by Michael R. Rand of BJS (Rand, 2009) in (see pages 9 and 16 of this paper) at http://www.fcsm.gov/09papers/Rand_X-B.doc, funds available to conduct the NCVS in FY2009 amounted to C* = $26M, and about 150,000 NCVS interviews were completed in 2008. These figures imply an average cost per completed interview of about CHH = $26M/150000 = $173 for the household stratum.
If the average per completed interview for the police records (administrative) stratum is two (2) times that of the household stratum (i.e., like the NCVS), then θ = CA/CM = 2 and thus CA = $346.
First determine the RSA rate for the household stratum as which makes PA = 0.83 larger than PHH by a factor of about The standard deviations of the 0/1 RSA status indicator for the two strata thus differ by a factor of Because of these substantial stratum differences in Ph and one might expect from Eq. (5.37) in Cochran (1977) that a cost-efficient stratum allocation in this dual-frame context will produce substantially greater precision in estimates of P than a single-frame approach relying solely on household sampling. We will see this to be case below.
Using Equations  and  above, we find that the most cost-efficient allocation of the dual-frame sample given C* for the police records stratum will be
and for the household stratum,
Thus, the total sample size for the DF design in this case would be