growth rate is independent of size is violated; we shall see this result later in Weiss) As a result, the variance of firm sizes does not increase indefinitely but tends to a finite limit which depends (positively)on th variance of growth rates (s ) and the magnitude of b. Correlation of Growth and Initial size (Weiss, 1963) Weiss recognises that the variance f logs of firm sizes as such measures inequality rather than concentration since it ignores firm numbers Increasing variance implies increasing concentration only if firm numbers do not alter. Define log(S where the size of firm in t, t=l, 2. Then we can write the identity x2-x1 is the growth of firm in proportional terms. Then Var(x2)=Var (X,)+ Var(x2-x1)+ 2Cov(X1,X2-x1) 2 Cov( where p 12 is the correlation of growth and initial ar(X1)Var(x2-X1 size. Gibrat's Law of Proportionate Effect assumes no correlation between growth and initial size, ie. p=o and as a result ntration will increase continuously. More generally, we know that when pzo then (as it has been shown, see p 2 for case bz1), variance in firm sizes (and thus concentration)will grow idefinitely. For a fixed number of firms: 2po For p>0, the change in concentration o -o is positively related to the variance of (the logs) of firm size changes a and to the correlation of growth with initial size. However, while if p<0 concentration might decrease, it is also true that the difference in concentration