A production function at time 𝑡 is given by
\(Y_t=A_tK^a_tL^{1-a}_t\) , 𝛼 ∈ (0, 1), 𝛼 ≠ 0.5,
where 𝑌 is output, 𝐾 is capital, 𝐿 is labour and 𝐴 is the level of Total Factor Productivity. Define per capita output as \(𝑦_𝑡 ≡ \frac{𝑌_𝑡}{ 𝐿_𝑡} \)and capital-output ratio as \(𝑘_𝑡 ≡\frac{ 𝐾_𝑡}{ 𝑌_𝑡}\) . For any variable 𝑥𝑡 , denote \(\frac{𝑑𝑥_𝑡}{ 𝑑𝑡}\) by 𝑥̇ . The per capita output growth rate is