Wages in Solow growth model with savings = 0 I am trying to understand the change of wage rate and rental rate in the Solow growth model with s = 0. It is clear that capital per capita will approach 0 (due to depreciation of capital). Also is clear to me the fact that the rental rate will rise because of decreasing marginal returns assumed on the production function. Since factors are paid their marginal products in case of Constant Returns to Scale, rental rates rise.
I am confused about the marginal product of labor overtime in a general setting. For example if I take $F(K,L)=K^aL^{1−a} ,0&lt;a&lt;1$ , then I can see that marginal product of labor will fall if we assume constant or increasing labor force. But I am unable to show this for a general $F$ with CRS.
Let 
$$Q = F(K,L)$$
Assume
a) $F(K,L)$ exhibits consant returns to scale.  

We need this to aggregate from the individual firms to the total.

b) Price taking behavior  and

c) Profit maximizing behavior  

from the part of the firms.  

Then, throughout the dynamic process,
$$w = \frac {\partial F(K,L)}{\partial L} \equiv F_L$$

i.e. the wage is equal to the marginal product of labor. For clarity, write 

$$\frac {\partial F(K,L)}{\partial L} \equiv h(K,L)$$

$$\dot w = \frac {d}{dt}\frac {\partial F(K,L)}{\partial L} = \frac {d}{dt}h(K,L)= \frac {\partial h(K,L)}{\partial K}\dot K + \frac {\partial h(K,L)}{\partial L}\dot L$$

$$\implies \dot w = F_{KL}\dot K + F_{LL}\dot L$$

Assume  further

d) complementarity of inputs, $F_{KL}&gt;0$, and  

e) diminishing marginal productss (not in the temporal dimension but in the static dimension, due to diminishing rate of returns), $F_{LL}&lt;0, F_{KK}&lt;0$.  

Then, if 

$$\dot K &lt;0, \dot L\geq 0  \implies \dot w &lt;0$$

The same treatment wil give us

$$\dot r = F_{KK}\dot K + F_{KL}\dot L  &gt;0$$