Question

Consider the following AK model where the production function is given by
$ 𝑌 = 𝐴𝐾$
where 𝑌 is output, 𝐾 is capital, and 𝐴 is a constant that reflects the level of technology. Suppose there is zero technological progress in the economy and 𝐴 = 0.50. In the economy, the savings rate equals 0.60 and the depreciation rate for the capital stock equals 0.05. The population growth rate equals zero and the size of the labour force is normalised to 1. Based on the AK model, the steady state growth rate of output per capita in the economy equals ______ percent (in integer).

Answer 1

Correct Answer: 25

Steady-State Growth Rate in the AK Model 

Step 1: Formula for the Steady-State Growth Rate

In the AK model, the steady-state growth rate of output per capita is given by:

\[ g_y = sA - \delta \]

where:

• \( s = 0.60 \) (savings rate)
• \( A = 0.50 \) (technology parameter)
• \( \delta = 0.05 \) (depreciation rate)

Step 2: Substituting Given Values

\[ g_y = (0.60)(0.50) - 0.05 \]

\[ = 0.30 - 0.05 \]

\[ = 0.25 \text{ or } 25\% \]

Final Answer:

The steady-state growth rate of output per capita in the economy is 25%.