Many seemingly different questions that arise in the analysis of population change can be phrased as the same technical question: How, within a given demographic model, would variable y change if the age- or time-specific function f were to change arbitrarily in shape and intensity? At present demography lacks the machinery to answer this question in analytical and general form. This paper suggests a method based on modern functional calculus for deriving closed-form expressions for the sensitivity of demographic variables to changes in input functions or schedules. It uses this “linkage method” to obtain closed-form expressions for the response of the intrinsic growth rate, birth rate, and age composition of a stable population to arbitrary marginal changes in its age patterns of fertility and mortality. It uses it also to obtain expressions for the transient response of the age composition of a nonstable population to time-varying changes in the birth sequence, and to age-specific fertility and mortality patterns that change over time. The problem of “bias” in period vital rates is also looked at.