Chapter 8 Demand and Supply of Health Insurance 1.What is Insurance 2.Risk and Insurance 3.The demand for Insurance 4.The supply for Insurance 5.The case of Moral Hazard 6.Health Insurance and the efficient allocation of resources

Characteristics of Insurance Program The number of insured should be large and they should be independently exposed to potential lost The losses covered should be definite in time, place and amount The chances of loss should be measurable The loss should be accidental from the viewpoint of the person who is insured

Insurance Terminology Premium, Coverage Coinsurance and Copayment Deductible Exclusion Limitation Pre-Existing Conditions Pure Premium Loading fees

Risk and Insurance Expected value (expected return) E=p1R1+p2R2+…+pnRn Acturaially fair insurance The marginal utility of wealth is diminishing (Figure 8-1) Example (Initial wealth=20000) a. Expected Wealth corresponding with Point D E(W)=0.95* *10000=19500 b. Expected Utility E(U)=0.95* *140=197 (Point C) loss due to risk = =2 unit of utility Q: is it a good deal for premium=500? Yes, Net wealth of 19500=> certainty utility is 199>197 The maximum amount to pay for risk: the distance FC

The demand for Insurance How much insurance ? (Figure 8-2) Marginal Benefit (cost) curve, MB1(MC1), is downward- sloping optimal insurance purchase=q*(MB1=MC1) Changes in premium Higher premium by reducing optimal coverage from q* to q** (MB2=MC2) Changes in Expected loss The expected loss will increase the amount of insurance purchased at Z, q***(MB3=MC1) Changes in Initial wealth more initial wealth MB1=>MB2 ( at higher wealth, smaller increment in utility) MC1=>MC3 (premium cost less in foregone marginal utility relative to the increased wealth) new equilibrium may be higher or lower than q*

The supply of Insurance Profit=Revenue-Payout=aq-(pq+t) where a : the premium, in fractional terms; p: the probability of payout ; q: the amount of payout is q; t: a processing cost With perfect competition, profit=0, so a=p+(t/q) the competitive value of a equals the probability of illness plus loading costs as a percentage of policy value actuarially fair base if t/q approach zero => a=p under perfect competition (with no loading cost) (1)Wealth (if well)=initial wealth-a*q (2) Wealth (If ill)=initial wealth- loss + q (coverage or insurance reimbursement)-a*q (insurance premium) Max the expected utility=> (1)=(2) q*=loss (optimal coverage=full health w/o transactions costs)

The case of Moral Hazard Figure 8.3 A: with inelastic demand, insurance has no impact on quantity ;B with elastic demand, insurance increases quantity from Q1 to Q3. This is moral hazard if premium is 0.5*P1Q1 (<0.5*P1Q2), then insurance company lose money. However, if premium is 0.5*P1Q2, agent chose “self-insured” Theory suggest 1. deeper (more complete) coverage for services with more elastic demand 2. first choose services with most inelastic demand and later for those with more elastic demand

Effects of Coinsurance and deductibles Premium=500, pay 0P1BQ1. The gain is Q1BQ2 (induced demand) Deductibles is raised from 500 to 700, the incremental health care from Q1 to Q3, (1)welfare loss=Q1BDQ3-Q1BFQ3=BDF (2)welfare gain=Q3FQ2 decision rule: buy insurance if (1)>(2)

Health Insurance and the Efficient Allocation of Resources The impact of coinsurance (Figure 8-4) Point A (no insurance) is an efficient allocation. Insurance shift the demand curve with new equilibrium point C. The incremental amount spent is ABQ1Q0. The incremental benefit is ACQ1Q0. Thus, the social welfare loss is ABC => agent is led by insurance to act as if he is not aware of the true resources cost of care he consumers Figure 8-6 shows the effect of insurance cost sharing with upward sloping price 1. price increase due to moral hazard 2. deadweight loss=JFK

The demand for Insurance and the price of care Feldstein (1973):the interaction of insurance and price of care (see Figure 7-8) I curve refer to impact of price of care on quantity of insurance; P curve refers to the impact of insurance on price of care through induced demand A->B: (1) increased care price due to moral hazard by insurance (vertical arrow); (2) induced demand from insurance (horizontal arrow)

The welfare loss of excess Health insurance Feldstein (1973) estimated welfare gain is 27.8 billion per year if average coinsurance rate is from 0.33 to 0.67 Q: why will society support insurance policy that seem only to result in misallocations of resources? A: the protection again risk