Use the following information to answer next questions. Consider an economy for which y = Akθ with the parameter values as listed: A=11, s=0.2, n=0.2, d=0.3 ,θ=0.6 . Compute the steady state values for k based on the parameters up to one decimal point. Report the value of k*.
Question
Use the following information to answer next questions. Consider an economy for which y = Akθ with the parameter values as listed: A=11, s=0.2, n=0.2, d=0.3 ,θ=0.6 . Compute the steady state values for k based on the parameters up to one decimal point. Report the value of k*.
Solution
The steady state capital per worker (k*) in the Solow model is given by the equation:
k* = [sA/(n+d)]^(1/(1-θ))
Given the values A=11, s=0.2, n=0.2, d=0.3, θ=0.6, we can substitute these into the equation to find k*.
k* = [0.2*11/(0.2+0.3)]^(1/(1-0.6))
First, calculate the denominator:
n+d = 0.2+0.3 = 0.5
Then, calculate the numerator:
sA = 0.2*11 = 2.2
Now, divide the numerator by the denominator:
2.2/0.5 = 4.4
Finally, raise this result to the power of 1/(1-θ):
k* = 4.4^(1/(1-0.6)) = 4.4^(1/0.4) = 4.4^2.5
Using a calculator, we find that k* ≈ 46.4
So, the steady state value for k, up to one decimal point, is 46.4.
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