Derive steady state values of consumption, capital stock, real interest rate, output etc. Suppose that representative agent maximises the following utility function, which is not additively separable into consumption and labour supply, given by: U = Et i=0 Bi [(Ct+i)' (1 Nt+i) P] | 1-y Where y is the relative risk aversion coefficient. The production function it's CobbDouglas function, represented by Y = (AN)K and the equation of motion of capital is Kt+1 = (18)Kt + Yt - Ct, where is the depreciation rate. According to this information, answer the following questions. a. Assemble the representative agent optimization problem, define the state and choice variables, and write the Bellman equation. b. Solve the problem set up in (a) and interpret (explain) the optimal conditions.