2. An economy has a production function:Yt = 3(squaredKt)(squaredLt). The economy has a saving rate of 24 percent, a depreciation rate of 3 percent,and Lt = 1 for all period (no population growth). There is no technologicalprogress. (a) What is the per-worker production function, yt = f(kt)? Define yt =YtLtand kt =KtLt.(b) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (c) Find the long-run growth rate of output per worker. Now the economy has the following production function:Yt = 3Kt but savings rate, depreciation rate, and population remain the same. (d) What is the per-worker production function, yt = f(kt)? Define yt =Yt/Lt (e) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (f) Find the long-run growth rate of output per worker. (g) Explain why the economy with production function (2) explain persistent growth without the assumption of exogenous technologicalprogress. How does this differ from the economy with production function (1)? I only need help with parts D and E, thank you.
2. An economy has a production function:
Yt = 3(squaredKt)(squaredLt).
The economy has a saving rate of 24 percent, a
and Lt = 1 for all period (no population growth). There is no technological
progress.
(a) What is the per-worker production function, yt = f(kt)? Define yt =
Yt
Lt
and kt =
Kt
Lt
.
(b) Find the equation for the evolution of capital per worker in terms of kt
and kt+1.
(c) Find the long-run growth rate of output per worker.
Now the economy has the following production function:
Yt = 3Kt
but savings rate, depreciation rate, and population remain the same.
(d) What is the per-worker production function, yt = f(kt)? Define yt =Yt/Lt
(e) Find the equation for the evolution of capital per worker in terms of kt
and kt+1.
(f) Find the long-run growth rate of output per worker.
(g) Explain why the economy with production function (2) explain persistent growth without the assumption of exogenous technological
progress. How does this differ from the economy with production function (1)?
I only need help with parts D and E, thank you.
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