c - usaid

40
At thi s stago, a graphical description of how R and K
affect Lhe shap of the u (t) curve by age may fac litate further
clarification of our argument. For this purpose, wa need not
consider 0 because its ro e is only for achieving consistency
between the ui I t) values and the overall u(t) , and not for
changing the shape of the u ( tI
curve.
In fi IjJre 4.1, the base-year u [0) values have the shape of
an inverted U-distribution, with its peak in the age-group 30-34.
For R=0, t he target year ui ( tI valuns are on a higher curve
which is parallel Lo the base year curve.
uft)
For R = ------ 1, each value of u (0] is multiplied by I+R,
u (01
which means that the highest va lues in the base year attain a
new
high peak, due to proportionate increase in the target year.
Such
a new high peak may be' neither necessary nor feasible, but wo
show it as a
limiting case.
For R -1, all u t] values become equal.
Now, the role of K is to change the shape of the
u.[0] curve and tilt it in favour of the age-groups 20-24 and 25­
29 in the target year. Such a transformation in tha shape of the
curve cannot be achieved by R, because R takes for granted the
shape of the u (0)
curve with its peak corresponding to age 30-34.
Contrary to this, K favours those a ge-g raupe in which age-specific
natural ferti lity rates are the highest. Only by such a shift can
" e hope to achieve new u 1 (t) values whicI can reduce the number
of bi rths at a faster rate than would be otherwise possible. Of
course, all such shifts have to be within Limits of feasibility,