The Supply of Health Service under the Congenital and Acquired Risks of Health:

Complete Information and Incomplete Information

Takanori Ida (Associate Professor, Graduate School of Economics, Kyoto University)Rei Watanabe (Graduate School of Economics, Kyoto University)Syuzo Nishimura (Professor, Graduate School of Economics, Kyoto University)

Presented for PSAM 5(11/30/2000)

Introduction

•Human Genome Project•Advance of Molecular Biology and Genetic Engineering

Dispute about using Genetic InformationSocio-economically as well asEthically

This paper;•Establish a model including congenital acquird health risks•Analyze the problem of adverse selection and moral hazard

Medical Background

•Genetic Medicine

　 From Single gene diseases to Multi-factorial disorders

•An aging society

Life-style diseases (mostly Multi-factorial )

(Ex.Hypertension, DM,Malignancies…..)

Differentiation of Heath RisksTotal heath risks =Congenital risk +Acquird ris

k

Incomplete Information

Total heath risks =Congenital risks +Acquired risks

•Congenital risks..Physical and Biological factors Predetermined congenitally*Adverse selection under Incomplete information•Acquired risks…Environmental and Living factors Determined through behavior*Moral hazaed under Incomplete information

Model Analysis

r; impaired QOL caused by illness

Basic definitions

θ: the impaired QOL determined by congenital risks　 e: the gained QOL (or avoided loss of QOL)by effort

r =θ −e

C ;disutility needed to make an effortC(e) >0, ′ C >0, ′ ′ C >0

*Government provides•Medical treatment recovering the former Pts’ QOL; r•Other health service than treatment; t •Total health service supply; t+r

U;patients’ net utility functionU =(t +r)−r −C(e)

=t−C(e) (3)

H; endowed QOLλ;social cost of public fundsW; social welfare funcition government maximize W =H +U −(1+λ)(t+r)

=H −(1+λ) r +C(e){ }−λU (4)

The Case of Complete Information

maxe,U

W =H −(1+λ) θ −e+C(e){ }−λU

s.t.U ≥0

Government’s problem

1st.order conditionU =0

′ C (e) =1 (5)

t =C(e∗) (6)

e* ;the effort which satisfy Eq. (5).•marginal disutility of effort = marginal QOL savings.• The existence of shadow cost of public funds implies that patients receives no excess net utility. •The government can extract patients’ effort at the level of e* by giving them non -treatment medical service C(e*), which compensates exactly their disutility by effort.

The Case of Incomplete Information

•Patients know θand e ,Government knows only the distribution of the total QOL loss r. (cannot distinguish congenital risks from acquired risk)•θ... hidden type of the patients. patients have the motive to cheat the government about their types. (Adverse selection)•e….the hidden action of the patients. patients have the motive to decrease the disutility of effort less than the optimum level. (Moral hazard) •The government can utilize the self-selecting contract to maximize the expected social welfare function.(θ ,θ) ;congenital health risks of each patient

(1-π,π) ;The ratio of the two types of patients

(r ,r) ;total risks of each patient

Self selecting contract that a patient truly tell the government his own type θ

U(θ)≥0 (IR1)

U(θ )≥0 (IR2)

U(θ |θ) ≥U(θ |θ) (IC1)

U(θ |θ )≥U(θ |θ ) (IC2)incentive compatibility conditions (IC)

individual rationality conditions (IR)

* It is well known that IR2 and IC1 are binding while IR1 and IC2 are not binding among the four constraints above.

That says;

U =0

U =C(θ −r )−C(θ −r )

•The government maximizes the following expected social welfare function with the constraints of IC1 and IR2.

W =πW(θ) +(1−π)W(θ )

Government’s problem

maxr,r

W =maxr,r

H −(1+λ)π r +C θ−r( ){ }

−(1−π )(1+λ)r +πλc(θ −r )−(1−π +λ)c(θ −r )

⎧ ⎨ ⎩

⎫ ⎬ ⎭

1st.order condition′ C (θ −r) =1

′ C (θ −r ) =(1−π)(1+λ)+πλ ′ C (θ−r )

1−π +λ≤

(1−π)(1+λ)+λπ1−π +λ

=1

•The effort level of low risk type= the optimum effort level, e*, •The effort level of high risk type is lower than e*

Conclusion

•We have proposed the necessity to analyze the distinction between congenital risk and acquired risk.

•For that, we have established the model that is composed of adverse selection and moral hazard.

•We have compared the case of incomplete information to that of complete information.

•We have found that the effort level of low risk type is equal to the optimum effort level while the effort level of high risk type is lower than the optimum effort level in the self selecting contract.