A Bianchi type-I metric of the Kasner form is used as input in Einstei
n's equations to explore which consequences thereby occur for the equa
tion of state for the cosmic fluid. Both shear viscosity and bulk visc
osity coefficients are assumed to be present. The solutions of Einstei
n's equations can naturally be categorized into two classes. Either th
e space becomes anisotropic, and the equation of state is determined o
nce the Kasner parameters p(i) are given. Or the space becomes isotrop
ic, and the equation of state emerges in the conventional form p/rho =
gamma-1 with a definite value of gamma. We also calculate the rate of
entropy production (sigma) overdot per particle, and find that (sigma
) overdot becomes as large as of order 10(4) s(-1) if we go back to th
e very early universe, t similar to 10(-4) s. We also discuss the poss
ibility of testing the anisotropy of the universe by means of redshift
experiments.