13. Consider the following version of Solow's model of economic growth with no technological progress: I- n = kg'' " ct = {:1 - \"J": I I: = S")?! ' kr+1 = I5r + 5}} - ('1 + it: o 5' = [1.12 0 r5 = 0.02 e n. = [LUZ a. If capital per worker {k} is 8 at time 0 {kg = 8.0L what will capital per worker be at times 1, 2, and 3? What will income per person {yl he at times t}, 1, 2 and 3? What will the growth rate of income per person {ddly} be between times D and 1, 1 and 2, and 2 and 3? h. Suppose the population size is 1.{i at time zero [Ln = 1). What will aggregate income {'1' = M] be at times {1. 1. 2. and 3? Hint: By denition, it\" = {1+nitr. What will the growth rate of aggregate income (say: be between times (i and 1, 1 and 2, and 2 and 3? c. What Is the steady state value of capital per worker ik'i for this model? What will income per person [y] be when k reaches its steady state value? d. What will the growth rate of Income per person i'oy] be when it reaches Its steady state value? What will the growth rate of aggregate Income may: be when capital per worker reaches Its steady state value? Explain. e. Suppose that the population growth rate in) falls from 2% per period to 056 per period. What would the post-shock steady state values be for capital per worker {k" i, income per person hr"), the growth rate of Income per-person itoyi, and the growth rate of aggregate Income laser]