Problem
This problem will ask you to consider in details how the economy in the Solow model adjusts to changes in productivity growth rate. Assume that at period t = 0 productivity growth rate decreased from g0 to a lower, yet, still positive rate g1: i.e. until period t = 0 productivity was growing at rate g0 and after t0 - it grows at rate g1. All other parameters - population growth rate n, depreciation rate d, savings rate s and production function F(., .) - remained the same.
1. Finally, compare output per worker in t = 0 and t = 1 (Y0/L0 and Y1/L1). Show that between t = 0 and t = 1 output per worker increased by a rate that belongs to the interval [g1, g0].
2. Depict how the output per worker changes around period t = 0 in axes t and log(Y/L). [Hint: before t = 0 output per worker grows at rate g0, after t = 0 the growth rate of Y/L adjusts and gradually converges to g1 which is lower than g0]
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.