Solution Question 2 i) The resource constrain in level terms Ct+It Yt ii) The model in per worker terms Yt=Kt0.5 Yt/Lt= (Kt0.5)/Lt...

Solution

Question 2

i) The resource constrain in level terms

Ct+It ≤ Yt

ii) The model in per worker terms

Yt=Kt0.5Lt0.5

Yt/Lt= (Kt0.5Lt0.5)/Lt

Yt/Lt={Kt0.5/Lt0.5,Lt0.5/Lt0.5}=  

yt = (kt0.510.5).

yt =f(kt0.5)

iii).the steady state of the economy

steady state capital stock per worker.

f{k}=Yt

I=f{yt}=s

∆k=sf{kt}-{∂+1}kt

At steady state ∆k=0 hence,

Sf{kt⃰⃰}={∂+1}kt

Steady state output per worker

yt⃰/kt⃰=s(k)=∂+1

yt⃰/kt⃰= f(kt⃰)=(∂+1)/s

iv).golden rule level of capital stock

c⃰=f(k⃰)-(∂+1)k⃰

c⃰=(sf(k)-∂+1)⃰

v). if y=1/3 and economy is at steady state the golden rule would be.

C⃰=sf{kt}-{∂+1}kt

c⃰={1/3(k)+∂+1}kt

Higher level of capital will result to higher level of output which result to higher consumption in the shortrun. Higher level of capital in the longrun leads to increase in output but does not lead to increase in consumption. Vice versa is also true.

Question 3 has been attached below, solve question 3 in details