International Justice in Elder Care: The Long Run

Abstract

In the short run, the cross-border migration of elder-care workers is a zero-sum game, with the source country losing and the host country gaining. This offends our sense of justice, especially since the host populations tend to be richer. In this chapter, I argue that we ought to direct our gaze beyond the short run, at the long run. Once we do that, we will see possibilities of non-zero-sum games that are mutually beneficial. The large question arises, though, as to how nations may choose among them by committing to some principle of justice.

This chapter was published as Lee (2011).

Appendix: Two Populations Linked by Migration

I assume that there are two populations in the world: the host and the source. In each population, the numbers of the elderly (E) and the young (Y) change according to linear differential equations:

$$\frac{\delta E}{\delta t} = aY - dE + i_{E}$$

(1)

$$\frac{\delta Y}{\delta t} = bY - cE + i_{Y}$$

(2)

where

a :

 the rate of aging

b :

the net replacement rate among the young

c :

the cost of caregiving in terms of young lives lost per elderly person

d :

the death rate among the elderly

i _E :

the flow of migration of elderly people (+ if host; − if source)

i _Y :

the flow of migration of young people (+ if host; − if source)

In my analysis, I assign numerical values to demographic parameters that ensure that both populations will converge in the long run. See Table 2.

Table 2 Demographic parameters