Cost Padding, Monitoring, and Regulation Shinji Kobayashi and - - PowerPoint PPT Presentation

Cost Padding, Monitoring, and Regulation

Shinji Kobayashi and Shigemi Ohba

Graduate School of Economics Nihon University

Shinji Kobayashi and Shigemi Ohba

October 2008

Objectives

We analyze the model of a government’s procurement of facilities from a firm that can do cost padding. To examine the optimal residual claimancy for the government. (Government versus Firm) To examine the optimal monitoring instruments for the government.

Related Literature

Khalil and Lawarree (1995) explore the asymmetric information model in which a principal can determine residual claimancy (principal or agent) and a monitoring instrument (input or agent) and a monitoring instrument (input or

• utput).

Laffont and Tirole (1992) analyze the procurement model with asymmetric information in which an agent exerts cost reduction effort (e) and does cost padding (a).

Model

ransfers Monetary t : and Cost : Revenue : benefits Social : τ t C R S

• claimant

residual a is Firm : claimant residual a is Gov. : ransfers Monetary t : and τ τ t t

• Gov. Payoff

Khalil-Lawarree (1995)

GI GO FO FI

π π π π ∗ > = >

2

: Firm's cost reduction effort disutility for Firm 2 e e

a e a e C + − = ) , , ( θ θ

1 2

2 : Firm's productivity types with w.p. and 1 : Firm's cost padding p p a θ θ θ < −

Monitoring Instruments

• Monitoring e & a

( , , ) C e a e a θ θ = − +

• Monitoring e & a
• Monitoring a & C
• Monitoring e & C

• Gov. as Residual Claimant

(Case 1) Monitoring a & e (Case 2) Monitoring e & C (Case 3) Monitoring a & C

2 : Payoff s Firm' : Payoff s ' Government

2

e a t U t C R S − + =

• −

− + = Π

Firm as Residual Claimant

(Case 4) Monitoring a & e (Case 5) Monitoring e & C (Case 6) Monitoring a & C

2 ) ( 2 : Payoff s Firm' : Payoff s ' Government

2 2

e e R e C a R U S − − − − = − − − + =

• +

= Π

• τ

θ τ τ

Timing

= t 1 = t 2 = t Time

G can decide on residual claimancy monitoring instruments

Nature chooses θ

2 = t 3 = t 4 = t

it refuses

• r

accepts F contract, a

• ffers

G

a e and makes F

is realized, monitoring is implemented

• r takes place

C t τ

Benchmark: without cost padding

residual claimant (government or firm)

As a benchmark, we consider the cost function C e θ = −

residual claimant (government or firm) and two monitoring instruments (cost reduction effort or cost)

• Gov. as R/C

monitoring

• Gov. as R/C

monitoring Firm as R/C monitoring Firm as R/C e C e

• +
• +
• +
• monitoring C

+

2 2 2

2 e t =

2 1 1

2 e t =

without cost padding: Gov. as R/C + Monitoring e

The government's problem is to maximize its payoff subject to two IRCs and two ICCs. The optimal mechanism is given by

2

2 1 1

2 e t − ≥

2 2 2

2 e t − ≥

2 2 1 2 1 2

2 2 e e t t − ≥ −

2 2 2 1 2 1

2 2 e e t t − ≥ − 2

2 2 2 1 2 2 1

ˆ 2 2 e e e t − = +

2 2 2

2 e t = without cost padding: Gov. as R/C + Monitoring C

The government's problem is to maximize its payoff subject to two IRCs and two ICCs. The optimal mechanism is given by

2

2 1 1

2 e t − ≥

2 2 2

2 e t − ≥

2 2 1 2 1 2

ˆ 2 2 e e t t − ≥ −

2 2 2 1 2 1

ˆ 2 2 e e t t − ≥ −

1 2 1 1 2 1 2 2

ˆ and ˆ with θ θ θ θ − + = − + = e e e e

2 1 1 1 1 2 1

( ) ( ) 2 e R e τ θ θ θ = − − − − −

2 2 2 2 2

( ) 2 e R e τ θ = − − −

without cost padding: Firm as R/C + Monitoring e

The government's problem is to maximize its payoff subject to two IRCs and two ICCs. The optimal mechanism is given by

2 1 1 1 1

( ) 2 e R e θ τ − − − − ≥

2

2 2 2 2 2

( ) 2 e R e θ τ − − − − ≥

2 2 1 2 1 1 1 1 2 2

( ) ( ) 2 2 e e R e R e θ τ θ τ − − − − ≥ − − − −

2 2 2 1 2 2 2 2 1 1

( ) ( ) 2 2 e e R e R e θ τ θ τ − − − − ≥ − − − −

2

1 2 1 1 2 1 2 2

ˆ and ˆ with θ θ θ θ − + = − + = e e e e

2 2 2 1 2 2 1 1 1

ˆ ( ) 2 2 e e e R e τ θ − = − − − −

2 2 2 2 2

( ) 2 e R e τ θ = − − −

without cost padding: Firm as R/C + Monitoring C

The government's problem is to maximize its payoff subject to two IRCs and two ICCs. The optimal mechanism is given by

2 2

2 1 1 1 1

( ) 2 e R e θ τ − − − − ≥

2 2 2 2 2

( ) 2 e R e θ τ − − − − ≥

2 2 1 2 1 1 1 1 2 2

ˆ ˆ ( ) ( ) 2 2 e e R e R e θ τ θ τ − − − − ≥ − − − −

2 2 2 1 2 2 2 2 1 1

ˆ ˆ ( ) ( ) 2 2 e e R e R e θ τ θ τ − − − − ≥ − − − −

2

1 2 1 1 2 1 2 2

ˆ and ˆ with θ θ θ θ − + = − + = e e e e

• Gov. as R/C

Firm as R/C

without cost padding: Cost reduction effort

1 2

A type's effort level is at the first best. A type's effort level is at the first best under monitoring and is distorted downward under monitoring . e C θ θ

1

2 1

= = =

fb

e e e

) ( 1 1 1

1 2 2 1

θ θ − − − = = = p p e e e

fb

e Monitoring C Monitoring

without cost padding: information rents

• Gov. as R/C

Firm as R/C

1 2

θ θ −

e Monitoring

e C − =θ

due to lower effort

2 ˆ2

2 2 2

e e −

( ) ( )( ) ( )

2 ˆ 2 1 2 ˆ

2 2 2 2 1 2 2 1 2 2 1 2 2 2 2 2 1 2

e e e e e − > − ⇔ > − + − − =         − − − θ θ θ θ θ θ θ θ

C Monitoring

• Gov. as R/C

Firm as R/C

1 + − + = θ π

θ

R S

F

1 ) 1 ( + − − − + = θ θ π

θ

p p R S

G

Monitoring

e C − =θ

without cost padding: Government’s payoffs

2 1 2 2

) ( ) 1 ( 2 2 1 θ θ θ π π − − + + − + = = p p R S

FO GO

2 1

2 +

− + = θ π

θ

R S

F

2 1 ) 1 (

2 1

+ − − − + = θ θ π

θ

p p R S

G

e Monitoring C Monitoring

Analysis: with cost padding

residual claimant (government or firm) and three cases of monitoring: +

. function cost he consider t We a e C + − = θ

(Case 1) Gov. as R/C monitoring and (Case 2) Gov. as R/C monitoring and (Case 3) Gov. as R/C monitoring and (Case 4 e a a C e C + + + ) Firm as R/C monitoring and (Case 5) Firm as R/C monitoring and (Case 6) Firm as R/C monitoring and e a a C e C + + +

2 2 2

2 e t =

2 1 1

2 e t =

Case 1: Gov. as R/C + Monitoring e and a

The government's problem is to maximize its payoff subject to two IRCs and two ICCs. The optimal mechanism is given by

2

2 1 1

2 e t − ≥

2 2 2

2 e t − ≥

2 2 1 2 1 2

2 2 e e t t − ≥ −

2 2 2 1 2 1

2 2 e e t t − ≥ − 2

2 2 2 1 2 2 1

ˆ 2 2 e e e t − = +

2 2 2

2 e t =

Case 2: Gov. as R/C + Monitoring a and C

The government's problem is to maximize its payoff subject to two IRCs and two ICCs. The optimal mechanism is given by

2

2 1 1

2 e t − ≥

2 2 2

2 e t − ≥

2 2 1 2 1 2

ˆ 2 2 e e t t − ≥ −

2 2 2 1 2 1

ˆ 2 2 e e t t − ≥ −

1 2 1 1 2 1 2 2

ˆ and ˆ with θ θ θ θ − + = − + = e e e e

Case 3: Gov. as R/C + Monitoring e and C

The government's problem is to maximize its payoff subject to two IRCs and two ICCs. The optimal mechanism is given by

2 2 2 2

2 a e t − =

1 2 1 2 1 1

2 θ θ − + − = a e t

2 1 1 1 1 2 2 2

ˆ and ˆ with θ θ θ θ − + = − + = a a a a

2 ˆ 2

2 2 2 2 2 1 1 1

e a t e a t − + ≥ − +

2

2 2 2 2

≥ − + e a t

2

2 1 1 1

≥ − + e a t 2 ˆ 2

2 1 1 1 2 2 2 2

e a t e a t − + ≥ − +

2

2

2 1 1 1 1 2 1

( ) ( ) 2 e R e τ θ θ θ = − − − − −

2 2 2 2 2

( ) 2 e R e τ θ = − − −

Case 4: Firm as R/C + Monitoring e and a

The government's problem is to maximize its payoff subject to two IRCs and two ICCs. The optimal mechanism is given by

2 1 1 1 1

( ) 2 e R e θ τ − − − − ≥

2

2 2 2 2 2

( ) 2 e R e θ τ − − − − ≥

2 2 1 2 1 1 1 1 2 2

( ) ( ) 2 2 e e R e R e θ τ θ τ − − − − ≥ − − − −

2 2 2 1 2 2 2 2 1 1

( ) ( ) 2 2 e e R e R e θ τ θ τ − − − − ≥ − − − −

2

2 2 2 1 2 2 1 1 1

ˆ ( ) 2 2 e e e R e τ θ − = − − − −

2 2 2 2 2

( ) 2 e R e τ θ = − − −

Case 5: Firm as R/C + Monitoring a and C

The government's problem is to maximize its payoff subject to two IRCs and two ICCs. The optimal mechanism is given by

2 2

2 1 1 1 1

( ) 2 e R e θ τ − − − − ≥

2 2 2 2 2

( ) 2 e R e θ τ − − − − ≥

2 2 1 2 1 1 1 1 2 2

ˆ ˆ ( ) ( ) 2 2 e e R e R e θ τ θ τ − − − − ≥ − − − −

2 2 2 1 2 2 2 2 1 1

ˆ ˆ ( ) ( ) 2 2 e e R e R e θ τ θ τ − − − − ≥ − − − −

2

1 2 1 1 2 1 2 2

ˆ and ˆ with θ θ θ θ − + = − + = e e e e

Case 6: Firm as R/C + Monitoring e and C

The government's problem is to maximize its payoff subject to two IRCs and two ICCs. The optimal mechanism is given by

2 1 1 1 1 2 1

( ) ( ) 2 e R e τ θ θ θ = − − − − −

2 2 2 2 2

( ) 2 e R e τ θ = − − −

2 1 1 1 1

( ) 2 e R e θ τ − − − − ≥

2 2 2 2 2

( ) 2 e R e θ τ − − − − ≥

2 2 1 2 1 1 1 1 2 2

ˆ ˆ ( ) ( ) 2 2 e e R e R e θ τ θ τ − − − − ≥ − − − −

2 2 2 1 2 2 2 2 1 1

ˆ ˆ ( ) ( ) 2 2 e e R e R e θ τ θ τ − − − − ≥ − − − −

2 1 1 1 1 2 2 2

ˆ and ˆ with θ θ θ θ − + = − + = a a a a

2 2

Payoffs with cost padding

Case 1 Case 6 Case 2

) ( 1 a p 2 1 ) 1 (

2 1

+ − − − + = Π = Π θ θ p p R S

FEC GEA

Case 2 Case 5 Case 3 Case 4

2 1

2 +

− + = Π = Π θ R S

FEA GEC

2 1 2 2

) ( )) ( 1 ( 2 ) ( 2 1 θ θ θ − − + + − + = Π = Π a p a p R S

FAC GAC

Conclusion

When the government is the residual claimant, it obtains

FEC GEA FAC GAC FEA GEC

Π = Π < Π = Π < Π = Π

When the government is the residual claimant, it obtains the highest payoff by monitoring effort and cost padding, and the lowest payoff by monitoring effort and cost. When the firm is the residual claimant, the government

• btains the highest payoff by monitoring effort and cost,

and the lowest payoff by monitoring effort and cost padding.