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.