]31=JConsider a Solow model in discrete time. The following system of equations fullydescribes the model economy:Ct + It = YtKt+1 = (18)Kt + ItIt = SYtY₁ = AK¤(Z₁N₁){¹-a}Where Ct is consumption in period t, It is investment in period t, Y is output in period t, Ktis capital in period t, N₁ is labour force at time t, Zt is labour augmenting technology attime t, & is the depreciation rate, s is the saving rate; A is total factor productivity in periodt. Assume that Nt+1 (1 + n)Nt and Zt+1 (1+z)Zt, where 0 < n < 1 and 0 < z < 1.Denote kt = Kt/ZtNt the level of capital per efficient labour.A) Derive the expression of the growth rate of capital y = (kt+1 − kt)/kt.B) How does a one-off permanent increase in the saving rate s affect output andconsumption in the steady-state? Explain.C) Derive and explain the intuition behind the steady-state level of capital per efficientworkers in terms of the model parameters. How the level of capital per efficientworker would change following an increase in population growth rate?

Solow growth model is an exogenous growth model. It is a long run model which explains the path of…

Answered: B) How does a one-off permanent…

B) How does a one-off permanent increase in the saving rate s affect output and consumption in the steady-state? Explain.

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Question

]
31
=
J
Consider a Solow model in discrete time. The following system of equations fully
describes the model economy:
Ct + It = Yt
Kt+1 = (18)Kt + It
It = SYt
Y₁ = AK¤(Z₁N₁){¹-a}
Where Ct is consumption in period t, It is investment in period t, Y is output in period t, Kt
is capital in period t, N₁ is labour force at time t, Zt is labour augmenting technology at
time t, & is the depreciation rate, s is the saving rate; A is total factor productivity in period
t. Assume that Nt+1 (1 + n)Nt and Zt+1 (1+z)Zt, where 0 < n < 1 and 0 < z < 1.
Denote kt = Kt/ZtNt the level of capital per efficient labour.
A) Derive the expression of the growth rate of capital y = (kt+1 − kt)/kt.
B) How does a one-off permanent increase in the saving rate s affect output and
consumption in the steady-state? Explain.
C) Derive and explain the intuition behind the steady-state level of capital per efficient
workers in terms of the model parameters. How the level of capital per efficient
worker would change following an increase in population growth rate?

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