The relationship between the utilization of nursing home care and its price is a subject of considerable policy interest. We assess price sensitivity by developing and applying “overlap polynomials” as a method to exploit the temporal price variation implicit in Medicare payment rules for nursing home care. Standard methods for measuring price responsiveness are inappropriate for measuring the effects of temporal price variation, and unmeasured quality variation often confounds cross-sectional price variation. Our empirical analysis assesses the magnitude of shifts in nursing home discharge rates attributable to the price changes that occur when Medicare coverage diminishes or ends. Our findings provide strong evidence that the duration of nursing home stays is sensitive to price in the population examined here.