Question 2 {Production Functions and Growth Accounting}. Suppose an economy is characterized by the aggregate production function 1r\"; = F[K, Lt} where H is total output, Kt is the capital input, and L1 is the labor input, or number of workers. a] If the production function takes the constant elasticity of substitution {GEE} form given by F{Kt, L1} = 14(ng + [1 oc]LU% where A 3:- {1,41- E [I], 1}, and 1" dz: 1, show that both marginal products are positive and decreasing. b] For the CES production function above, show that there are constant returns to scale. c] It can be shown that the CES production function approaches the CobbDouglas pro duction function F[K._,Lt} = Alifill\" as r 3- I]. Find the wage rate and the rental rate of capital under the assumption that inputs are chosen to maximize prots. d] With the CobbDouglas production function ab ove, write down the growth rate of total output Y, as a function of the growth rates of capital 3g and labor a. e) Under the assumptions of the Solow growth model with Cobb-Douglas production, write down the growth rate of consumption per capita as a function of g}; and n