This paper examines some of the implications, including geographic and residential considerations, of adopting a relative poverty defintion which would fix the poverty threshold at some proportion of median income. The major virtues of such a definition are that it is explicitly relative and it is easy to understand and construct. The major flaw is that, in the absence of a major shift in the income distribution, the proportion of persons in poverty would remain constant over time. The evidence in this paper indicates that such a poverty measure would have the effect of identifying as poor a nearly fixed proportion of the population. In the absence of significant shifts in the income distribution, the proportion of the population in poverty would not be lowered by a growth in the average level of real income. Using a definition based on median income would also allow the possibility of introducing inter-area differentials through the use of sub-national medians. However, even though the application of a single national poverty standard causes some inequities, the data suggests that the adoption of a poverty standard based on sub-national medians would create its own inequities. The only realistic way of introducing inter-area differentials into a poverty definition is to develop a survey which will produce acceptable data on inter-area differences in living costs. (Author/AM)