ANYONE WHO has had a serious illness lately doesn't need to be told that the cost of hospital care is high and rising fast. Hospital costs have outpaced other prices in recent years partly because hospitals are now able to offer more sophisticated--and costly--types of diagnosis and treatment and because a larger proportion of the population is advanced in age. Last year, however, while other prices were beginning to moderate, hospital costs soared by 19 percent.

While many factors were involved, last year's record spurt in hospital costs certainly owed something to the demise of the Carter administration's cost control proposals and to the Reagan administration's initial laissez-faire attitude toward the medical sector. More recently Health and Human Services Secretary Schweiker and Senate Finance Committee Chairman Dole have warned the hospital industry that a repetition of last year's performance would provoke strong governmental reaction.

To head off the possibility of direct government cost controls, the hospital industry--through its primary trade group, the American Hospital Association--this week unveiled a cost limitation plan of its own. The idea behind the plan is that if the government will agree in advance to reimburse hospitals a certain amount for each Medicare patient they admit--irrespective of the patient's treatment or length of stay--hospitals will have an incentive to keep their actual costs within those bounds.

Whether the plan would be a good deal for the government--and the Medicare population--depends crucially on the level of reimbursement set. Since the industry devised the plan, the initial formulation deals quite generously with the hospitals. Each hospital can build into its rate base not only the average payment it now gets from Medicare, but also above-average costs and other charges now disallowed by Medicare. This base would be adjusted annually by an inflation index to be specified--the industry suggests a 9 percent starting rate, well above the expected general rate of inflation.

Hospitals would be given additional payment incentives if they agreed to accept the Medicare allowance as full payment of patient costs. However, hospitals could elect instead to levy additional charges on patients--something not currently allowed--up to a maximum of $1,000. All hospitals, moreover, would benefit from simpler bookkeeping requirements, and the assurance of prompt, guaranteed reimbursements.

The industry estimates that few hospitals would choose to bill patients separately and that the plan would save the government $1 billion in 1983. That estimate, however, depends heavily on holding down growth in hospital admissions--despite the obvious incentive that the fixed per-patient fee would provide for hospitals to step up short-term admissions. These are not assumptions that Congress should buy without stronger controls. But the idea of making hospitals live within limited Medicare budgets deserves serious attention as part of efforts to curb the seemingly endless rise in health-care costs.