Does Pareto-efficency take into account growth? I'll try to state my question clearly:

&nbsp;

For a given a "wealth" allocation Wt = (w1, w2, w3, ... ) for individuals I = (i1, i2, i3, ... ).

And a distribution of D= (w1/|W|, w2/|W|, w3/|W|, ... ), that is, as a percentage of the total.

Where Wt is Pareto Efficient at a given time frame &nbsp;t&nbsp;, and W(t+1) is Pareto Efficient at &nbsp;t+1&nbsp;.

When there is growth such that &nbsp; &nbsp;&nbsp;|W(t+1)| > |Wt| 

Is Dt=D(t+1)?

If so, why? If not, how do you allocate say, capital, whose value is intrinsically linked to growth?

I understand many of my assumptions may be plain wrong or badly stated, I am still an undergrad. Sorry about that. And thanks in advance.



Further clarifications:

For each element &nbsp;w&nbsp; of Wt = (w1, w2, w3, ... ),

w= P * B

Where P is the price vector of a commodity bundle B.

I hope that my representation of growth as an increase in the magnitude of the W vector is correct. This is what has been bugging me the most. It's safe to assume that growth causes an increase in |W|, right?
It seems to me that as long as every person likes wealth any allocation $W_t$ will be Pareto-optimal.

Even if this was not the case, so supposing that $w_1, w_2,...$ are not real numbers representing wealth but vectors representing bundles of goods the distribution from one time to another can change drastically if you do not specify how growth occurs. At $t=1$ someone might have everything, then at $t=2$ someone else might have everything. Both of these states are Pareto-optimal, but the distributions are quite different.

So no, it does not follow from your conditions that $D_t$ necessarily equals $D_{t+1}$.