Olg model question for my hw, please help

Reply Sun 10 May, 2020 08:21 am
Consider an economy with aggregate production function
Yt = AK1−α
t L
All markets are competitive, the labor supply is normalized to 1, capital fully
depreciates after use, and the government imposes a linear tax on capital income
at the rate τ, and uses the proceeds for government consumption. Consider two
specifications of preferences:
· All agents are infinitely lived with preferences: P∞
ln ct
· An overlapping generations model where agents work in the first period,
and consume the capital income from their savings in the second period. The
preferences of a generation born at time t, defined over consumption when young
and old, are given by: ln ct + β ln dt+1.
Characterize the equilibria in these two economies, and show that in the first
economy, taxation reduces output, while in the second, it does not. Interpret
this result, and in the light of this result discuss the applicability of models
which try to explain income differences across countries with differences in the
rates of capital income taxation.
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