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

Cost Padding, Monitoring, and Regulation Shinji Kobayashi and Shigemi Ohba Shinji Kobayashi and Shigemi Ohba Graduate School of Economics Nihon University 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 output). � 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 • S : Social benefits • R : Revenue • C : Cost • • τ τ t t and and : : Monetary t Monetary t ransfers ransfers t : Gov. is a residual claimant τ : Firm is a residual claimant ∗ π GI > π GO = π FO > π FI Gov. Payoff Khalil-Lawarree (1995)

θ = θ − + C e a e a ( , , ) e : Firm's cost reduction effort e 2 disutility for Firm 2 2 θ θ < θ : Firm's productivity types with 1 2 − p p w.p. and 1 a : Firm's cost padding

Monitoring Instruments θ = θ − + C e a e a ( , , ) ● Monitoring e & a ● 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 • Π = + − − S R C t Government ' s Payoff : e 2 • = + − U t a Firm' s Payoff : 2

Firm as Residual Claimant (Case 4) Monitoring a & e (Case 5) Monitoring e & C (Case 6) Monitoring a & C • Π = + τ S Government ' s Payoff : e 2 • = + − − τ − U R a C Firm' s Payoff : 2 e 2 = − θ − − τ − R e ( ) 2

Timing Time = t 0 G can decide on residual claimancy monitoring instruments = t 1 Nature chooses θ = = t t 2 2 G offers a contract, F accepts or refuses it = t 3 e a F makes and = t 4 C is realized, monitoring is implemented τ t or takes place

Benchmark: without cost padding As a benchmark, we consider the cost function = θ − C e residual claimant (government or firm) residual claimant (government or firm) and two monitoring instruments (cost reduction effort or cost) • + e Gov. as R/C monitoring • + C Gov. as R/C monitoring • + e Firm as R/C monitoring • + monitoring C Firm as R/C

R/C + Monitoring e without cost padding: Gov. as The government's problem is to maximize its payoff subject to two IRCs and two ICCs. The optimal mechanism is given by e e 2 2 = = t t 1 2 1 2 2 2 2 2 e 2 e e 2 2 t − ≥ 1 − ≥ − t t 0 1 2 1 2 1 2 2 2 e e e 2 2 2 t − ≥ − ≥ − t t 2 0 2 1 2 2 1 2 2 2

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 − e e e e 2 2 2 2 ˆ = + t t = 1 2 2 2 1 2 2 2 2 2 = + θ − θ = + θ − θ e e e e ˆ ˆ with and 2 2 1 2 1 1 2 1 e 2 e e 2 2 ˆ t − ≥ − ≥ − 1 t t 0 1 2 1 2 1 2 2 2 e 2 e e 2 2 ˆ t − ≥ 2 − ≥ − 0 t t 2 1 2 2 2 1 2 2

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 e e 2 2 τ = − θ − − − θ − θ R e τ = − θ − − R e 1 2 ( ) ( ) ( ) 1 1 1 2 1 2 2 2 2 2 2 2 = + θ − θ = + θ − θ e e e e ˆ ˆ with and 2 2 1 2 1 1 2 1 e e e 2 2 2 − θ − − − τ ≥ − θ − − − τ − θ − − − τ ≥ R e R e R e 1 2 ( ) ( ) 1 ( ) 0 1 1 1 1 2 2 1 1 1 2 2 2 e e e 2 2 2 − θ − − − τ ≥ − θ − − − τ ≥ − θ − − − τ R e R e R e 2 2 1 ( ) 0 ( ) ( ) 2 2 2 2 2 2 2 1 1 2 2 2

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 e 2 − e e e 2 2 2 ˆ τ = − θ − − R e τ = − θ − − − R e 2 ( ) 1 2 2 ( ) 2 2 2 1 1 1 2 2 2 2 2 2 = + θ − θ = + θ − θ e e e e ˆ ˆ with and 2 2 1 2 1 1 2 1 e e 2 2 ˆ e 2 − θ − − − τ ≥ − θ − − − τ R e R e 1 2 − θ − − − τ ≥ ˆ ( ) ( ) R e 1 ( ) 0 1 1 1 1 2 2 2 2 1 1 1 2 e e 2 2 ˆ e 2 − θ − − − τ ≥ − θ − − − τ R e R e − θ − − − τ ≥ 2 1 R e ˆ ( ) ( ) 2 ( ) 0 2 2 2 2 1 1 2 2 2 2 2 2

without cost padding: Cost reduction effort θ A type's effort level is at the first best. 1 θ e A type's effort level is at the first best under monitoring 2 C and is distorted downward under monitoring . Gov. as R/C Firm as R/C Monitoring = = = fb e e e 1 1 2 e = fb = e e 1 1 Monitoring p = − θ − θ e C 1 ( ) − 2 p 2 1 1

without cost padding: information rents = θ − C e Gov. as R/C Firm as R/C Monitoring θ − θ 0 e 2 1 due to e − e 2 ˆ 2 Monitoring lower effort 2 2 C 2 ( )   − θ − θ e e 2 2 2 ˆ ( ) ( )( )   θ − θ − = θ − θ − + > e 2 2 2 1 1 0   2 1 2 1 2   2 2 − e e 2 2 ˆ ⇔ θ − θ > 2 2 2 1 2

without cost padding: Government’s payoffs = θ − C e Gov. as R/C Firm as R/C Monitoring Monitoring 1 1 1 1 π π G G θ θ = = + + − − θ θ − − − − θ θ + + π π θ θ = = + + − − θ θ 2 + + S S R R p p p p F F S S R R ( ( 1 1 ) ) 1 2 e 2 2 Monitoring p 1 π GO = π FO = + − θ + + θ − θ S R 2 ( ) C − 2 p 2 1 2 2 ( 1 )

Analysis: with cost padding = θ − + C e a We consider t he cost function . residual claimant (government or firm) and three cases of monitoring: + + e a (Case 1) Gov. as R/C monitoring and + a C (Case 2) Gov. as R/C monitoring and + e C (Case 3) Gov. as R/C monitoring and + e a (Case 4 ) Firm as R/C monitoring and + a C (Case 5) Firm as R/C monitoring and + e C (Case 6) Firm as R/C monitoring and

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 e e 2 2 = = t t 1 2 1 2 2 2 2 2 e 2 e e 2 2 t − ≥ 1 − ≥ − t t 0 1 2 1 2 1 2 2 2 e e e 2 2 2 t − ≥ − ≥ − t t 2 0 2 1 2 2 1 2 2 2

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 − e e e e 2 2 2 2 ˆ t = = + t 2 1 2 2 1 2 2 2 2 2 = + θ − θ = + θ − θ e e e e ˆ ˆ with and 2 2 1 2 1 1 2 1 e 2 e e 2 2 ˆ t − ≥ − ≥ − 1 t t 0 1 2 1 2 1 2 2 2 e 2 e e 2 2 ˆ t − ≥ 2 − ≥ − 0 t t 2 1 2 2 2 1 2 2

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 e e 2 2 = − + θ − θ = − t a t a 1 2 1 1 2 1 2 2 2 2 2 2 = + θ − θ = + θ − θ a a a a ˆ ˆ with and 2 2 2 1 1 1 1 2 e e 2 2 e 2 + − ≥ + − t a t a 1 2 ˆ + − ≥ t a 1 0 1 1 2 2 2 2 1 1 2 e e e 2 2 2 + − ≥ + − ≥ + − t a t a t a 2 2 1 ˆ 0 2 2 2 2 1 1 2 2 2

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 e e 2 2 τ = − θ − − − θ − θ R e τ = − θ − − R e 1 2 ( ) ( ) ( ) 1 1 1 2 1 2 2 2 2 2 2 2 e e e 2 2 2 − θ − − − τ ≥ − θ − − − τ − θ − − − τ ≥ R e R e R e 1 2 ( ) ( ) 1 ( ) 0 1 1 1 1 2 2 1 1 1 2 2 2 e e e 2 2 2 − θ − − − τ ≥ − θ − − − τ ≥ − θ − − − τ R e R e R e 2 2 1 ( ) 0 ( ) ( ) 2 2 2 2 2 2 2 1 1 2 2 2