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A production function at time 𝑑 is given by
\(Y_t=A_tK^a_tL^{1-a}_t\) , 𝛼 ∈ (0, 1), 𝛼 β‰  0.5, 
where π‘Œ is output, 𝐾 is capital, 𝐿 is labour and 𝐴 is the level of Total Factor Productivity. Define per capita output as \(𝑦_𝑑 ≑ \frac{π‘Œ_𝑑}{ 𝐿_𝑑} \)and capital-output ratio as \(π‘˜_𝑑 ≑\frac{ 𝐾_𝑑}{ π‘Œ_𝑑}\) . For any variable π‘₯𝑑 , denote \(\frac{𝑑π‘₯_𝑑}{ 𝑑𝑑}\) by π‘₯Μ‡ . The per capita output growth rate is
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