2. One theory which has been advanced to describe the recent outcomes in the US is that the rate of productivity growth has declined permanently. We will analyze this problem using the optimal growth model. Fbr simplicity assume population is constant at Nt = 1. Then a social planner nds the optimal allocation: 0] 3X2: 0:3t1_ t {Ctsna?{t+llt subject to: Ct =KE'A1K3H + {16 (5)3}, Vt, Kg given where technology At initially grows at the constant rate 9: At = (1 +)At1: An = 1 Suppose that the economy begins on a balanced growth path with total factor productivity growth 9. Then there is an unexpected permanent fall in the growth rate to 9'" <: what happens to the: levels and of consumption capital output growth rates immediately when this change is realized then in the following periods. re- member rst consider dynamics with a transformed or normalized system kt nd implications for>