answer question 1

Question 1 (Growth Accounting) Consider the following Cobb-Douglas function for aggregate economy. Y=A1KaLH1 (1) where Y is aggregate output, A] is the level of technology, K is capital stock, and L is total labor hours. 1. Express the equation (2) with respect to time. Take log and take derivative with respect to time. Provide an equation of growth rate of aggregate output. 2. In the economic growth model, A1 is also called Solow residual (i.e., TFP). What factors (e.g., these are factors affecting technology according to our denition of technology) can be in A] ? Now consider a model that decompose total labor into quality and quantity of work as follows. Y = A,K'(A2L) "0' = AlxaAg\"Lla = AlAg\"KD'L' '0' (2) where L total hour and A2 quality of labor hour (e. g., this value increase as overall skill-level of labor improve one hour of average labor used to produce 5 output for given capital but now one hour of average labor produce 10 output with the same capital) 3. Express the equation (3) with respect to time. Take log and take derivative with respect to time. Provide an equation of growth rate of aggregate output. Interpret the equation in growth rate form. Y = Ale' K2\"? (A212) "HI\"2 (3) where K] is Capital of A] (more of equipment) or [CT (information-communication technology) related capital and K2 is traditional capital (e. g., factory or places to produce). 4. Express the equation (4) with respect to time. Take log and take derivative with respect to time. Provide an equation of growth rate of aggregate output. Interpret the equation in growth rate form