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 rule.
In the AK model the per capita output growth rate is
\[ g=sA-(n+\delta) \]

Step 2: List the values.
Here $g=0.04$, $n=0.02$, $\delta=0.04$ and $A=0.5$.

Step 3: Plug in.
\[ 0.04=0.5s-(0.02+0.04)=0.5s-0.06 \]

Step 4: Solve for s.
\[ 0.5s=0.10\;\Rightarrow\;s=0.20 \]

Step 5: As a percent.
That is a savings rate of $20\%$.
\[ \boxed{20\%} \]