100, 7A = Consider the simple model of technological progress. y = Akhl-a, where y is output per worker, A is productivity, k is physical capital per worker, and his human capital per worker. Assume that L = 0.1 and 4 = 1000. Output in the manufacturing sector is given by Y = A Ly; assume that initially, A = 1. (a) What is the initial growth rate per capita? What is the initial output per capita? (b) If there is a sudden increase in YA there will be an acceleration of the growth rate of y, but there will also be an immediate reduction in y, because workers are taken from Y and put into A. Assume that YA is doubled to 0.2. What will the new growth rate be? How large is the immediate reduction in Y? How long will it take for the economy to return to the initial output per capita level (time t*)? How long will it take before it reaches as higher output per capita than it would have had if it hadn't doubled their R&D efforts (time t**)? (c) Assume that the real rate of interest is r = 0.10. Will it be worthwhile for the economy to make this investment in R&D? Hint: Use Excel to calculate the cost each year in terms of lost output, until the time (***) that you found in b) is reached. Thereafter output per capita is higher so from this point on the benefits are reaped. However, both costs and benefits should be discounted to the present (t = 0). (d) Use Excel to first find the interest rate that makes the net present value equal to zero, given the suggested change in A. Secondly, as- sume that r = 0.10 and change a until NPV = 0. 100, 7A = Consider the simple model of technological progress. y = Akhl-a, where y is output per worker, A is productivity, k is physical capital per worker, and his human capital per worker. Assume that L = 0.1 and 4 = 1000. Output in the manufacturing sector is given by Y = A Ly; assume that initially, A = 1. (a) What is the initial growth rate per capita? What is the initial output per capita? (b) If there is a sudden increase in YA there will be an acceleration of the growth rate of y, but there will also be an immediate reduction in y, because workers are taken from Y and put into A. Assume that YA is doubled to 0.2. What will the new growth rate be? How large is the immediate reduction in Y? How long will it take for the economy to return to the initial output per capita level (time t*)? How long will it take before it reaches as higher output per capita than it would have had if it hadn't doubled their R&D efforts (time t**)? (c) Assume that the real rate of interest is r = 0.10. Will it be worthwhile for the economy to make this investment in R&D? Hint: Use Excel to calculate the cost each year in terms of lost output, until the time (***) that you found in b) is reached. Thereafter output per capita is higher so from this point on the benefits are reaped. However, both costs and benefits should be discounted to the present (t = 0). (d) Use Excel to first find the interest rate that makes the net present value equal to zero, given the suggested change in A. Secondly, as- sume that r = 0.10 and change a until NPV = 0