Insurance
Health Economics (ECON 3018)
Session 1
Lecture 6: Demand and Supply of Health Insurance (FGS - Chapter 8)
Outline
Insurance Basics & Risk
Demand for Insurance
Supply of Insurance
Health Insurance: A Hot Topic
Private health insurance is undergoing significant changes, including premium adjustments and a focus on mental health.
Queenslanders face higher private health insurance costs compared to other regions in Australia.
Young Australians are being targeted with premium discounts as part of the overhaul.
Many health funds are delaying premium increases due to current circumstances.
The average premium increase was supposed to be 2.92%, the lowest since 2001.
A table shows the average premium increases by Insurer.
Health Insurance and Crisis (COVID-19)
The private health industry is critical to healthcare systems worldwide.
During recessions, private health insurance membership is at risk as people may opt out.
The COVID-19 economic recession will have a significant impact on private health insurance.
People facing financial difficulties might drop their health insurance.
Low private health cover participation can have a ripple effect throughout the entire healthcare system.
What is Insurance? and Why does it matter?
Insurance allows individuals to smooth consumption across different states of the world (good vs. bad).
Example: Fire insurance improves the financial state if a house burns down.
Example: Health insurance covers the cost of dental surgery ($X), transferring wealth from good health states ($X is small) to bad health states ($X is large).
Individuals pay a premium to increase consumption in adverse situations, reducing consumption when things are good.
The decision to buy insurance depends on individual preferences and premium costs.
Example of a Simple Insurance Scheme
A club has 1,000 members with similar risk profiles.
Each year, one member randomly incurs healthcare costs of .
Members pay a premium of annually, creating a club bank of .
Each member receives coverage for up to in medical care costs.
Insurance in Healthcare Markets
In most countries, individuals do not directly pay for all health care costs.
Governments or insurance companies pay the majority, with individuals covering the remaining portion.
Even with public health insurance, the theory of private health insurance demand explains why people are better off with coverage.
Health itself is uninsurable, but healthcare services are. This is because healthcare expenditures can be significant and unpredictable.
Insurance versus Social Insurance
Private Insurance: Purchased by individuals.
Social Insurance: Government programs like Medicare and Social Security.
Social insurance is often heavily subsidized and acts as a redistribution scheme.
Premiums are often heavily or completely subsidized.
Eligibility is limited by government-set rules, such as income limits for Medicaid.
Insurance Demand Key Concepts: Risk, Uncertainty & Premiums
Risk: Quantifiable probability.
Uncertainty: Not quantifiable.
Premium = Actuarial Value + Loading Costs
Key Premises Underlying Demand for Health Insurance – Risk and Uncertainty
Economists differentiate between risk and uncertainty.
Risk: Quantifiable, e.g., a 0.2 probability of a car accident.
Uncertainty: Not quantifiable, e.g., a global economic crisis.
Future healthcare service expenditures during a policy year are uncertain.
Uncertainty requires hoping for the best, while risk can be managed with insurance.
It is possible to be over-insured or under-insured; moral hazard can lead to welfare losses that exceed the gains from risk protection.
Insurance Concepts and Terminology
First-party insurance: Protects policyholders against loss (accident, injury).
Third-party insurance: Protects against loss incurred by others (physicians, motor vehicle operators).
Pecuniary and non-pecuniary loss:
Health insurance does not cover non-pecuniary loss.
Non-pecuniary loss is real; third-party insurance covers these losses.
Expected loss
Preexisting conditions: Medical problems not covered if they existed before the policy purchase.
Price of Insurance
Premium: Payment for a given amount of coverage.
Actuarially fair insurance: Expected benefit paid out equals the premium.
Loading fees: General costs of insurance companies, e.g., sales, advertising, profit.
Understanding Demand: Why Buy Insurance?
The theory of demand for insurance explains:
Why people purchase insurance.
Why not self-insure (precautionary saving).
Why pay a price instead of self-insure.
Why people pay a load on an insurance policy.
Understanding Demand: Why Buy Insurance?
Diminishing marginal utility of wealth.
Risk aversion motivates insurance purchases.
Self-insurance v.s. Market insurance
Expected Utility Model
Certainty Equivalent v.s. Expected Wealth
Visualize with utility curves
Possible Relationships between Wealth and the Utility of Wealth: Diminishing Marginal Utility of Wealth
The relationship between utility and wealth: \frac{\Delta U}{\Delta W} > 0; slope differs.
Utility rises with wealth but at different rates.
Three possibilities:
Marginal utility of wealth does not depend on wealth (B).
Marginal utility of wealth increases with increases in wealth (C).
I can't provide multiple choice questions as flashcards. However, I can provide regular flashcards containing a term and a definition.
Concepts of Expected Loss, Expected Utility
Expected utility is distinct from expected loss.
At a given time, an individual can have either wealth if healthy or wealth if sick.
Wh > Ws, and expected loss
Individuals derive utility from having , , and utility from having , , where U(Wh) > U(Ws)
Health affects utility through its impact on personal wealth.
Expected Loss, and Wealth if Healthy or Sick
If the person remains well, L=0, wealth =
If they become ill, the loss is L and the person is left with
Ex ante, it is expected loss (EL), not loss per se (L), that matters in deciding whether to purchase insurance E(L) < L.
reflects the weighted average
At the end of the year, the individual will either have (if sick) or (if healthy).
Risk Neutral, Risk Averting, and Risk Loving Individuals
Risk-neutral individuals:
Have constant marginal utility of wealth.
Do not want to pay more than actuarially fair value.
Certainty utility equals expected utility.
Risk-averse individuals:
Have decreasing marginal utility of wealth.
Motivated to purchase insurance when the certainty utility curve shows diminishing marginal utility.
Risk-loving individuals:
Have increasing marginal utility of wealth.
Motivated to gamble.
Expected Utility of Wealth
The expected utility of wealth is given by:
= probability of getting sick
Deriving Maximum Willingness to Pay for Insurance Policy
Now, suppose the probability of becoming sick rose from to .
Then becomes , and EU’ < EU.
If , then
Expected loss and expected utility vary as varies.
Deriving Maximum Willingness to Pay for Insurance Policy
If the insurer sets the premium at actuarial value , the level of wealth after paying the premium corresponds to utility levels at C and D. Utility at D is higher than at C.
Point D is the utility this risk-averse individual would obtain if wealth level were certain.
Without full insurance, is an expected value, not a certain value.
The risk-averse individual prefers certainty to the chance that they will end up with
The difference in utility between certain and uncertain wealth of is the vertical distance between D and C.
Risk and Insurance: Expected Value
Expected value of an uncertain outcome is the sum of possible outcomes weighted by their probability.
Expected value (or expected return) of a coin-flip game:
If the coin is flipped and turns up heads, elizabeth wins $1; if it turns up tails, she will win nothing. How much should she be willing to pay to play the game?
Expected value (coin flip) = pr(heads) x (return if heads, $1) + pr(tails) x (return if tails, $0)
e = (0.5 \times $1) + (0.5 \times $0) = $0.50
Optimal Coverage: Elizabeth's Choice
Evaluate MB vs. MC
Effect of premium changes
Risk and Insurance: Expected Value
Elizabeth’s expected benefit is $0.50. She plays the game any time it costs her less than $0.50.
More generally, with n outcomes, expected value is written:
Where is the probability of outcome i, and is the return if outcome i occurs. The sum of the probabilities equals 1.
The special case where the price of the gamble is exactly $0.50, and equals the expected return, is called the actuarially fair premium.
This is analogous to an insurance situation in which the expected benefit paid out by the insurance company equals the premium taken in. This is called an actuarially fair insurance policy.
Marginal Utility of Wealth and Risk Aversion
The coin-flip game assumes Elizabeth is indifferent to risk i.e. pleasure of winning=displeasure of losing.
If she is not, then her decision may change. Consider offering her the same coin toss, but increase the bet so that a heads outcome yields $100 payoff and she must pay $50 to play.
The expected benefit of the bet is still $50.
The expected cost is $50.
Actuarially this is the same bet as before. This is an actuarially fair premium.
The cost of the gamble is equal to the expected benefits; disutility of losing $50 may exceed the utility of winning $50.
She may not take the bet if she is risk averse.
The utility from an extra dollar is marginal utility of wealth.
Marginal utility of wealth and risk aversion
E(W) = (prob.well \times wealth if well) + (prob.ill \times wealth if ill) = (0.90 \times $20,000) + (0.10 \times $10,000) = $19,000
Utility from purchasing actuarially fair insurance rate Point – D
Risk of loss reduces utility from 198 to 194.
Suppose Elizabeth’s wealth is $10,000 giving her utility of . Point A.
Wealth rises to $20,000 giving her utility . Point B.
Probability she falls ill= 0.10; wealth falls to $10,000.
Expected wealth:
Marginal utility of wealth and risk aversion
C’D’ maximizes the gains from buying insurance.
The closer the Certainty equivalent is to Expected Utility, the less attractive is insurance. If Elizabeth is almost certain to get ill, reaching point A, then her gains from buying insurance decrease and she should self-insure.
Suppose Elizabeth can buy an insurance policy costing $1,000 per year that will maintain her wealth no matter what happens to her health
Is it a good buy?
Net wealth = initial wealth- insurance premium = $20,000 - $1,000 = $19,000
Her certainty utility is 198, point D. Point D is welfare improving over point C, which has a utility of 194.
Insure if getting certain wealth makes her better off than facing the risky prospect. Aversion to risk (FC)
Marginal utility of wealth and risk aversion
To summarise:
Risk-averse consumers buy insurance.
Expected utility is the average measure.
If insurance companies buy more than actuarially fair premium, people will have less wealth from insuring than not insuring. Increased well being comes from the elimination of risk.
Willingness to buy insurance comes from the distance between the utility curve and the expected utility line.
At B - Gains from insurance are small.
At C - Probability of illness 0.5, E(w)=$15K, . Gains from insurance C’D’.
At A – certain to fall ill. Better off self-insuring.
The Demand for Insurance How much Insurance to buy?
Pauly, 1968:
Optimal purchase of insurance using Marginal Benefit and Marginal Costs.
Rule: Use Marginal benefit greater than marginal cost to maximize net benefit
Example:
Recall Elizabeth
Consider a policy where Elizabeth pays a 20% premium ($100) for her insurance, or $2 for every $10 of coverage that she purchases. Should she buy the $500 in coverage?
The Demand for Insurance – How much insurance?
The table describes Elizabeth’s wealth if she gets sick. Her original wealth of $20,000 is decreased by the $10,000 medical care and insurance premium costs, and increased by the insurance proceeds, leaving her with “new wealth” of $10,400.
Marginal benefit from the $500 from insurance = from the additional $400 ($500 minus the $100 premium).
Marginal cost = that the $100 premium costs.
If Elizabeth is averse to risk: MB (point A) > MC (point A), Policy is a Good Buy!
Changes in Premiums – Insurer Raises Price
Suppose the premium increases to $125 from $100.
The table describes Elizabeth’s wealth if she gets sick. Her original wealth of $20,000 is decreased by the $10,000 medical care and insurance premium costs, and increased by the insurance proceeds, leaving her with “new wealth” of $10,375.
With a higher premium, Elizabeth’s MB (=$375), curve shifts to the left to MB2 and the marginal cost curve shifts to the left to MC2 Elizabeth’s insurance coverage will fall to q’
Effect of a Change in Expected Loss
The table describes Elizabeth’s wealth if she gets sick. Her original wealth of $20,000 is decreased by the $16,600 medical care and insurance premium costs, and increased by the insurance proceeds, leaving her with “new wealth” of $5,400.
Suppose the expected loss is $15,000 instead of $10,000 if ill.
MC remains same ($19,900). Higher expected loss.
MB3 shifts upwards. Equilibrium Z, $q^{***}=$3500.
Effect of an Increase in Original Wealth
The table describes Elizabeth’s wealth if she gets sick. Her original wealth of $25,000 is decreased by the $10,000 medical care and insurance premium costs, and increased by the insurance proceeds, leaving her with “new wealth” of $15,400.
Insurance policy gives a smaller increment to utility. MB shifts down to MB2. Downward shift in MC to MC3. Eqm at W. New equilibrium can be > or < than q
Suppose the original wealth increases to $25,000.
Case Study: Optimal Insurance Decision
Elizabeth example: varying premium, risk, and wealth.
Student poll.
Implications for policy design.
Case Study
Context Elizabeth is a risk-averse individual facing a 10% chance of illness that would reduce her wealth from $20,000 to $10,000. She can buy full health insurance from a competitive market at varying premium levels.
“Would Elizabeth buy full insurance if the premium options are: a) $1,000 (actuarially fair) Raise hand to vote: Yes
Case Study
Option A: $1,000 (Actuarially Fair) – If YES then Why?
This premium equals her expected loss (10% × $10,000).
A risk-averse individual like Elizabeth maximizes expected utility, not expected wealth.
Case Study
Context Elizabeth is a risk-averse individual facing a 10% chance of illness that would reduce her wealth from $20,000 to $10,000. She can buy full health insurance from a competitive market at varying premium levels.
“Would Elizabeth buy full insurance if the premium options are: b) $1,300 (includes $300 loading) Raise hand to vote: Yes
Case Study
$1,300 (Includes $300 loading) – If vote YES then Why?
Even though it’s more than the expected loss, the utility from peace of mind (certainty) may still outweigh the marginal cost.
Real-world insurance often includes loading – this introduces a discussion about how much extra a person is willing to pay for certainty.
Case Study
Context Elizabeth is a risk-averse individual facing a 10% chance of illness that would reduce her wealth from $20,000 to $10,000. She can buy full health insurance from a competitive market at varying premium levels.
“Would Elizabeth buy full insurance if the premium options are: c) $1,600 (above expected cost) Raise hand to vote: Yes
Case Study
$1,600 (Above Expected Cost) – Mixed responses Why?
More risk-averse students might still say YES.
Cost-sensitive or rationally skeptical students may say NO, arguing that expected utility gain no longer justifies the price.
This is a great moment to apply the utility curve to see diminishing returns.
Case Study
Context Elizabeth is a risk-averse individual facing a 10% chance of illness that would reduce her wealth from $20,000 to $10,000. She can buy full health insurance from a competitive market at varying premium levels.
Would Elizabeth buy full insurance if the premium options is: d) $2,000 (Equal to Maximum Loss) Raise hand to vote: Yes
Case Study
$2,000 (Equal to Maximum Loss) – Most votes NO Why?
If the premium equals her total potential loss, insurance no longer provides financial benefit.
She’s paying $2,000 to avoid a $2,000 loss — essentially breaking even in wealth but worse off in utility due to the loading.
This is financially irrational unless she’s extremely risk-averse or misperceives probabilities.
Implications for policy design
A. Premium = $1,000 (Actuarially Fair)
Answer: Most say YES
Policy Implication:
Competitive insurance markets can efficiently allocate risk when information is perfect and administrative costs are low.
No need for government subsidy or regulation—market works well for risk-averse individuals.
But in practice, actuarially fair premiums rarely exist due to admin costs and asymmetric information.
Policy takeaway: In an ideal world, markets work. But we rarely have an ideal world.
B. Premium = $1,300 (With $300 loading)
Answer: Many YES, some NO
Policy Implication:
Mild market inefficiencies (loading) may deter some risk-averse individuals from buying insurance.
Especially problematic if loading deters low-income or younger people, risking adverse selection.
May justify targeted subsidies or mandatory coverage to maintain a broad risk pool.
Policy takeaway: Subsidies or regulation (like community rating or mandates) can help offset market imperfections.
C. Premium = $1,600 (Significantly above expected cost)
Answer: Mixed
Policy Implication:
When loading is high, even risk-averse people may opt out.
Healthy people disproportionately exit → death spiral begins.
If PHI is seen as a public good (e.g., reducing public hospital burden), policy must address affordability.
Policy takeaway: Introduce means-tested subsidies, premium regulation, or risk equalization to keep insurance viable.
D. Premium = $2,000 (Equal to potential loss)
Student Choice: Most say NO
Policy Implication:
At this price, insurance becomes pointless—no welfare gain.
Reflects severe market failure or unsustainable pricing.
Left unchecked, this leads to complete market unraveling—especially if only high-risk individuals remain.
Policy takeaway: Without intervention (e.g., mandates, subsidies, reforms), insurance markets can collapse.
Elizabeth’s example teaches that price alone does not determine optimal insurance policy.
Government must:
Balance efficiency (actuarially fair pricing) with equity (universal access).
Use incentives, mandates, and subsidies wisely.
Recognize how risk preferences and market structure interact.
Implications for policy design
Elizabeth’s example teaches that price alone does not determine optimal insurance policy.
Government must:
Balance efficiency (actuarially fair pricing) with equity (universal access).
Use incentives, mandates, and subsidies wisely.
Recognize how risk preferences and market structure interact.
Determinants of Health Insurance
Pinilla, J., López-Valcárcel, B.G. Income and wealth as determinants of voluntary private health insurance: empirical evidence in Spain, 2008– 2014. BMC Public Health 20, 1262 (2020).
Used a longitudinal database (2008, 2011, 2014) from the Bank of Spain to analyse the financial behaviour of approximately six thousand families per wave.
Estimated income and wealth semi-elasticities of voluntary (VPHI) in Spain considering personal and family characteristics (age, sex, level of health, education, composition of the household), i.e., changes in the probability of buying VPHI as a result of a 1% change in income or wealth.
There are no significant differences among 60% of the most disadvantaged families, while the families of the two upper wealth quintiles show clearly differentiated behaviour with a higher probability of insurance.
Supply of Insurance
Competitive markets: zero profit equilibrium
Profit = Premium – Expected Cost – Admin cost
Entry lowers premiums
The Supply of Insurance
Elizabeth’s insurance case:
Potential illness with a probability of 0.10.
Bought $500 insurance from Asteroid insurance.
Asteroid charged her $100 for each block or a premium of 20% (20% of 500=100).
Assume it cost Asteroid $8 to process each insurance policy.
Competition and Normal Profits:
In a perfectly competitive market, insurers will earn zero excess profit, a normal profit
Profit = Total Revenue – Total Cost
Following the previous example, revenues are $100 per policy
Costs:
For those who do not get sick (90% of the policies), the only cost would be the cost of processing the policy payments, say $8 per policy
For those who do get sick (10% of the policies), the cost would be the $500 payment plus the $8 processing cost, or $508
Calculation of Insurer’s Profit
Profit = $100-(prob of illness x cost if ill) - (prob of no illness x cost if no illness) = $100 – (0.10X$508) – (0.90 x $8) = $100 - $50.80 – $7.20 = $42
Asteroid’s per policy profit is calculated at $42: positive profit.
Enter competing firm:
Comet insurance with the same costs ($8 per policy).
When firms can make positive economic profits, firms enter a market, driving down price.
New entrants will charge lower premiums (Comet charges 15%) to attract new clients.
Profit (premium=15%) = $75(revenue) - $58 (cost) = $17 (positive profit).
Until positive economic profits, excess profits, are competed away (premium =11%; cost=$58=revenue).
Competitive Premium
Let
a = premium(in fraction terms)
q= amount of payout
p = probability of a payout
t = processing cost
Derive Competitive Premium
Profit = Total Revenue(aq) – Cost(pq +t) = aq –pq-t
Perfect competition would set profit = 0
0 = aq – pq - ta = p + ( \frac{t}{q} )\overline{I}\widetilde{I}\overline{I}).
If WTP is $3 without insurance then with insurance it is 3 + \overline{I}\overline{p}0x_h0x{m1}0\overline{x}s\overline{p}0x_h0x{m2}0\overline{x}syy$$ of the monthly prescription and the insurer pays the rest.
Insurance has no effect on demand up to the copay amount.
The demand curve is completely inelastic above the copay amount – pivots at B.
What is the rationale for copays:
Compare copays with coinsurance: Coinsurance refers to a percentage. Copayment refers to a dollar amount.
Alternative Forms of Health Insurance and Their Impacts on the Demand Curve
Type of Insurance | Definition | Economic Effect on Demand Curve |
|---|---|---|
Fixed dollar subsidy (indemnity) | The insurer pays a fixed dollar amount for a particular type of service. | Pure income effect: a parallel shift in the demand curve occurs without changing the relative price of health care. |
Ad valorem subsidy (coinsurance) | The insurer pays a specific percentage of the price. | A change in the relative price of health care occurs; the demand curve rotates outward (becomes less elastic). |
Deductible | The insured person bears the full cost of health care up to a threshold amount (e.g., US $1,000); the insurer pays the rest of the health care cost above the threshold amount. | No effect on the demand curve occurs before the threshold amount is reached; the demand curve becomes a vertical curve above the threshold amount. |
Copay | The insured person pays a fixed dollar per unit of service and the insurer pays the rest. | No effect on the demand curve below the copay amount occurs; the demand curve becomes inelastic (vertical curve) above the copay amount. |
Australian Healthcare System and Insurance
Two components:
Medicare:
Universal health care system.
Healthcare is available to all and is financed, in part, through a 2% tax on our wages (the Medicare levy).
Access to general practitioners and public hospitals are just some of the benefits.
This system provides coverage for citizens, permanent residents, and even many people with temporary visas. There is a program for visiting students and even people seeking asylum get coverage while their cases are under review.
Allows free in-patient care, public hospitals, free access to most medical services, and prescription drugs