If the Japanese production function is Cobb–Douglas with capital share 0.3, output growth is 3 percent per year, depreciation is 4 percent per year, and the capital–output ratio is 2.5, the saving rate that is consistent with steady-state growth is:.

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

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