For decades, US policymakers and economists have searched for ways to slow the growth of spending on health care. One approach currently taken by thirty-five states is to restrict the supply of health care by requiring new and growing providers to show that they serve an “economic need.” Hospitals and certain other health providers must obtain a certificate of need (CON) from a state board before opening or expanding. I show that in a simple model where CON restricts supply, the effect of CON on spending depends on the price elasticity of market demand for health care. CON will work to restrain spending when demand is elastic; however, most estimates show the demand for health care to be quite inelastic. I therefore predict that CON will increase prices for health care without much reducing its use, leading to an increase in spending. ________________________________________