when a=0, would economy accumulate more physical capital? Why? Utility function is 

$U(c_t,l_t)=(1-a)ln(c_t)+aln(l_t)$

$l_t$ is leasure time

$c_t$ is consumption 

Production function is $y_t=k_t^e(1-l_t)^{1-e}$

$k_{t+1}=i_t+(1-\delta )k_t$

where k is capital delta is capital depreciation rate. i is investment. 

My question is 

when a=0, would economy accumulate more physical capital? Why?

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I think that, when a=0, agents get utility only from consumption. They don’t get utility from leisure time so they have a more tendency to work. So output increases, which leads to capital accumulation. 

Does this make sense? How can more correctly interpret this? 

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In addition to interpretation, I have essentially following question

I derive optimal physical capital equation for delta=1and for the maximization problem

$$v(k_t)=max\sum B^tu(c_t,l_t)$$

$$k_{t+1}=Bey^*_t$$

But I could not demonstrate this is locally stable. 

Please give me a hint. Thanks. 

If you want, I can write my solution in detail.
From the looks of this question, it seems like a typical consumption-saving problem with possibly endogenous leisure. 
I am assuming the production function is constant returns to scale. I am assuming that $a\in[0,1]$
The problem is:

$\underset{\{c_t,k_{t+1},l_t\}} {Max} \sum_{t=0}^{\infty} \beta^t U[c_t,l_t] = (1-a)ln[c_t]+aln[l_t]$  

subject to $k_{t+1} = f[k_t,l_t]+(1-\delta)k_t-c_t$  

The Bellman Equation:

$V[k_t] = U[c_t,l_t]+\beta V[k_{t+1}] $

Differentiating w.r.t $k_{t+1}$ and using the envelope condition you will find the Euler as: 

$\frac{c_{t+1}}{c_t} = \beta (f_{k_{t+1}}+(1-\delta))$

Which at steady state gives you:
$k^* =(1-l^*)(\frac{e}{\frac{1}{\beta}-(1-\delta)})^{\frac{1}{1-e}}$

If a = 0, there is no labor selection problem and $l^*=0$ leading to full use of available time for labor. Clearly, there is more capital in the steady state equilibrium.