Health insurance does not insure health. It reimburses the costs of health care, and enables potential users of care to pool their risks. But public health insurance is qualitatively different from private, in that risk pooling is not its only or even its primary function. Public systems also redistribute, deliberately, from low to high risk individuals. Perhaps even more important, public insurance is a mechanism for the collective purchase of care. It enables buyers, through their political representatives, to bargain with providers over both price and quantity of care, and thus to control overall system costs, in a way that individual patients cannot. This paper contrasts the experience of public insurance in Canada with private coverage in the U.S., to show how universal public coverage, used as a 'collective purchasing agency', has led to both better coverage and lower costs. Current policy changes in the U.S., described as 'competitive', are in fact efforts to create private collective purchasing agencies to bargain with providers on behalf of individuals. Yet economic analysis has been largely incapable of grasping this process, continuing to treat public and private insurance alike as simply reductions in the price of care faced by individual consumers, and thus generating erroneous predictions and analyses of the behaviour of public systems. It has encouraged a fruitless concern with the prices faced by patients, while ignoring the overwhelming significance of the structure and objectives of the insurer. This failure may be traceable to fundamental flaws in the concept of a transactor in economic theory.