Introduction
Health insurance plays a crucial role in protecting individuals from the financial risks associated with medical expenses. However, in both private and public insurance systems, achieving optimal participation and contribution is challenging, especially due to the issue of free riders. In this blog, we will explore the conditions of optimality for purchasing health insurance and how the presence or absence of free riders affects the outcome.
Understanding the Free Rider Problem
A free rider is someone who benefits from a service without paying for it or contributing their fair share. In health insurance, especially in social or public insurance schemes, individuals may choose not to buy insurance but still receive care during emergencies (e.g., public hospitals cannot turn them away). This leads to inefficiencies in financing and delivering healthcare.
1. Optimality in the Absence of Free Riders
Let’s first consider a scenario where there are no free riders, and individuals must either buy insurance or bear full medical costs.
Assumptions:
- Individuals are risk-averse
- Two possible states: healthy or sick
- Insurance offers full coverage at actuarially fair premium
Optimality Condition:
Under expected utility theory, an individual will choose to buy insurance if the expected utility with insurance is higher than without insurance.
Expected Utility without Insurance:
EU₁ = p × U(I - M) + (1 - p) × U(I)
- I = income
- p = probability of falling sick
- M = medical expenses
Expected Utility with Insurance:
EU₂ = U(I - π)
- π = insurance premium (equal to p × M in actuarially fair insurance)
Condition:
U(I - π) > p × U(I - M) + (1 - p) × U(I)
If this inequality holds, the individual will optimally choose to buy insurance. This reflects risk aversion and preference for income smoothing.
2. Optimality in the Presence of Free Riders
Now consider a scenario where people can access emergency care without paying or being insured. This creates an incentive to avoid paying for insurance while expecting to receive benefits when needed.
Consequences:
- Healthy individuals may opt out, especially if they feel low risk
- Insurance pool becomes riskier and more expensive
- Leads to adverse selection and insurance market failure
Modified Utility without Insurance (with free rider benefit):
EU₁ = p × U(I - αM) + (1 - p) × U(I)
- α < 1: Individual pays only a fraction of the medical cost (due to public subsidies or emergency coverage)
Revised Optimality Condition:
U(I - π) > p × U(I - αM) + (1 - p) × U(I)
Here, the presence of free rider benefits (αM instead of full M) reduces the incentive to purchase insurance. The utility without insurance becomes closer to utility with insurance, making individuals less likely to buy coverage.
Policy Implications
To address the inefficiencies caused by free riders, governments and insurers adopt certain measures:
- Mandating Insurance: Making health insurance compulsory (e.g., under national schemes like Ayushman Bharat or the Affordable Care Act in the US)
- Subsidies: Reducing the premium burden to encourage wider participation
- Risk Pooling: Encouraging both healthy and sick individuals to enroll to balance costs
- Penalties for Non-Enrollment: Financial penalties for those who do not buy insurance despite availability
Conclusion
Optimality in health insurance requires individuals to weigh the costs and benefits of coverage. In the absence of free riders, risk-averse individuals find it optimal to insure. However, the presence of free riders distorts these choices, often leading to under-enrollment and market inefficiencies. Effective policy design must consider these behavioral responses and strive to create systems that encourage broad participation while minimizing moral hazard and adverse selection.