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
Yt=AtLyt where, at time 𝑡,
Lyt is the amount of consumption good produced, 𝐴𝑡 is the stock of existing knowledge, and
Lyt is the amount of labour devoted to production of consumption good. It is known that
A0=1.
The production function for new ideas is given by
At+1−At=2501At𝐿_{𝑎𝑡}
where 𝐿𝑎𝑡 is the amount of labour devoted to production of new ideas at time 𝑡. Suppose that for all 𝑡,
Lat = 10 and
Lyt = 90. Then, the growth rate of the consumption good (
Yt) at 𝑡 = 50 is _____ percent (in integer).