What we ll be discussing

14  Download (0)

Full text


Lecture 7 (29.09.14)

Uncertainty and the welfare gain

from health insurance




Teaching programme: Master of Public Health, University of Tromsø, Norway Course: Health economics and policy (HEL3007)

Main text: JA Olsen (2009): Principles in Health Economics and Policy, Oxford University Press, Oxford

What we’ll be discussing

• The insurance motive for free health care

• For which risk*loss combinations do we most

prefer insurance?


The principle of insurance in all its simplicity...

“Suppose that, out of a village of 1,000 people, one whose identity is now unknown will need to pay $5,000 for medical care next year. The 1,000 villagers can each put $5 into a pot, and the resulting $5,000 will be available to bail out the unlucky person next year.

Most people do not like to face the possibility of financial losses, especially large financial losses (they are risk averse), and would view this as a good deal. That is how markets for insurance of all kinds have arisen: auto, homeowners’, renters’, etc”

The key issues

• Each villager has similar probability 1/1000

• They are averse to the prospect of loosing $5000

• The villagers form a risk pool by contributing $5 each

• The financial risk disappears 


2 alternatives

• Alternative A (uninsured)

– Healthy: p = 99% Income 200,000 – Sick: p = 1% Income 100,000

• Alternative B (insured)

– Healthy: Income 199,000 – Sick: income 199,000

• Would you prefer A or B?

Same expected loss

• A: p = 1%

of loosing 100,000

• C: p = 50%

of loosing 2,000

– i.e. expected loss is identical: 1,000

• Insurance premium 1,000 for each of A & C

• Which insurance would you buy, A and/or C?


The welfare gain model


- Risk aversion, i.e. certain outcomes are preferred to gambles - Diminishing marginal utility, i.e. utility increases with wealth, but at a diminishing rate

Without insurance:

If healthy, you enjoy wealth, W

If ill, you suffer a ‘money equivalent loss’, L, thus resulting in wealth W–L.

Probability of illness, q

Probability of not being ill: 1–q.

The welfare gain model

Expected utility, E(U):



= q U(W – L) + (1 – q) U(W)

Wealth without insurance = Wealth with insurance

(when p = qL):

(2) q (W – L) + (1 – q) W = W – qL

The utility of wealth with insurance is higher

than the expected utility without insurance:


q U(W – L) + (1 – q)U(W) < U(W – qL)


B – A = (potential) welfare gains

C – A = p* - qL = (potential) administration costs and profits


C = the highest WTP for insurance: same utility level as if uninsured p* = the highest premium that insurance company can charge

 no welfare gains to the consumer, BUT profits (p* - qL) to the company

Health insurance premium

• Actuarially fair premium = expected health

care costs (= qL)

• Real world premium (p*) = expected health

care costs + loading


Loading factor by group size

70 35 25 17,5 11,5 6,5 20 0 10 20 30 40 50 60 70 80 Indi vidu al p olic ies Sm all g roup s (1 -10) Mod erat e gr oups (1 1-100) Med ium gro ups (100 -200 ) Larg e gr oups (201 -100 0) Ver y la rge grou ps (o ver 1 000) Wei ghte d av erag e al l pla ns L o a d in g f e e a s % o f b e n e fi ts

Source: Phelps, Health Economics, 1992, p. 297.

The probability and the loss:

Aversion to large losses

Small probability and high loss vs high probability and small loss


qS = 0.01 LH = 5,000

qH = 0.5 LS = 100


The large loss situation: high (potential) welfare gains The small loss situation: small (potential) welfare gains


• Risk aversion involves welfare gains from insurance

 Demand for insurance

• Smaller losses involve smaller welfare gains

 Less demand for insurance

• Higher probabilities involve less scope for loading


Moral hazard

Moral hazard (MH) refers to any tendency for the presence of

insurance to increase the probability of loss or its amount. Ex ante MH – the probability increases:

The insured becomes less cautious to avoid the incidence

Ex post MH – its amount (costs) increases:

This supplier moral hazard may exist when doctors have discretion over the type of care they provide

Moral hazard depends on:

Ex ante MH

The extent to which there are non-monetary losses involved in the consequence of risky behaviour.

If significant non-monetary losses, the insured will be cautious to avoid the incidence.

Ex post MH

The types of remuneration system and control/regulation.


The welfare loss from insurance

XP=0 X* MC D P P = MC P = 0 X

Reducing the welfare loss: ‘co-insurance’

XP=0 X* MC D P P = MC P = 0 X XP>0 P > 0

Co-insurance reduces ‘excess consumption’ from XP=0 to XP>0 and the ‘welfare loss’ to the dark blue triangle.


A contradiction – or a dilemma

• The welfare loss evaporates when p = MC

• but that implies no insurance

• and thus no welfare gain is being exhausted

Community rating

Premium = expected loss

p = q L

‘Community rating’



= q




But, we all differ, both in terms of probability and of loss

There is ex ante cross-subsidisation


Actuarially fair insurance

The expected losses differ across sub-groups q1L1 < q2L2 < … < qCLC < … < qN-1LN-1 < qNLN

Community rating: ‘net-contributors’ to the left of qCLC, where the expected loss is less than community premium: q1L1 < q2L2 < pC

What happens to the average premium when the left tale opts out?

Actuarially fair insurance = individual rating pi = qiLi

No ex ante cross-subsidisation

Adverse selection

Problem with actuarially fair insurance:

Asymmetric information about the risks faced by individuals - Buyers of insurance wish to signal a lower than true risk - Sellers need to identify and separate false risks from true risks

A solution is to offer two types of contracts:

- Reduced coverage (deductibles or co-insurance) - Complete coverage

The solution induces self-selection

- Low risk buyers go for reduced coverage - High risk buyers go for complete coverage


Adverse selection


Problem is: Low-risk buyers might still prefer complete coverage if it were available at actuarially fair rates,

but complete coverage contracts are offered at rates that reflect the expected losses of high-risk groups.

Low-risk buyers are faced with the choice between - Partial insurance at a low rate, or

- Full insurance at an excessively high rate

Adverse selection and transaction costs

“Private insurance is bureaucratic and costly, requiring

armies of accountants, actuaries, billers, checkers,

fraud detectors, lawyers, managers and secretaries”.

Culyer (1989)


Efficiency arguments for public insurance

A single tax-financed system involves less administrative costs:

1) No additional costs involved with revenue collection when ‘health taxes’ (set independent of individual risk) are included in an existing tax system

2) Providers of health care face no costs of collecting

reimbursements from the insurance companies

3) No costs involved in designing insurance packages for different risk groups

4) No advertising costs of the kind found in competitive insurance markets.

Key characteristics of three different health insurance systems

Private health insurance

Social health insurance


Cost of managing the system

(revenue collection, and determining access)

Expensive From quite expensive to quite cheap


Coverage Limited Formal sector only (or

extended to universal)


Choice of participation Voluntary Compulsory for all in the formal sector


Cross subsidization No Across other members

of the formal sector


Source of funding Individual premia Pay roll tax Direct and indirect taxes

Contributions based on

Health risks Income Income and

consumption Access

based on

Willingness and ability to pay

Needs Needs

Secure funding Yes, increased costs increased premia

Yes, earmarked to sickness funds

Depends on political system

Incentive on healthy behaviour (i.e. link between own premium and own expected use)




Related subjects :