For the problem of estimation of all elementary treatment contraata, restrictina ourselves to PBIBD's with two clus association schemea under a mixed model we follow the approach of Sinha and Sinha (1969) to study the behaviour of tho average variance
as a function of
and also as a function of the auociation scheme to some extent. The functional form of
turna out to be the Jame as that under fixed effects model and either
for all admissible θ>0. We got that when a BIB dosian does not exist with tho alven parameters a GO design with
if it exists, is A-optimal within the class of all PBIB designs with two associate class association schemes. This proves that in respect of A-optimality, the result of Chong (1978) can be extended to all GD designs with
if we restrict ourselves to such PBIB dosigns.
