1. (Impulse and Propagation) Calculate time paths for the capital-labor ratio (k), output per person (y), investment (i) and the wage rate (w) in the life-cycle model economy when it is hit with a temporary increase in the technology level. Calculate these four variables for time periods t = 0, 1, 2, 3, 4 and graph them. Assumptions: 0: = .5 - preference parameter ([3, (5) = (.5, .5) - capital's share of output and the depreciation rate A0 = 10, A1 = 11, A2 = 10, A3 = 10, A4 = 10 - technology level over time k0 = 6.25 - the capital-labor ratio at time t = 0 Hint: First calculate kt using the law of motion: kt+1 = (1 a)(1 ['3)Atkf. Then use the fact that all the other variables are simple functions of the capital- labor ratio: y. = Atkf', wt = (1 mAtkf and it = kt+1 an 5)