| Abstract: |
We develop a formula for the optimal size of a joint savings association
between individuals who share the same financial goal and who can save towards
that goal at the same rate. Our motivating example and the core of our
analysis is a Rotating Savings and Credit Association (ROSCA). We measure the
efficiency of a ROSCA by the expected waiting time that it takes a participant
to attain his goal when no participant reneges on his commitment to contribute
to the common fund, and when each of the participants receives (once) the
funds needed to meet his goal. Given this criterion, we define the optimal
size of a ROSCA as the number of participants that results in the minimal
expected waiting time. We show that an optimal size of a ROSCA exists, that it
is limited, and that it is a multiple of the number of time periods that it
takes an individual to save on his own. Somewhat surprisingly, we find that
when treated as a function of the size of a ROSCA, the expected waiting time
is not monotonic when the size builds up from an individual saving on his own
to the optimal size. A similar result obtains when we study cases where a
ROSCA is enlarged beyond the optimal size. Our findings help explain the
limited size as well as other features of ROSCAs observed in developing
countries all over the world. |