  The concept of a Minkowski arrangement was introduced by Fejes T\'oth in 1965
as a family of centrally symmetric convex bodies with the property that no
member of the family contains the center of any other member in its interior.
This notion was generalized by Fejes T\'oth in 1967, who called a family of
centrally symmetric convex bodies a generalized Minkowski arrangement of order
$\mu$ for some $0 < \mu < 1$ if no member $K$ of the family overlaps the
homothetic copy of any other member $K'$ with ratio $\mu$ and concentric with
$K'$. In this note we prove a sharp upper bound on the total area of the
elements of a generalized Minkowski arrangement of order $\mu$ of finitely many
circular disks in the Euclidean plane. This result is a common generalization
of a similar result of Fejes T\'oth for Minkowski arrangements of circular
disks, and a result of B\"or\"oczky and Szab\'o about the maximum density of a
generalized Minkowski arrangement of circular disks in the plane. In addition,
we give a sharp upper bound on the density of a generalized Minkowski
arrangement of homothetic copies of a centrally symmetric convex body.
