Answer: The saving rate is 0.30
Explanation:
The Golden Rule savings rate is referred to as the rate of savings which maximizes steady state level or growth of consumption.
Let k be the capital/labour ratio (i.e., capital per capita), y be the resulting per capita output ( y = f(k) ), and s be the savings rate. The steady state is referred to as a situation in which per capita output is unchanging, which implies that k be constant. This requires that the amount of saved output be exactly what is needed to one quip any additional workers and two replace any worn out capital.
In a steady state, therefore: sf(k)=(n+d)k
Growth rate of output =3%
Depreciation rate= 4%
Capital output ratio is (K/Y)
= 2.5
Begin the steady state condition:
S= ( σ + n + g) (k/Y)
S= (0.03+0.04) (2.5)
S= 0.175
Golden rule steady state
MPK= (0.03+0.04)= 0.07
Capital output ratio=
K/Y= Capital share / MPK
K/Y= 0.3/0.07
K/Y= 4.29
In the golden state, the capital output ratio is equal to 4.29 in comparison to the current capital ratio 2.5.
The saving rate consistent with the steady growth rate
S= ( σ + n + g) (k/Y)
S= (0.03 +0.04) (4.29)
S= 0.30
The saving rate that is consistent with the steady growth rate is 0.30
