Why are some countries rich and some countries poor? Question 1 Computing long run equilibrium and the golden rule Suppo

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Why are some countries rich and some countries poor?
Question 1 Computing long run equilibrium and the golden
rule
Suppose that the production function is given by: 𝑌𝑡 = 100 𝐾𝑡
0.6𝑁𝑡 0.4
and the evolution of capital stock given by: 𝐾𝑡+1 = (1 − 𝛿)𝐾𝑡 +
𝐼𝑡
and in equilibrium 𝐼𝑡 = 𝑆𝑡 = 𝑠𝑌𝑡
a. Derive the steady state levels of capital per worker k* =
(Kt/Nt) * in terms of the saving rate (s) and the depreciation rate
(). Explain why and how s and  affect k*.
b. Derive the equation for steady-state output per worker (y*)
and steady-state consumption per worker (c*) in terms of s and .
Explain why and how s and  affect y* and c*.
c. Suppose that  = 10% (=0.1) and s = 5% (=0.05). Calculate k*,
y* and c*. Calculate saving per worker (s*=S*/N=sY*/N=sy*))
d. Show these solutions for k*, y*, c* and s* on the Solow-Swan
diagram.