Question

An economy produces a consumption good and also has a research sector which produces new ideas. Time is discrete and indexed by 𝑡 = 0, 1, 2, …
The production function for the consumption good is given by
$𝑌_𝑡 = 𝐴_𝑡 𝐿_{𝑦𝑡}$
where, at time 𝑡, $𝐿_{𝑦𝑡}$ is the amount of consumption good produced, 𝐴𝑡 is the stock of existing knowledge, and $𝐿_{𝑦𝑡}$ is the amount of labour devoted to production of consumption good. It is known that $𝐴_0 = 1$.
The production function for new ideas is given by
$𝐴_{𝑡+1} − 𝐴_𝑡 = \frac{1}{250} 𝐴_𝑡$𝐿_{𝑎𝑡}$where 𝐿𝑎𝑡 is the amount of labour devoted to production of new ideas at time 𝑡. Suppose that for all 𝑡,$𝐿_{a𝑡}$= 10 and$𝐿_{𝑦𝑡}$= 90. Then, the growth rate of the consumption good ($Y_{𝑡}$) at 𝑡 = 50 is _____ percent (in integer).

Answer 1

The correct answer is :4