ≥ θHv(qL)− TL > θLv(qL)− TL ≥ 0.
IRH is redundant → ICH holds with equality.I If not, principal can increase tH until ICH holds with equality.
ICH + ICL → qH ≥ qL (monotonicity):
θH [v(qH)− v(qL)] ≥ TH − TL ≥ θL[v(qH)− v(qL)]→ qH ≥ qL.
ICH holds with equality + (qH ≥ qL) → ICL is redundant.
θH [v(qH)− v(qL)] = TH − TL
→ θL[v(qH)− v(qL)] ≤ TH − TL
→ θLv(qL)− TL ≥ θLv(qH)− TH .
ICL is redundant → IRL should hold with equality.I If not, principal can increase tL until IRL holds with equality.
(Cheng Chen (HKU)) Econ 6006 13 / 14
Screening: Two Types (Section 2.1) Theory
IC Contracts: Two Binding Constraints
IRH is redundant, because
θHv(qH)− TH ≥ θHv(qL)− TL > θLv(qL)− TL ≥ 0.
IRH is redundant → ICH holds with equality.I If not, principal can increase tH until ICH holds with equality.
ICH + ICL → qH ≥ qL (monotonicity):
θH [v(qH)− v(qL)] ≥ TH − TL ≥ θL[v(qH)− v(qL)]→ qH ≥ qL.
ICH holds with equality + (qH ≥ qL) → ICL is redundant.
θH [v(qH)− v(qL)] = TH − TL
→ θL[v(qH)− v(qL)] ≤ TH − TL
→ θLv(qL)− TL ≥ θLv(qH)− TH .
ICL is redundant → IRL should hold with equality.I If not, principal can increase tL until IRL holds with equality.
(Cheng Chen (HKU)) Econ 6006 13 / 14
Screening: Two Types (Section 2.1) Theory
IC Contracts: Two Binding Constraints
IRH is redundant, because
θHv(qH)− TH ≥ θHv(qL)− TL > θLv(qL)− TL ≥ 0.
IRH is redundant → ICH holds with equality.I If not, principal can increase tH until ICH holds with equality.
ICH + ICL → qH ≥ qL (monotonicity):
θH [v(qH)− v(qL)] ≥ TH − TL ≥ θL[v(qH)− v(qL)]→ qH ≥ qL.
ICH holds with equality + (qH ≥ qL) → ICL is redundant.
θH [v(qH)− v(qL)] = TH − TL
→ θL[v(qH)− v(qL)] ≤ TH − TL
→ θLv(qL)− TL ≥ θLv(qH)− TH .
ICL is redundant → IRL should hold with equality.I If not, principal can increase tL until IRL holds with equality.
(Cheng Chen (HKU)) Econ 6006 13 / 14
Screening: Two Types (Section 2.1) Theory
IC Contracts: Two Binding Constraints
IRH is redundant, because
θHv(qH)− TH ≥ θHv(qL)− TL > θLv(qL)− TL ≥ 0.
IRH is redundant → ICH holds with equality.I If not, principal can increase tH until ICH holds with equality.
ICH + ICL → qH ≥ qL (monotonicity):
θH [v(qH)− v(qL)] ≥ TH − TL ≥ θL[v(qH)− v(qL)]→ qH ≥ qL.
ICH holds with equality + (qH ≥ qL) → ICL is redundant.
θH [v(qH)− v(qL)] = TH − TL
→ θL[v(qH)− v(qL)] ≤ TH − TL
→ θLv(qL)− TL ≥ θLv(qH)− TH .
ICL is redundant → IRL should hold with equality.I If not, principal can increase tL until IRL holds with equality.
(Cheng Chen (HKU)) Econ 6006 13 / 14
Screening: Two Types (Section 2.1) Theory
IC Contracts: Two Binding Constraints
IRH is redundant, because
θHv(qH)− TH ≥ θHv(qL)− TL > θLv(qL)− TL ≥ 0.
IRH is redundant → ICH holds with equality.I If not, principal can increase tH until ICH holds with equality.
ICH + ICL → qH ≥ qL (monotonicity):
θH [v(qH)− v(qL)] ≥ TH − TL ≥ θL[v(qH)− v(qL)]→ qH ≥ qL.
ICH holds with equality + (qH ≥ qL) → ICL is redundant.
θH [v(qH)− v(qL)] = TH − TL
→ θL[v(qH)− v(qL)] ≤ TH − TL
→ θLv(qL)− TL ≥ θLv(qH)− TH .
ICL is redundant → IRL should hold with equality.I If not, principal can increase tL until IRL holds with equality.
(Cheng Chen (HKU)) Econ 6006 13 / 14
Screening: Two Types (Section 2.1) Theory
IC Contracts: Simpli�ed Problem
Reduced problem:
maxqL,qH
β[θLv(qL)− cqL] + (1− β)[θHv(qH)− (θH − θL)v(qL)− cqH ],
where (θH − θL)v(qL) captures information rents.
Solution:I No distortion at the top: θHv
′(q∗H ) = c .
I Downward distortion at the bottom (due to information rents):
θLv′(q∗L) =
c
1−(
1−ββ
θH−θLθL
) > c .
Tradeo� between allocative e�ciency and rent reduction.
(Cheng Chen (HKU)) Econ 6006 14 / 14
Screening: Two Types (Section 2.1) Theory
IC Contracts: Simpli�ed Problem
Reduced problem:
maxqL,qH
β[θLv(qL)− cqL] + (1− β)[θHv(qH)− (θH − θL)v(qL)− cqH ],
where (θH − θL)v(qL) captures information rents.
Solution:I No distortion at the top: θHv
′(q∗H ) = c .
I Downward distortion at the bottom (due to information rents):
θLv′(q∗L) =
c
1−(
1−ββ
θH−θLθL
) > c .
Tradeo� between allocative e�ciency and rent reduction.
(Cheng Chen (HKU)) Econ 6006 14 / 14
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