  We prove a necessary optimality condition for isoperimetric problems under
nabla-differentiable curves. As a consequence, the recent results of [M.R.
Caputo, A unified view of ostensibly disparate isoperimetric variational
problems, Appl. Math. Lett. (2008), doi:10.1016/j.aml.2008.04.004], that put
together seemingly dissimilar optimal control problems in economics and
physics, are extended to a generic time scale. We end with an illustrative
example of application of our main result to a dynamic optimization problem
from economics.
