Question

Let us consider an AK growth model where the growth rate of per-capita output, population growth rate, and depreciation rate are \(4\%\), \(2\%\), and \(4\%\), respectively. If productivity parameter \((A)\) is \(0.5\), then savings rate (in %) is (in integer).

Hint:

In the AK model, use \(g=sA-(n+\delta)\). Always convert percentage values into decimals before calculation.

Answer 1

Correct Answer: 20

Step 1: Recall the AK growth model equation.
In the AK growth model, the growth rate of per-capita output is given by
\[ g = sA - (n+\delta) \]
where \(g\) is growth rate of per-capita output, \(s\) is savings rate, \(A\) is productivity parameter, \(n\) is population growth rate, and \(\delta\) is depreciation rate.

Step 2: Substitute the given values.
Given,
\[ g=4\%=0.04 \] \[ n=2\%=0.02 \] \[ \delta=4\%=0.04 \] \[ A=0.5 \]
Substitute these values in the formula:
\[ 0.04=s(0.5)-(0.02+0.04) \]

Step 3: Simplify the equation.
\[ 0.04=0.5s-0.06 \]
Adding \(0.06\) on both sides,
\[ 0.10=0.5s \]

Step 4: Solve for savings rate.
\[ s=\frac{0.10}{0.5} \] \[ s=0.20 \]

Step 5: Convert into percentage.
\[ s=0.20 \times 100 \] \[ s=20\% \]

Step 6: Final conclusion.
Hence, the savings rate is
\[ \boxed{20} \]