Answer:
a. Rate of 17.5
b. 0.12
c. 0.07
d.4.29
e. 0.3
Explanation:
a. A Cobb-Douglas function has the form y =, where a is capital's share of income. The question tell us that a=0.3, so, we know the production function is y =
.
- In the steady state we know that the growth rate of output equals 3%, so we know that (n+g)=0.03.
- The depreciation rate d=0.04.
- The capital-output ratio K/Y = 2.5. Because k/y= K*(L*A)/Y*(L*A)=K/Y.
Begin with the steady state condition sy=(d+n+g)k. Rewriting this equation leads to a formula for saving in the steady state:
s=(0.04+0.03)(2.5)=0.175
The initial rate is 17.5
b.
MPK=a/(K/Y)
MPK=0.3/2.5=0.12
c. MPK=(n+g+d)
MPK=(0.03+0.04)=0.07
In the Golden Rule Steady State, the capital-output ratio equals 4.29. Compared to the current capital ratio of 2.5
d. K/Y=a/MPK
K/Y=0.3/0.07=4.29
e.
s=(n+g+d)(k/y)
s=(n+g+d)(K/Y)
s=(0.04+0.03)(4.9)=0.175
s=0.3
To reach the Golden Rule Steady State, the saving rate must rise from 17.5 to 30 percent.