Consider the following variant of the Solow growth model. The production technology is Y = AK? N-a (1) Output is used for both consumption, C, and investment. I. Y = C + It.. given by Investment is used to create new capital (2) I = K+1 - K + dk. (3) Suppose there is no labor growth so the pupulation size is constant at N, N for all time. Finally. suppose that savings are given by I = sY - hk where h captures a decreasing marginal propensity to save with wealth. (a) Define output per worker, capital per worker, consumption per worker and investment per worker as y=Y/N, k = Kt/N. t = C/N, and i, = 1/N. Rewrite the equations of the model, (1)-(4), in terms of these per-worker variables. (b) What are steady state capital per worker and consumption per worker as a function of s.d. h. A. and a? (e) How will an increase in s affect steady state capital per worker? (d) How will an increase in h affect steady state capital per worker? (e) If steady state consumption per worker is maximized when steady state capital per worker is k = (4) * what choice of s will maximize steady state consumption taking A. d. h, and a as given? (f) If A = 1, a=0.5, 0.3, h = 0.1 and d= 0.1 what will be the capital stock in year 1, K, if the capital stock in year 0 is Ko= 1? What will be the growth rate of output from year 0 to year 1?