Coinsurance is the practice whereby the insured person shares a fraction of an insured loss with the insurer. For example, the insurance policy may require the insured person to pay 10 per cent of the expenses of medical care, with the insurer paying 90 per cent. The sum paid by the insured person is known as a copayment, so if the expenses are $1000 and the coinsurance rate is 10 per cent, the copayment is $100. Some policies require deductibles, sometimes known as the ' excess ', to be paid. Under this arrangement the insured person pays a fixed sum if health care is needed in any given year and the insurer pays all other expenses (usually with further copayments). Thus, if the deductible is $100 and the coinsurance rate 10 per cent, should the event involve an expense of $1000, the insured person pays $190 ($100 plus $90 copayment).
The effects of deductibles and coinsurance can be shown using the figure, which assumes that individuals are expected utility maximizers. The vertical axis shows the price of health care P (assumed - perhaps implausibly - to be set equal to marginal cost) and the marginal value placed upon health care consumption by an individual. The horizontal axis indicates the rate of consumption of health care (so much per day, week, month, etc.). The diagonal curve, roughly equivalent to the demand curve, is the marginal value curve and the horizontal line is the (constant, for ease of exposition) marginal cost curve. In a world of no insurance, the individual faces a price 0P, at which 0C1 care will be consumed when ill. Let the individual (while healthy) consider buying insurance. Suppose neither the individual nor the insurer is in any doubt about the probability, p, of illness striking in any period (another tall order). Given that the insured, when uninsured, would consume $0PaC1 the actuarially fair premium is p of this amount. We assume also that there is zero loading - that is, the insurer adds nothing to the premium to cover the administrative costs of operating the insurance service. Now let an individual consider insurance.
They are comparing consumption (if sick) C1 at a user price P and no premium, with consumption C3 at a zero price and the payment of a premium. The difference between C3 and C1 is due to moral hazard. The fair premium payable will be p (the probability of the event occurring) times the cost of care (0PdC3). Given such a premium, whether the individual buys insurance cover will partly depend on whether Pea > adC3. (Note that the individual will definitely buy insurance if the insurer foolishly sets the premium at p times 0PaC1, the expense that will be incurred under self-insurance.)
Suppose that cover is purchased: the individual judging that it is worth buying insurance to avoid the financial risk. A policy containing a deductible may still be to the individual's advantage. A deductible does not affect the marginal cost of consumption so, once an individual is insured, they will consume C3. Suppose there is a deductible of $100. If insurance is taken out, the individual will thus pay $100 and consume C3 care. If the value of the additional consumption over self-insurance (C3 - C1) exceeds $100, this will seem a good deal and the care will be purchased. Whether insurance will be purchased, however, depends on the premium combined with the effects of the deductible. The deductible reduces the net benefit of the additional consumption (C1aC3) by $100. So long as the advantage of avoiding the risk of the financial consequences of ill-health remains high enough, the individual will purchase this policy. Plainly, there will be some deductible high enough to overwhelm this advantage and the individual will then self-insure. Deductibles, by reducing the number of small claims (i.e. claims at or below the value of the deductible), may reduce insurance companies' administrative costs and hence enable the loading element of the premium to fall.
With coinsurance, the individual pays a percentage of the cost, say 0P1, which causes a fall in the amount demanded when insured (from C3 to C2) leading to a reduction in the actuarially fair premium as the cost of the care chosen fall. Coinsurance thus can reduce the effect of moral hazard and reduce premiums. Taken to the extreme, let the coinsurance rate approach P. Plainly, at P, there is self-insurance, the premium is zero (and so is moral hazard). The consumer is fully exposed to the financial risk of ill-health. One might expect an optimal coinsurance rate to exist between 0 and P, though it needs to take account of external effects. The 'excess' consumption that the coinsurance reduces is in excess only of the optimum seen from the particular individual's viewpoint and, from a wider social viewpoint may not be excessive at all (a second best solution is preferable to attempting a first best one).