On planet Terra, total population is 10000 and 10% of the population engages in research, i.e. works on developing new ideas.

Production function for new ideas is given by AAt+1 = 0.00002AtLat Where At is the stock of existing knowledge and Lat is the number of researchers in the economy. The initial stock of ideas in year 2000 (A2000) is 0.1. Production function for output is given by Yt = AtLyt (a) How many researchers are there on Terra? (Hint: Lat?) (1 point) (b) Compute the growth rate of ideas. (2 points) (c) How many pe0p1e work in production of output? (Hint: Lyt?) (1 point) ((1) What is the level of output per person in year 2000? (2 points) (e) What is the level of ideas in 2050? (Hint: A2000 = 0.1, compute A2050.) (2 points) (f) What is the growth rate of output per person? (2 points) (g) What is the level of output per person in 2050? (2 points) (h) While the Terra economy remains unchanged, the fraction of the Terra population engaged in research increases to 15% in 2050 in the parallel universe (let's call this planet: Terra II). Note that the original Terra and Terra II looked identical until 2050, but then experiences of two planets started to diverge. o What is the growth rate of ideas in Terra 11 after the change? (2 points) 0 What is the level of ideas in 2051 in Terra II? (1 point) Hint: Recall that the growth rate changed. 0 What is the level of output in 2051 in Terra II? (1 point) 0 What is the level of output per person in 2051 in Terra II? (2 points) a What is the level of output per person in 2051 in the original Terra? (2 points) 0 How long does it take for the level of output per person in Terra II to catch up with the level of output per person in the original Terra? (5 points)