Why are some countries rich and some countries poor? Question 1 Computing long run equilibrium and the golden rule Suppo
Posted: Mon May 09, 2022 12:00 pm
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: ππ‘ = 100 πΎπ‘
0.6ππ‘ 0.4
and the evolution of capital stock given by: πΎπ‘+1 = (1 β πΏ)πΎπ‘ +
πΌπ‘
and in equilibrium πΌπ‘ = ππ‘ = π ππ‘
a. Derive the steady state levels of capital per worker k* =
(Kt/Nt) * in terms of the saving rate (s) and the depreciation rate
(ο€). Explain why and how s and ο€ 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 ο€.
Explain why and how s and ο€ affect y* and c*.
c. Suppose that ο€ = 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.
Question 1 Computing long run equilibrium and the golden
rule
Suppose that the production function is given by: ππ‘ = 100 πΎπ‘
0.6ππ‘ 0.4
and the evolution of capital stock given by: πΎπ‘+1 = (1 β πΏ)πΎπ‘ +
πΌπ‘
and in equilibrium πΌπ‘ = ππ‘ = π ππ‘
a. Derive the steady state levels of capital per worker k* =
(Kt/Nt) * in terms of the saving rate (s) and the depreciation rate
(ο€). Explain why and how s and ο€ 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 ο€.
Explain why and how s and ο€ affect y* and c*.
c. Suppose that ο€ = 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.