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

Question

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

cdquestions Admin · Accepted Answer

The correct option is (A): $𝛼$ $\frac{y}{y}=\frac{1}{(1-α)}\frac{A}{A}+\frac{α}{(1-α)}\frac{k}{k}$

Answer

$𝛼$$\frac{y}{y}=\frac{1}{(1-α)}\frac{A}{A}+\frac{α}{(1-α)}\frac{k}{k}$

Answer

$𝛼$$\frac{y}{y}=\frac{α}{(1-α)}\frac{A}{A}+\frac{1}{(1-α)}\frac{k}{k}$

Answer

$𝛼$$\frac{y}{y}=(1-α)\frac{A}{A}+α\frac{k}{k}$

Answer

$𝛼$$\frac{y}{y}=α\frac{A}{A}+(1-α)\frac{k}{k}$

Year	Population of the Economy	GDP of the Economy (in crore)
2010	20,000	25,000
2020	25,000	40,000

The Correct Option is A

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