1. This question concerns the economic growth model and data matching. Let's use a growth model to understand data. Assume a closed economy has a constant return to scale production technology as Y = 2F{K,N}, where Y denotes the aggregate output of consumption goods, :2: denotes the total factor productivity, K denotes aggregate capital stocks, and N denotes the labor size. The capital stock accumulation function is: Klr = [1 5}K + I where K' represents the aggregate capital stock of tomorrow, K denotes the aggregate capital stock of today, 6 is the depreciation rate of capital, and I is today's aggregate investment. The rate of growth in the population equals to n which is a constant over time. Households consume a constant fraction of income. Le. C = [1 s}Y, where s E (El, 1) is the saving rate, Y 2:: , and C is the aggregate consumption. (a) Characterize the statestate for this economy. {6 marks [1' {b} Assume there are two identical countries in this world but they differ on capital level. Let's denote the high capital country as the rich country and the other country as the poor country. Show why the poor country should grow faster than the rich one in this model. (7 marks) {c} However, data do not support this prediction on {b}. Provide a modication of the model or purpose a model you have learnt, in detail, so we can use this model to match data better. {7 marks)