d. which of the following three factors: productivity, physical capital per worker, human capital per worker contributed the most to output per worker growth from 2004 to 2014'? which of these three factors contributed the least to output per worker growth from 2004 to 2014? (10 points}. e. Using only the average annual growth rates of the output per worker, physical capital per worker, human capital per worker, derive the average annual productivity growth rate using the growth decomposition equation seen in class. Why is this growth rate different from the one computed in c? (10 points} III. A Two-Country Model (35 points) Let us consider a tlyo-oountry model with two production sectors in which All denotes the level of technology at time tin country jforjE{1_,2}. The country with the highest! is the technology leader and the country with the lowest A is the technology follower. The rate of technological progress from time tto t-l-I in the technology leader country is: A} _AJ' Pd . r-l-l . r = _L.J A: J\"! where #1, is the cost of inventing assumed to be equal to 1, yistands for the fraction of workers engaged in R810 in country j and Udenotes the size of the total population of workers in country j. The rate of technological progress from time tto t+1 in the technology follower country is: 21-? _AJ' .. j r+l t = Li A: Jall} where at is the cost of copying at time twhich depends on the technology gap: _ 1\": 'uc'r _ ALmw ! AFoIfoIll-'sr 1' Country 1 has a total population of workers of size 1 and country 2 has a total population of workers of size 2. In country 1, 20% of the population of workers is engaged in R&D and country 2 has 15% of its workers engaged in mm. The aggregate output in country j at time tis given by: 1:: = A: [:1 for\" At time 0, each county has the same initial level of technology assumed to be equal to 10. a. Derive at time 0 the income per worker in country 1 and in country 2. (5 points} b. Derive the level of technology at time 1 in country 1 and in country 2. At time 1, which country is the technology leader? (5 points)